def elastic_transform2(image, gx, gy, s):
"""Elastic deformation as in pulling the image in a random coordinate
"""
#if random_state is None:
# random_state = numpy.random.RandomState(None)
shape = image.shape
x, y = numpy.meshgrid(numpy.arange(shape[0]), numpy.arange(shape[1]))
#s = random()*0.003
dx = (gx - x)
dy = (gy - y)
dx = numpy.sign(dx)*dx**2
dy = numpy.sign(dy)*dy**2
dx = dx*s
dy = dy*s
#indices =
#dx = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
#dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
indices = numpy.reshape(y+dy, (-1, 1)), numpy.reshape(x+dx, (-1, 1))
if len(shape) == 3:
ch1 = map_coordinates(image[:,:,0], indices, order=1).reshape(image[:,:,0].shape)
ch2 = map_coordinates(image[:,:,1], indices, order=1).reshape(image[:,:,0].shape)
ch3 = map_coordinates(image[:,:,2], indices, order=1).reshape(image[:,:,0].shape)
return numpy.dstack((ch1,ch2,ch3))
return map_coordinates(image, indices, order=1).reshape(shape)
def ijll(self):
"""Add vectors with lat-lon positions of particles."""
from scipy.ndimage.interpolation import map_coordinates
self.lon = map_coordinates(self.llon, [self.y-0.5, self.x-0.5])
self.lat = map_coordinates(self.llat, [self.y-0.5, self.x-0.5])
self.lon[self.lon==0] = np.nan
self.lat[self.lat==0] = np.nan
def elastic_transform(image, gt, alpha, sigma, random_state=None):
"""
:param image: image
:param gt: ground truth
:param alpha: deformation coefficient (high alpha -> strong deformation)
:param sigma: std of the gaussian filter. (high sigma -> smooth deformation)
:param random_state:
:return: deformation of the pair [image,mask]
"""
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape
d = 4
sub_shape = (shape[0]/d, shape[0]/d)
deformations_x = random_state.rand(*sub_shape) * 2 - 1
deformations_y = random_state.rand(*sub_shape) * 2 - 1
deformations_x = np.repeat(np.repeat(deformations_x, d, axis=1), d, axis = 0)
deformations_y = np.repeat(np.repeat(deformations_y, d, axis=1), d, axis = 0)
dx = gaussian_filter(deformations_x, sigma, mode="constant", cval=0) * alpha
dy = gaussian_filter(deformations_y, sigma, mode="constant", cval=0) * alpha
x, y = np.meshgrid(np.arange(shape[0]), np.arange(shape[1]))
indices = np.reshape(y+dy, (-1, 1)), np.reshape(x+dx, (-1, 1))
elastic_image = map_coordinates(image, indices, order=1).reshape(shape)
elastic_gt = map_coordinates(gt, indices, order=1).reshape(shape)
elastic_gt = preprocessing.binarize(np.array(elastic_gt), threshold=0.5)
return [elastic_image, elastic_gt]
def errfun_warp_deriv(x, im1, im2, mask, reg_param=0.0): mask = gen_mask(im1.shape) x = np.array(x) ncoeffs = len(x) poly_deg = int(int(len(x)/2)**0.5) coeffs_x = x[:len(x)/2].reshape((poly_deg,poly_deg)) coeffs_y = x[len(x)/2:].reshape((poly_deg,poly_deg)) coords = coords_c(im1.shape, coeffs_x, coeffs_y) gx, gy = np.gradient(im1) im3 = map_coordinates(im1, coords, order=1) gx = map_coordinates(gx, coords, order=1) gy = map_coordinates(gy, coords, order=1) diffim = (im2 - im3) cd = chebderivs(im1.shape, poly_deg) derivs = np.zeros(ncoeffs) for i in range(ncoeffs): gradim = gy*cd[i,1] + gx*cd[i,0] derivs[i] = np.sum(-2.0*mask*diffim*gradim)/np.prod(im1.shape) nx, ny = np.meshgrid(range(poly_deg), range(poly_deg)) total_deg = nx+ny weights = np.tile(total_deg.flatten(), 2) penalty = weights * np.sign(x) return derivs + reg_param*penalty
def marsfilter(imfile):
img = mpimg.imread(imfile)
mask = np.ones_like(img)
mask[:,:,1]*= 0.465
mask[:,:,2]*= 0.25
marsimg = img*mask
x = np.arange(marsimg.shape[0]).reshape(-1,1)
y = np.arange(marsimg.shape[1]).reshape(-1,1)
xy = np.array(list(product(x,y))).reshape(-1,2)
center = np.mean(xy, axis=0)
xc, yc = (xy - center).T
# Polar coordinates
r = np.sqrt(xc**2 + yc**2)
theta = np.arctan2(yc, xc)
a = 0.00022219029946345079
b = 422.33975030901962
k = a/(b - (np.max([img.shape[0], img.shape[1]])))
d = np.linspace(np.min(r) +k*np.min(r)**3, np.max(r)+k*np.max(r)**3, 10000)
u = d + k*(d**3)
f = interp1d(u, d, bounds_error=False)
s = f(r)
newx = (np.round(s*np.cos(theta))).astype(int).reshape(len(x), len(y)) + int(center[0])
newy = (np.round(s*np.sin(theta))).astype(int).reshape(len(x), len(y)) + int(center[1])
one_image = interpolation.map_coordinates(marsimg[:,:,0], coordinates=[newx.flatten(), newy.flatten()]).reshape(marsimg.shape[0],marsimg.shape[1], 1)
two_image = interpolation.map_coordinates(marsimg[:,:,1], coordinates=[newx.flatten(), newy.flatten()]).reshape(marsimg.shape[0],marsimg.shape[1], 1)
three_image = interpolation.map_coordinates(marsimg[:,:,2], coordinates=[newx.flatten(), newy.flatten()]).reshape(marsimg.shape[0],marsimg.shape[1], 1)
new_image = np.append(one_image, np.append(two_image, three_image, axis=2), axis=2)
imsavefile = 'marsfiter_'+imfile
return mpimg.imsave(imsavefile, new_image, dpi=100)
def get_uv(self, lat, lon, t):
# map_coordinates wants columns, so we have transpose and make the
# coords array two dimensional
coords = (((lat, lon, t) - self.p0) * self.inv_dp)[:,np.newaxis]
u = map_coordinates(self.u_coeffs, coords, prefilter=False, mode='nearest')
v = map_coordinates(self.v_coeffs, coords, prefilter=False, mode='nearest')
return u, v
def evaluate(self, y, x):
#Calculates the maximum length from point to the edges.
maximum_length = np.min([self.shape[1]-x,np.min([y+1,self.shape[0]-y])])
# Creates an indexing array from point to the edge with spacing of 1 pixel.
stepsize = 1.0/(np.sqrt(2)*self.step)
indexarray = np.r_[0:maximum_length:stepsize]
# Coordinate arrays for both the positive and the negative e.
coords1 = np.asarray([float(y)/self.step-indexarray,float(x)/self.step + indexarray])
coords2 = np.asarray([float(y)/self.step+indexarray,float(x)/self.step + indexarray])
# Values of the array at these locations.
e1 = map_coordinates(self.data, coords1, output=float, order=3)
e2 = map_coordinates(self.data, coords2, output=float, order=3)
# Logarithmic strain
e1log = np.log(e1)
e2log = np.log(e2)
index = np.log(r_[0:e1.shape[0]])
k11, k12 = np.polyfit(index, e1log, 1)
k21, k22 = np.polyfit(index, e2log, 1)
norm =
return -norm
def interpolate_geolocation_cartesian(lon_array, lat_array):
"""Interpolate MODIS navigation from 1000m resolution to 250m.
Python rewrite of the IDL function ``MODIS_GEO_INTERP_250`` but converts to cartesian (X, Y, Z) coordinates
first to avoid problems with the anti-meridian/poles.
:param nav_array: MODIS 1km latitude array or 1km longitude array
:returns: MODIS 250m latitude array or 250m longitude array
"""
num_rows,num_cols = lon_array.shape
num_scans = num_rows / ROWS_PER_SCAN
lons_rad = np.radians(lon_array)
lats_rad = np.radians(lat_array)
x_in = EARTH_RADIUS * np.cos(lats_rad) * np.cos(lons_rad)
y_in = EARTH_RADIUS * np.cos(lats_rad) * np.sin(lons_rad)
z_in = EARTH_RADIUS * np.sin(lats_rad)
# Create an array of indexes that we want our result to have
x = np.arange(RES_FACTOR * num_cols, dtype=np.float32) * 0.25
y = np.arange(RES_FACTOR * ROWS_PER_SCAN, dtype=np.float32) * 0.25 - 0.375
x,y = np.meshgrid(x,y)
coordinates = np.array([y,x]) # Used by map_coordinates, major optimization
new_x = np.empty( (num_rows * RES_FACTOR, num_cols * RES_FACTOR), dtype=np.float32 )
new_y = new_x.copy()
new_z = new_x.copy()
nav_arrays = [(x_in, new_x), (y_in, new_y), (z_in, new_z)]
# Interpolate each scan, one at a time, otherwise the math doesn't work well
for scan_idx in range(num_scans):
# Calculate indexes
j0 = ROWS_PER_SCAN * scan_idx
j1 = j0 + ROWS_PER_SCAN
k0 = ROWS_PER_SCAN * RES_FACTOR * scan_idx
k1 = k0 + ROWS_PER_SCAN * RES_FACTOR
for nav_array, result_array in nav_arrays:
# Use bilinear interpolation for all 250 meter pixels
map_coordinates(nav_array[ j0:j1, : ], coordinates, output=result_array[ k0:k1, : ], order=1, mode='nearest')
# Use linear extrapolation for the first two 250 meter pixels along track
m = (result_array[ k0 + 5, : ] - result_array[ k0 + 2, : ]) / (y[5,0] - y[2,0])
b = result_array[ k0 + 5, : ] - m * y[5,0]
result_array[ k0 + 0, : ] = m * y[0,0] + b
result_array[ k0 + 1, : ] = m * y[1,0] + b
# Use linear extrapolation for the last two 250 meter pixels along track
m = (result_array[ k0 + 37, : ] - result_array[ k0 + 34, : ]) / (y[37,0] - y[34,0])
b = result_array[ k0 + 37, : ] - m * y[37,0]
result_array[ k0 + 38, : ] = m * y[38,0] + b
result_array[ k0 + 39, : ] = m * y[39,0] + b
# Convert from cartesian to lat/lon space
new_lons = get_lons_from_cartesian(new_x, new_y)
new_lats = get_lats_from_cartesian(new_x, new_y, new_z)
return new_lons, new_lats
def ijll(self,ps=None):
from scipy.ndimage.interpolation import map_coordinates
self.lon = map_coordinates(self.llon, [self.y,self.x])
self.lat = map_coordinates(self.llat, [self.y,self.x])
self.lon[self.lon<-180] = self.lon[self.lon<-180] + 360
self.lon[self.lon> 180] = self.lon[self.lon> 180] - 360
self.lon[self.lon==0] = np.nan
self.lat[self.lat==0] = np.nan
def warplk(src, target, warp, warp_jac, p0, mask=None): ny, nx = src.shape nparam = len(p0) grad_im = np.gradient(src)[::-1] grad_warped = np.zeros((2,) + src.shape) interp_order=1 p = np.copy(p0) p_list = [] sd_im = np.zeros((nparam,) + src.shape) eps = 1e-2 iter_count = 0 while iter_count < 20: p_list.append(p) iter_count += 1 #print "p: " + str(p) coords = warp(src.shape, p) src_warped = map_coordinates(src, coords, order=interp_order) for i in range(2): grad_warped[i] = map_coordinates(grad_im[i], coords, order=interp_order) err_im = target - src_warped print iter_count, np.sum(np.abs(err_im)) jac = warp_jac(src.shape, p) #compute steepest descent images for i in range(nparam): sd_im[i] = grad_warped[0]*jac[0,i] + grad_warped[1]*jac[1,i] #form hessian hess = np.zeros((nparam, nparam)) if mask != None: for iy in range(ny): for ix in range(nx): hess += np.outer(sd_im[:,iy,ix],sd_im[:,iy,ix])*mask[iy,ix] else: for iy in range(ny): for ix in range(nx): hess += np.outer(sd_im[:,iy,ix],sd_im[:,iy,ix]) if mask != None: errgrad = np.sum(sd_im*err_im*mask, axis=(1,2)) else: errgrad = np.sum(sd_im*err_im, axis=(1,2)) hess_inv = linalg.inv(hess) delta_p = np.dot(hess_inv, errgrad) delta_norm = np.linalg.norm(delta_p) p = p + delta_p #print "delta_p: " + str(delta_p) if delta_norm < eps: break return p
def interpolate(I1, I2, VF, n, VB=None):
"""Interpolate n frames between two images by using forward and backward
motion fields computed from two images. The time range between the images is
equally divided into n subintervals.
Parameters
----------
I1 : array-like
The first input image.
I2 : array-like
The second input image (must have the same shape as I1).
VF : array-like
The forward motion field (must have the same shape as I1 and I2).
n : int
Number of frames to interpolate between the input images.
VB : array-like
The backward motion field (must have the same shape as I1 and I2). If not
given, VB is assumed to be -VF.
Returns
-------
out : list
List of length n containing the interpolated frames between the images.
The input images are not included in the list.
"""
if len(I1.shape) != 2:
raise ValueError("I1 and I2 must be two-dimensional arrays")
if I1.shape != I2.shape:
raise ValueError("I1 and I2 must have the same shape")
if VF.shape[0:2] != I1.shape or VF.shape[0:2] != I2.shape or \
(VB != None and (VB.shape[0:2] != I1.shape or VB.shape[0:2] != I2.shape)):
raise ValueError("V must have the same shape as I1 and I2")
if VB == None:
VB = -VF
X,Y = meshgrid(arange(size(I1, 1)), arange(size(I1, 0)))
XY = dstack([X, Y])
tws = 1.0*arange(1, n+1) / (n + 1)
I_result = []
for tw in tws:
XYW = XY + tw*VB[:,:,0:2]
XYW = [XYW[:, :, 1], XYW[:, :, 0]]
I1_warped = reshape(map_coordinates(I1, XYW, order=1, mode="constant",
cval=nan), I1.shape)
XYW = XY + (1.0-tw)*VF[:,:,0:2]
XYW = [XYW[:, :, 1], XYW[:, :, 0]]
I2_warped = reshape(map_coordinates(I2, XYW, order=1, mode="constant",
cval=nan), I2.shape)
I_result.append((1.0-tw)*I1_warped + tw*I2_warped)
return I_result
def rotational_expand(vals,N,D,interp_order=1):
interp_coords = n.sqrt(n.sum(gencoords(N,D).reshape((N**D,D))**2,axis=1)).reshape((1,) + D*(N,))
if n.iscomplexobj(vals):
rotexp = 1.0j*spinterp.map_coordinates(vals.imag, interp_coords,
order=interp_order, mode='nearest')
rotexp += spinterp.map_coordinates(vals.real, interp_coords,
order=interp_order, mode='nearest')
else:
rotexp = spinterp.map_coordinates(vals, interp_coords,
order=interp_order, mode='nearest')
return rotexp
def interpolate_3d (self,l,m,thetaphi=False,rotate=None,time=None,freq=None,freqaxis=None,output=None,mask=None,extra_axes=0):
"""Interpolates beam into the given l/m (default) or theta/phi (thetaphi=True) coordinates,
and optionally freq/time, etc.
If extra_axis>0, then l/m arrays will have that many extra axes (at the front), i.e. the real freq
axis is actually freqaxis+extra_axis
See transformCoordinates() above for a description of the parameters. An output array
may be specified (it will be resized to the correct shape just in case).
Returns array of interpolated coordinates.
""";
# transform coordinates
dprint(3,"transforming coordinates");
coords,output_shape,mask = self.transformCoordinates(l,m,thetaphi=thetaphi,
rotate=rotate,time=time,freq=freq,freqaxis=freqaxis,extra_axes=extra_axes,mask=mask);
# prepare output array
if output is None:
output = numpy.zeros(output_shape,complex);
elif output.shape != output_shape:
output.resize(output_shape);
global _print_first;
verbose = _print_first and _verbosity.get_verbose()>1;
if verbose:
l0,m0,freq0 = coords[:,0];
dprint(1,"First interpolation point is at",l0,m0,freq0);
dprint(1,"Frequencies are",self._freq_grid);
for l in int(l0),int(l0)+1:
for m in int(m0),int(m0)+1:
dprint(1,l,m,"amplitudes",abs(self._beam[l,m,:]));
dprint(1,l,m,"phases",numpy.angle(self._beam[l,m,:])/DEG);
dprint(3,"interpolating %s coordinate points to output shape %s"%(coords.shape,output_shape));
# interpolate real and imag parts separately
output.real = interpolation.map_coordinates(self._beam_real,coords,order=self._spline_order,mode='nearest',
prefilter=(self._spline_order==1)).reshape(output_shape);
output.imag = interpolation.map_coordinates(self._beam_imag,coords,order=self._spline_order,mode='nearest',
prefilter=(self._spline_order==1)).reshape(output_shape);
output[~(numpy.isfinite(output))] = 0;
if mask is not None:
output[mask] = 0;
output_ampl = interpolation.map_coordinates(self._beam_ampl,coords,order=self._spline_order,mode='nearest',
prefilter=(self._spline_order==1)).reshape(output_shape);
output_ampl[~(numpy.isfinite(output_ampl))] = 0;
phase_array = numpy.angle(output);
output.real = output_ampl * numpy.cos(phase_array);
output.imag = output_ampl * numpy.sin(phase_array);
dprint(3,"interpolated value [0] is",output.ravel()[0]);
# dprint(4,"interpolated value is",output);
if verbose:
_print_first = None;
for i in range(coords.shape[1]):
if coords[0,i] == l0 and coords[1,i] == m0:
dprint(0,"Interpolated amplitude at frequency %f is %f"%(coords[2,i],abs(output.ravel()[i])));
return output;
def cmap_file2d(data, cmap, roll_x=0.):
cmap[:, -1] = cmap[:, 0]
data_dim, nrows, ncols = data.shape
data2 = np.copy(data)
#data2[1] = (data2[1] - roll_x) % 1.0
data2[0] *= cmap.shape[0]
data2[1] *= cmap.shape[1]
data2 = data2.reshape(data_dim, nrows, ncols)
r = map_coordinates(cmap[:, :, 0], data2, order=1, mode='nearest')
g = map_coordinates(cmap[:, :, 1], data2, order=1, mode='nearest')
b = map_coordinates(cmap[:, :, 2], data2, order=1, mode='nearest')
rgb = np.array([r, g, b])
rgb = rgb.reshape(3, nrows, ncols).transpose(1, 2, 0)
return rgb
def cart_to_irregular_spline(cartgrid, values, newgrid, **kwargs):
"""
Map array ``values`` defined by cartesian coordinate array ``cartgrid``
to new coordinates defined by ``newgrid`` using spline interpolation.
Keyword arguments are fed through to
:func:`scipy:scipy.ndimage.map_coordinates`
Parameters
----------
cartgrid : numpy ndarray
3 dimensional array (nx, ny, lon/lat) of floats
values : numpy 2d-array
2 dimensional array (nx, ny) of data values
newgrid : numpy ndarray
Nx2 dimensional array (..., lon/lat) of floats
kwargs : :func:`scipy:scipy.ndimage.map_coordinates`
Returns
-------
interp : numpy ndarray
array with interpolated values of size N
Examples
--------
See :ref:`/notebooks/beamblockage/wradlib_beamblock.ipynb#\
Preprocessing-the-digitial-elevation-model`.
"""
# TODO: dimension checking
newshape = newgrid.shape[:-1]
xi = newgrid[..., 0].ravel()
yi = newgrid[..., 1].ravel()
nx = cartgrid.shape[1]
ny = cartgrid.shape[0]
cxmin = np.min(cartgrid[..., 0])
cxmax = np.max(cartgrid[..., 0])
cymin = np.min(cartgrid[..., 1])
cymax = np.max(cartgrid[..., 1])
# this functionality finds the floating point
# indices into the value array (0:nx-1)
# can be transferred into separate function
# if necessary
xi = (nx - 1) * (xi - cxmin) / (cxmax - cxmin)
# check origin to calculate y index
if util.get_raster_origin(cartgrid) is 'lower':
yi = (ny - 1) * (yi - cymin) / (cymax - cymin)
else:
yi = ny - (ny - 1) * (yi - cymin) / (cymax - cymin)
# interpolation by map_coordinates
interp = map_coordinates(values, [yi, xi], **kwargs)
interp = interp.reshape(newshape)
return interp
def mapping_on_plane(img_in,xi1,xi2,dsi): nsx, nsy = np.shape(img_in) xt1 = (xi1)/dsi+nsx/2.0 xt2 = (xi2)/dsi+nsy/2.0 points = np.array([np.array(xt1.flat),np.array(xt2.flat)]) img_out = sn.map_coordinates(img_in,points,order=1,mode='constant') return img_out.reshape((nsx,nsy))
def apply_shift(img_data, coords, shift_data, axis=1, sign=1):
"""
Interpolates image along phase encoding direction
Parameters
----------
img_data: (x, y, z) array
Image to interpolate
coords: (3, p) list
Coordinates to sample img_data at
shift_data: (p, ) array
Shifts to apply to coodinates in coords
axis: int
Dimension to apply shift_data to. Must be 1, 2, or 3
sign: int
Direction to apply shift_data to. Must to 1 or -1.
Returns
-------
img_interp: (p,) array
Interpolated img_data
"""
#Apply shift to coordinates
shift_coords = np.float32(coords)
shift_coords[axis] += shift_data * sign
#Interolate image at shifted coordinates
return interp.map_coordinates(img_data, shift_coords, order=1)
def elastic_transform(image, alpha=2000, sigma=40, alpha_affine=40, random_state=None):
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape
shape_size = shape[:2]
# Random affine
center_square = np.float32(shape_size) // 2
square_size = min(shape_size) // 3
pts1 = np.float32([center_square + square_size, [center_square[0]+square_size, center_square[1]-square_size], center_square - square_size])
pts2 = pts1 + random_state.uniform(-alpha_affine, alpha_affine, size=pts1.shape).astype(np.float32)
M = cv2.getAffineTransform(pts1, pts2)
for i in range(shape[2]):
image[:,:,i] = cv2.warpAffine(image[:,:,i], M, shape_size[::-1], borderMode=cv2.BORDER_REFLECT_101)
image = image.reshape(shape)
blur_size = int(4*sigma) | 1
dx = cv2.GaussianBlur((random_state.rand(*shape_size) * 2 - 1), ksize=(blur_size, blur_size), sigmaX=sigma) * alpha
dy = cv2.GaussianBlur((random_state.rand(*shape_size) * 2 - 1), ksize=(blur_size, blur_size), sigmaX=sigma) * alpha
x, y = np.meshgrid(np.arange(shape[1]), np.arange(shape[0]))
indices = np.reshape(y+dy, (-1, 1)), np.reshape(x+dx, (-1, 1))
def_img = np.zeros_like(image)
for i in range(shape[2]):
def_img[:,:,i] = map_coordinates(image[:,:,i], indices, order=1).reshape(shape_size)
return def_img
def get_rgb(im, y, x, order=1):
im = np.asarray(im)
ni, nj, nc = im.shape
points = np.zeros((len(x), nc), dtype=im.dtype)
for c in range(nc):
points[:, c] = map_coordinates(im[:, :, c], [y, x], order=order)
return points
def get_image_values(img,x,y,normal,dist,npts):
'''
Get the image values along a normal line from a point x.
Traverse along this line dist pixels with npts
'''
# normal is [dx, dy] but may have unknown length
normal = normal/np.sqrt(normal[0]**2 + normal[1]**2)
# now normal is of length 1, and is in the form [dx,dy]
xMin = x
xMax = x + dist*normal[0]
yMin = y
yMax = y + dist*normal[1]
#print "original", [xMin, yMin]
#print "ending", [xMax,yMax]
#print "distance", np.sqrt((xMax - xMin)**2 + (yMax - yMin)**2)
# make a new array
xcoords = np.linspace(xMin, xMax, npts)
ycoords = np.linspace(yMin, yMax, npts)
#print xcoords
#print ycoords
# travel along points, get image values put them in array
return imginterp.map_coordinates(img,[xcoords,ycoords])
def _interpolate_cube(self, lon, lat, egy=None, interp_log=True):
"""Perform interpolation on a healpix cube. If egy is None
then interpolation will be performed on the existing energy
planes.
"""
shape = np.broadcast(lon, lat, egy).shape
lon = lon * np.ones(shape)
lat = lat * np.ones(shape)
theta = np.pi / 2. - np.radians(lat)
phi = np.radians(lon)
vals = []
for i, _ in enumerate(self.hpx.evals):
v = hp.pixelfunc.get_interp_val(self.counts[i], theta,
phi, nest=self.hpx.nest)
vals += [np.expand_dims(np.array(v, ndmin=1), -1)]
vals = np.concatenate(vals, axis=-1)
if egy is None:
return vals.T
egy = egy * np.ones(shape)
if interp_log:
xvals = utils.val_to_pix(np.log(self.hpx.evals), np.log(egy))
else:
xvals = utils.val_to_pix(self.hpx.evals, egy)
vals = vals.reshape((-1, vals.shape[-1]))
xvals = np.ravel(xvals)
v = map_coordinates(vals, [np.arange(vals.shape[0]), xvals],
order=1)
return v.reshape(shape)
def errfun(x): mask = gen_mask(im1.shape) coords = fill_coords2(im1.shape, x[0],x[1]) im3 = map_coordinates(im1, coords) diffim = (im2 - im3) err = np.sum(np.abs(diffim)*mask) return err
def warp_grid(grid, mapping_function, order=3, mode="nearest"):
"""
warp grid with a mapping function
phi_1 = grid
phi_2 = mapping_function
the result is
phi_1(phi_2)
Parameters
----------
grid : ndarray
a grid which is going to be warped
mapping_function : ndarray
the grid will be deformed by this mapping function
Returns
-------
warped_grid : ndarray
grid deformed by the mapping function
"""
if len(grid) != len(mapping_function):
raise ValueError("the dimension of the two inputs are the same")
warped_grid = np.zeros_like(grid)
for i, lines in enumerate(grid):
warped_grid[i] = map_coordinates(lines, mapping_function, order=order, mode=mode)
return warped_grid
def elastic_transform(image, alpha, sigma, alpha_affine, random_state=None):
"""Elastic deformation of images as described in [Simard2003]_ (with modifications).
.. [Simard2003] Simard, Steinkraus and Platt, "Best Practices for
Convolutional Neural Networks applied to Visual Document Analysis", in
Proc. of the International Conference on Document Analysis and
Recognition, 2003.
Based on https://gist.github.com/erniejunior/601cdf56d2b424757de5
"""
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape
shape_size = shape[:2]
# Random affine
center_square = np.float32(shape_size) // 2
square_size = min(shape_size) // 3
pts1 = np.float32([center_square + square_size, [center_square[0]+square_size, center_square[1]-square_size], center_square - square_size])
pts2 = pts1 + random_state.uniform(-alpha_affine, alpha_affine, size=pts1.shape).astype(np.float32)
M = cv2.getAffineTransform(pts1, pts2)
image = cv2.warpAffine(image, M, shape_size[::-1], borderMode=cv2.BORDER_REFLECT_101)
dx = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma) * alpha
dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma) * alpha
dz = np.zeros_like(dx)
x, y, z = np.meshgrid(np.arange(shape[1]), np.arange(shape[0]), np.arange(shape[2]))
indices = np.reshape(y+dy, (-1, 1)), np.reshape(x+dx, (-1, 1)), np.reshape(z, (-1, 1))
return map_coordinates(image, indices, order=1, mode='reflect').reshape(shape)
def getE(self, axis, xcoord, ycoord, angle): derarray = np.diff(self.diffs[axis], 1, axis) xcoord = xcoord/self.step ycoord = ycoord/self.step angle = radians(angle) xcoords = np.array([], dtype=float) ycoords = np.array([], dtype=float) xcoordplus = cos(angle)/self.step ycoordplus = - sin(angle)/self.step maxX = derarray.shape[1] - 1 maxY = derarray.shape[0] - 1 while True: if xcoord < 0 or xcoord >= maxX or ycoord <= 0 or ycoord >= maxY: break xcoords = np.append(xcoords, xcoord) ycoords = np.append(ycoords, ycoord) xcoord += xcoordplus ycoord += ycoordplus return map_coordinates(derarray, [ycoords, xcoords], order=3)
def grid_interpolation_linear(known_coords, known_values, interp_coords): """ Interpolate between known values on a regular grid of coordinates *known_coords is array of shape \product(ith grid length) x (# of dimensions) *known_values is array of shape \product(ith grid length) *interp_coords is array of shape (# of events) x (# of dimensions) """ #known_coords is array of shape \product(ith grid length) x (# of dimensions), use to find mapping between coords and grid indices ndim = np.shape(known_coords)[-1] grid_lens = np.array(np.shape(known_coords)[:-1]) grid_starts = np.zeros(ndim) grid_factors = np.zeros(ndim) for dim in xrange(ndim): #Find min and max of grid coordinates for each dimension and use these to construct mapping to grid indices ind_min = np.zeros(ndim+1,dtype='int') ind_min[-1] = dim ind_max = np.zeros(ndim+1,dtype='int') ind_max[dim] = -1 ind_max[-1] = dim grid_starts[dim] = known_coords[tuple(ind_min)] grid_factors[dim] = (known_coords[tuple(ind_max)] - known_coords[tuple(ind_min)]) / float(grid_lens[dim] - 1.) #known_values is array of shape \product(ith grid length), values map fine to grid indices as is grid_known_values = known_values #interp_coords is array of shape (# of events) x (# of dimensions), need to map into grid indices and then take transpose grid_interp_coords = np.transpose( (interp_coords - grid_starts) / grid_factors ) #With everything mapped to grid indices, we can now interpolate between "pixels" return ndimage_interp.map_coordinates(input=grid_known_values, coordinates=grid_interp_coords, output=float, order=1, mode='nearest')
def get_image_values_2(img, markerPos, DeltaMarker, fname, step=y_resampling):
img = np.flipud(img)
ds = np.sqrt(DeltaMarker[:,0]*DeltaMarker[:,0] + DeltaMarker[:,1]*DeltaMarker[:,1])
nSteps = img.shape[0] / step
stepSize = step / ds
n = np.linspace(0., nSteps, nSteps+1)
sampleOffset = np.einsum('i,ik,j->ijk', stepSize, DeltaMarker, n)
sampleStart = np.empty(markerPos.shape, dtype='f8')
sampleStart[:,:] = markerPos[:,:]
nMarkers, tmp = markerPos.shape
sampleStart.shape = (nMarkers, 1, 2)
sampleStart = np.repeat(sampleStart, nSteps+1, axis=1)
samplePos = sampleStart + sampleOffset
samplePos.shape = (nMarkers*(nSteps+1),2)
resampImg = imginterp.map_coordinates(img.T, samplePos.T, order=1)
resampImg.shape = (nMarkers, nSteps+1)
resampImg = resampImg.T
scan = str(fname[-5])
# CONVERSION
# Convert from pixel value to HAp density
# In this case, HAp density is calculated with mu values, keV(1)=119
if scan == 'g':
resampImg *= 2.**16
resampImg *= 0.0000689219599491
resampImg -= 1.54118269436172
else:
resampImg *= 2.**16
resampImg *= 0.00028045707501
resampImg -= 1.48671229207043
return resampImg[:,:]
def apply_affine_itk_transform_on_image(input_image, transform, center, reference_image=None, order=None):
"""
"""
input_data = np.float32(input_image.get_data())
if reference_image is None:
reference_image = input_image
#set the interpolation order to 1 if not specified
if order is None:
order = 1
ref_data = np.float32(reference_image.get_data())
#create index for the reference space
i = np.arange(0,ref_data.shape[0])
j = np.arange(0,ref_data.shape[1])
k = np.arange(0,ref_data.shape[2])
iv,jv,kv = np.meshgrid(i,j,k,indexing='ij')
iv = np.reshape(iv,(-1))
jv = np.reshape(jv,(-1))
kv = np.reshape(kv,(-1))
#convert the transform from itk (LPS) to nibabel (RAS)
nb_transform, nb_center = convert_itk_transform_to_affine_transform(transform,center)
#compute the coordinates in the input image
pointset = np.zeros((4,iv.shape[0]))
pointset[0,:] = iv
pointset[1,:] = jv
pointset[2,:] = kv
pointset[3,:] = np.ones((iv.shape[0]))
#no need to specify the center here because it is included in itk-based nb_transform
#pointset = transform_a_set_of_points(pointset,nb_transform,reference_image.affine,np.linalg.inv(input_image.affine))
pointset = transform_a_set_of_points(pointset,nb_transform,reference_image.affine,np.linalg.inv(input_image.affine),nb_center)
#compute the interpolation
val = np.zeros(iv.shape)
map_coordinates(input_data,[pointset[0,:],pointset[1,:],pointset[2,:]],output=val,order=order)
output_data = np.reshape(val,ref_data.shape)
return nibabel.Nifti1Image(output_data, reference_image.affine)
def warp_image(self, img, px,py, mode='nearest'):
sh = img.shape
dx = self.wcoords_from_params1d(px, sh)
dy = self.wcoords_from_params1d(py, sh)
xi,yi = np.meshgrid(np.arange(sh[1]), np.arange(sh[0]))
return map_coordinates(img, [yi+ dy, xi+dx], mode=mode)
return self.warp_image(img,dx,dy)
def rescale(img,
scale,
shape=None,
mask=None,
order=3,
mode='nearest',
unitary=True):
"""Rescale an image by interpolation.
Parameters
----------
img : array_like
Image to rescale
scale : float
Scaling factor. Scale factors less than 1 will shrink the image. Scale
factors greater than 1 will grow the image.
shape : array_like or int, optional
Output shape. If None (default), the output shape will be the input img
shape multiplied by the scale factor.
mask : array_like, optional
Binary mask applied after rescaling. If None (default), a mask is
created from the nonzero portions of img. To skip masking operation,
set ``mask = np.ones_like(img)``
order : int, optional
Order of spline interpolation used for rescaling operation. Default is
3. Order must be in the range 0-5.
mode : {'constant', 'nearest', 'reflect', 'wrap'}, optional
Points outside the boundaries of the input are filled according to the
given mode. Default is 'constant'.
unitary : bool, optional
Normalization flag. If True (default), a normalization is performed on
the output such that the rescaling operation is unitary and image power
(if complex) or intensity (if real) is conserved.
Returns
-------
img : ndarray
Rescaled image.
Note
----
The post-rescale masking operation should have no real effect on the
resulting image but is included to eliminate interpolation artifacts that
sometimes appear in large clusters of zeros in rescaled images.
See Also
--------
:func:`rebin`
"""
img = np.asarray(img)
if mask is None:
# take the real portion to ensure that even if img is complex, mask will
# be real
mask = np.zeros_like(img).real
mask[img != 0] = 1
if shape is None:
shape = np.ceil(
(img.shape[0] * scale, img.shape[1] * scale)).astype(np.int)
else:
if np.isscalar(shape):
shape = np.ceil((shape * scale, shape * scale)).astype(np.int)
else:
shape = np.ceil(
(shape[0] * scale, shape[1] * scale)).astype(np.int)
x = (np.arange(shape[1], dtype=np.float64) -
shape[1] / 2.) / scale + img.shape[1] / 2.
y = (np.arange(shape[0], dtype=np.float64) -
shape[0] / 2.) / scale + img.shape[0] / 2.
xx, yy = np.meshgrid(x, y)
mask = map_coordinates(mask, [yy, xx], order=1, mode='nearest')
mask[mask < np.finfo(mask.dtype).eps] = 0
if np.iscomplexobj(img):
out = np.zeros(shape, dtype=np.complex128)
out.real = map_coordinates(img.real, [yy, xx], order=order, mode=mode)
out.imag = map_coordinates(img.imag, [yy, xx], order=order, mode=mode)
else:
out = map_coordinates(img, [yy, xx], order=order, mode=mode)
if unitary:
out *= np.sum(img) / np.sum(out)
out *= mask
return out
def propcustom_dm(wf, dm_z0, dm_xc, dm_yc, spacing=0., **kwargs):
"""
Generate a deformable mirror surface almost exactly like PROPER.
Simulate a deformable mirror of specified actuator spacing, including the
effects of the DM influence function. Has two more optional keywords
compared to proper.prop_dm
Parameters
----------
wf : obj
WaveFront class object
dm_z0 : str or numpy ndarray
Either a 2D numpy array containing the surface piston of each DM
actuator in meters or the name of a 2D FITS image file containing the
above
dm_xc, dm_yc : list or numpy ndarray
The location of the optical axis (center of the wavefront) on the DM in
actuator units (0 ro num_actuator-1). The center of the first actuator
is (0.0, 0.0)
spacing : float
Defines the spacing in meters between actuators; must not be used when
n_act_across_pupil is specified.
Returns
-------
dmap : numpy ndarray
Returns DM surface (not wavefront) map in meters
Other Parameters
----------------
FIT : bool
Switch that tells routine that the values in "dm_z" are the desired
surface heights rather than commanded actuator heights, and so the
routine should fit this map, accounting for actuator influence functions,
to determine the necessary actuator heights. An iterative error-minimizing
loop is used for the fit.
NO_APPLY : bool
If set, the DM pattern is not added to the wavefront. Useful if the DM
surface map is needed but should not be applied to the wavefront
N_ACT_ACROSS_PUPIL : int
Specifies the number of actuators that span the X-axis beam diameter. If
it is a whole number, the left edge of the left pixel is aligned with
the left edge of the beam, and the right edge of the right pixel with
the right edge of the beam. This determines the spacing and size of the
actuators. Should not be used when "spacing" value is specified.
XTILT, YTILT, ZTILT : float
Specify the rotation of the DM surface with respect to the wavefront plane
in degrees about the X, Y, Z axes, respectively, with the origin at the
center of the wavefront. The DM surface is interpolated and orthographically
projected onto the wavefront grid. The coordinate system assumes that
the wavefront and initial DM surface are in the X,Y plane with a lower
left origin with Z towards the observer. The rotations are left handed.
The default rotation order is X, Y, then Z unless the /ZYX switch is set.
XYZ or ZYX : bool
Specifies the rotation order if two or more of XTILT, YTILT, or ZTILT
are specified. The default is /XYZ for X, Y, then Z rotations.
inf_fn : string
specify a new influence function as a FITS file with the same header keywords as
PROPER's default influence function. Needs these values in info.PrimaryData.Keywords:
'P2PDX_M' % pixel width x (m)
'P2PDY_M' % pixel width y (m)
'C2CDX_M' % actuator pitch x (m)
'C2CDY_M' % actuator pitch y (m)
inf_sign : {+,-}
specifies the sign (+/-) of the influence function. Given as an option because
the default influence function file is positive, but positive DM actuator
commands make a negative deformation for Xinetics and BMC DMs.
Raises
------
ValueError:
User cannot specify both actuator spacing and N_ACT_ACROSS_PUPIL
ValueError:
User must specify either actuator spacing or N_ACT_ACROSS_PUPIL
"""
if "ZYX" in kwargs and "XYZ" in kwargs:
raise ValueError('PROP_DM: Error: Cannot specify both XYZ and ZYX ' +
'rotation orders. Stopping')
elif "ZYX" not in kwargs and 'XYZ' not in kwargs:
XYZ = 1 # default is rotation around X, then Y, then Z
# ZYX = 0
elif "ZYX" in kwargs:
# ZYX = 1
XYZ = 0
elif "XYZ" in kwargs:
XYZ = 1
# ZYX = 0
if "XTILT" in kwargs:
xtilt = kwargs["XTILT"]
else:
xtilt = 0.
if "YTILT" in kwargs:
ytilt = kwargs["YTILT"]
else:
ytilt = 0.
if "ZTILT" in kwargs:
ztilt = kwargs["ZTILT"]
else:
ztilt = 0.
if type(dm_z0) == str:
dm_z = proper.prop_fits_read(dm_z0) # Read DM setting from FITS file
else:
dm_z = dm_z0
if "inf_fn" in kwargs:
inf_fn = kwargs["inf_fn"]
else:
inf_fn = "influence_dm5v2.fits"
if "inf_sign" in kwargs:
if(kwargs["inf_sign"] == '+'):
sign_factor = 1.
elif(kwargs["inf_sign"] == '-'):
sign_factor = -1.
else:
sign_factor = 1.
n = proper.prop_get_gridsize(wf)
dx_surf = proper.prop_get_sampling(wf) # sampling of surface in meters
beamradius = proper.prop_get_beamradius(wf)
# Default influence function sampling is 0.1 mm, peak at (x,y)=(45,45)
# Default influence function has shape = 1x91x91. Saving it as a 2D array
# before continuing with processing
dir_path = os.path.join(os.path.dirname(os.path.realpath(__file__)),
"data")
inf = proper.prop_fits_read(os.path.join(dir_path, inf_fn))
inf = sign_factor*np.squeeze(inf)
s = inf.shape
nx_inf = s[1]
ny_inf = s[0]
xc_inf = nx_inf // 2
yc_inf = ny_inf // 2
dx_inf = 0.1e-3 # influence function spacing in meters
dx_dm_inf = 1.0e-3 # nominal spacing between DM actuators in meters
inf_mag = 10
if spacing != 0 and "N_ACT_ACROSS_PUPIL" in kwargs:
raise ValueError("PROP_DM: User cannot specify both actuator spacing" +
"and N_ACT_ACROSS_PUPIL. Stopping.")
if spacing == 0 and "N_ACT_ACROSS_PUPIL" not in kwargs:
raise ValueError("PROP_DM: User must specify either actuator spacing" +
" or N_ACT_ACROSS_PUPIL. Stopping.")
if "N_ACT_ACROSS_PUPIL" in kwargs:
dx_dm = 2. * beamradius / int(kwargs["N_ACT_ACROSS_PUPIL"])
else:
dx_dm = spacing
dx_inf = dx_inf * dx_dm / dx_dm_inf # Influence function sampling scaled
# to specified DM actuator spacing
if "FIT" in kwargs:
x = (np.arange(5, dtype=np.float64) - 2) * dx_dm
if proper.use_cubic_conv:
inf_kernel = proper.prop_cubic_conv(inf.T, x/dx_inf+xc_inf,
x/dx_inf+yc_inf, GRID=True)
else:
xygrid = np.meshgrid(x/dx_inf+xc_inf, x/dx_inf+yc_inf)
inf_kernel = map_coordinates(inf.T, xygrid, order=3,
mode="nearest")
(dm_z_commanded, dms) = proper.prop_fit_dm(dm_z, inf_kernel)
else:
dm_z_commanded = dm_z
s = dm_z.shape
nx_dm = s[1]
ny_dm = s[0]
# Create subsampled DM grid
margin = 9 * inf_mag
nx_grid = nx_dm * inf_mag + 2 * margin
ny_grid = ny_dm * inf_mag + 2 * margin
xoff_grid = margin + inf_mag/2 # pixel location of 1st actuator center in subsampled grid
yoff_grid = xoff_grid
dm_grid = np.zeros([ny_grid, nx_grid], dtype = np.float64)
x = np.arange(nx_dm, dtype=int) * int(inf_mag) + int(xoff_grid)
y = np.arange(ny_dm, dtype=int) * int(inf_mag) + int(yoff_grid)
dm_grid[np.tile(np.vstack(y), (nx_dm,)),
np.tile(x, (ny_dm, 1))] = dm_z_commanded
dm_grid = ss.fftconvolve(dm_grid, inf, mode='same')
# 3D rotate DM grid and project orthogonally onto wavefront
xdim = int(np.round(np.sqrt(2) * nx_grid * dx_inf / dx_surf)) # grid dimensions (pix) projected onto wavefront
ydim = int(np.round(np.sqrt(2) * ny_grid * dx_inf / dx_surf))
if xdim > n: xdim = n
if ydim > n: ydim = n
x = np.ones((ydim, 1), dtype=int) * ((np.arange(xdim) - xdim // 2) * dx_surf)
y = (np.ones((xdim, 1), dtype=int) * ((np.arange(ydim) - ydim // 2) * dx_surf)).T
a = xtilt * np.pi / 180
b = ytilt * np.pi / 180
g = ztilt * np.pi /180
if XYZ:
m = np.array([[cos(b)*cos(g), -cos(b)*sin(g), sin(b), 0],
[cos(a)*sin(g) + sin(a)*sin(b)*cos(g), cos(a)*cos(g)-sin(a)*sin(b)*sin(g), -sin(a)*cos(b), 0],
[sin(a)*sin(g)-cos(a)*sin(b)*cos(g), sin(a)*cos(g)+cos(a)*sin(b)*sin(g), cos(a)*cos(b), 0],
[0, 0, 0, 1] ])
else:
m = np.array([ [cos(b)*cos(g), cos(g)*sin(a)*sin(b)-cos(a)*sin(g), cos(a)*cos(g)*sin(b)+sin(a)*sin(g), 0],
[cos(b)*sin(g), cos(a)*cos(g)+sin(a)*sin(b)*sin(g), -cos(g)*sin(a)+cos(a)*sin(b)*sin(g), 0],
[-sin(b), cos(b)*sin(a), cos(a)*cos(b), 0],
[0, 0, 0, 1] ])
# Forward project a square
edge = np.array([[-1.0, -1.0, 0.0, 0.0],
[1.0, -1.0, 0.0, 0.0],
[1.0, 1.0, 0.0, 0.0],
[-1.0, 1.0, 0.0, 0.0]])
new_xyz = np.dot(edge, m)
# determine backward projection for screen-raster-to-DM-surce computation
dx_dxs = (new_xyz[0, 0] - new_xyz[1, 0]) / (edge[0, 0] - edge[1, 0])
dx_dys = (new_xyz[1, 0] - new_xyz[2, 0]) / (edge[1, 1] - edge[2, 1])
dy_dxs = (new_xyz[0, 1] - new_xyz[1, 1]) / (edge[0, 0] - edge[1, 0])
dy_dys = (new_xyz[1, 1] - new_xyz[2, 1]) / (edge[1, 1] - edge[2, 1])
xs = (x/dx_dxs - y*dx_dys/(dx_dxs*dy_dys)) / \
(1 - dy_dxs*dx_dys/(dx_dxs*dy_dys))
ys = (y/dy_dys - x*dy_dxs/(dx_dxs*dy_dys)) / \
(1 - dx_dys*dy_dxs/(dx_dxs*dy_dys))
xdm = (xs + dm_xc * dx_dm) / dx_inf + xoff_grid
ydm = (ys + dm_yc * dx_dm) / dx_inf + yoff_grid
if proper.use_cubic_conv:
grid = proper.prop_cubic_conv(dm_grid.T, xdm, ydm, GRID = False)
grid = grid.reshape([xdm.shape[1], xdm.shape[0]])
else:
grid = map_coordinates(dm_grid.T, [xdm, ydm], order=3,
mode="nearest", prefilter = True)
dmap = np.zeros([n, n], dtype=np.float64)
nx_grid, ny_grid = grid.shape
xmin, xmax = n // 2 - xdim // 2, n // 2 - xdim // 2 + nx_grid
ymin, ymax = n // 2 - ydim // 2, n // 2 - ydim // 2 + ny_grid
dmap[ymin:ymax, xmin:xmax] = grid
if "NO_APPLY" not in kwargs:
proper.prop_add_phase(wf, 2 * dmap) # convert surface to WFE
return dmap
def rz2rho(self,
r_in,
z_in,
t_in=None,
coord_out='rho_pol',
extrapolate=True):
"""Equilibrium mapping routine, map from R,Z -> rho (pol,tor,r_V,...)
Fast for a large number of points
Input
----------
t_in : float or 1darray
time
r_in : ndarray
R coordinates
1D (time constant) or 2D+ (time variable) of size (nt,nx,...)
z_in : ndarray
Z coordinates
1D (time constant) or 2D+ (time variable) of size (nt,nx,...)
coord_out: str
mapped coordinates - rho_pol, rho_tor, r_V, rho_V, Psi
extrapolate: bool
extrapolate coordinates (like rho_tor) for values larger than 1
Output
-------
rho : 2D+ array (nt,nx,...)
Magnetics flux coordinates of the points
"""
if not self.eq_open:
return
if self.debug: print(('Remapping from {R, z} to %s' % coord_out))
if t_in is None:
t_in = self.t_eq
tarr = np.atleast_1d(t_in)
r_in = np.atleast_2d(r_in)
z_in = np.atleast_2d(z_in)
dr = (self.Rmesh[-1] - self.Rmesh[0]) / (len(self.Rmesh) - 1)
dz = (self.Zmesh[-1] - self.Zmesh[0]) / (len(self.Zmesh) - 1)
nt_in = np.size(tarr)
if r_in.shape != z_in.shape:
raise Exception( 'Not equal shape of z_in and r_in %s,%s'\
%(str(z_in.shape), str(z_in.shape)) )
if np.size(r_in, 0) != nt_in and np.size(r_in, 0) != 1:
r_in = r_in[None]
z_in = z_in[None]
if np.size(r_in, 0) == 1:
r_in = np.broadcast_to(r_in, (nt_in, ) + r_in.shape[1:])
z_in = np.broadcast_to(z_in, (nt_in, ) + z_in.shape[1:])
self._read_pfm()
Psi = np.empty((nt_in, ) + r_in.shape[1:], dtype=np.single)
scaling = np.array([dr, dz])
offset = np.array([self.Rmesh[0], self.Zmesh[0]])
unique_idx, idx = self._get_nearest_index(tarr)
for i in unique_idx:
jt = idx == i
coords = np.array((r_in[jt], z_in[jt]))
index = ((coords.T - offset) / scaling).T
Psi[jt] = map_coordinates(self.pfm[i],
index,
mode='nearest',
order=2,
prefilter=True)
rho_out = self.rho2rho(Psi,
t_in=t_in,
extrapolate=extrapolate,
coord_in='Psi',
coord_out=coord_out)
return rho_out
def interpolate_tau(self, j, w, t, r, s):
"""Interpolate the optical depth grid."""
idxs = self.indices(j, w, t, r, s)
return map_coordinates(self.grid[j, 1], idxs, order=1, mode='nearest')
def resample_data_or_seg(data,
new_shape,
is_seg,
axis=None,
order=3,
do_separate_z=False,
order_z=0):
"""
separate_z=True will resample with order 0 along z
:param data:
:param new_shape:
:param is_seg:
:param axis:
:param order:
:param do_separate_z:
:param cval:
:param order_z: only applies if do_separate_z is True
:return:
"""
assert len(data.shape) == 4, "data must be (c, x, y, z)"
if is_seg:
resize_fn = resize_segmentation
kwargs = OrderedDict()
else:
resize_fn = resize
kwargs = {'mode': 'edge', 'anti_aliasing': False}
dtype_data = data.dtype
shape = np.array(data[0].shape)
new_shape = np.array(new_shape)
if np.any(shape != new_shape):
data = data.astype(float)
if do_separate_z:
print("separate z, order in z is", order_z, "order inplane is",
order)
assert len(axis) == 1, "only one anisotropic axis supported"
axis = axis[0]
if axis == 0:
new_shape_2d = new_shape[1:]
elif axis == 1:
new_shape_2d = new_shape[[0, 2]]
else:
new_shape_2d = new_shape[:-1]
reshaped_final_data = []
for c in range(data.shape[0]):
reshaped_data = []
for slice_id in range(shape[axis]):
if axis == 0:
reshaped_data.append(
resize_fn(data[c, slice_id], new_shape_2d, order,
**kwargs))
elif axis == 1:
reshaped_data.append(
resize_fn(data[c, :, slice_id], new_shape_2d,
order, **kwargs))
else:
reshaped_data.append(
resize_fn(data[c, :, :, slice_id], new_shape_2d,
order, **kwargs))
reshaped_data = np.stack(reshaped_data, axis)
if shape[axis] != new_shape[axis]:
# The following few lines are blatantly copied and modified from sklearn's resize()
rows, cols, dim = new_shape[0], new_shape[1], new_shape[2]
orig_rows, orig_cols, orig_dim = reshaped_data.shape
row_scale = float(orig_rows) / rows
col_scale = float(orig_cols) / cols
dim_scale = float(orig_dim) / dim
map_rows, map_cols, map_dims = np.mgrid[:rows, :cols, :dim]
map_rows = row_scale * (map_rows + 0.5) - 0.5
map_cols = col_scale * (map_cols + 0.5) - 0.5
map_dims = dim_scale * (map_dims + 0.5) - 0.5
coord_map = np.array([map_rows, map_cols, map_dims])
if not is_seg or order_z == 0:
reshaped_final_data.append(
map_coordinates(reshaped_data,
coord_map,
order=order_z,
mode='nearest')[None])
else:
unique_labels = np.unique(reshaped_data)
reshaped = np.zeros(new_shape, dtype=dtype_data)
for i, cl in enumerate(unique_labels):
reshaped_multihot = np.round(
map_coordinates(
(reshaped_data == cl).astype(float),
coord_map,
order=order_z,
mode='nearest'))
reshaped[reshaped_multihot > 0.5] = cl
reshaped_final_data.append(reshaped[None])
else:
reshaped_final_data.append(reshaped_data[None])
reshaped_final_data = np.vstack(reshaped_final_data)
else:
print("no separate z, order", order)
reshaped = []
for c in range(data.shape[0]):
reshaped.append(
resize_fn(data[c], new_shape, order, **kwargs)[None])
reshaped_final_data = np.vstack(reshaped)
return reshaped_final_data.astype(dtype_data)
else:
print("no resampling necessary")
return data
def _map(input, indices, shape):
return np.expand_dims(map_coordinates(input, indices,
order=1).reshape(shape),
axis=0)
def Find_Boundaries(distmap,
S_features,
gaussian_size=0.25,
lower_ind_thres=-5,
make_plot=True):
"""Primary algorithm to find domain boundaries
Inputs:
distmap: distance map for a chromosome, 2d-array
S_features: tuple or list of features, list or tuple of 2d-array
gaussian_size: sigma for gaussian filter applied to features to better call local maximum, float
lower_ind_thres: lower boundary for accepted indices along off-diagonal lines, int
make_plot: whether make plots, bool
Outputs:
selected_pk_coords: selected peaks in feature maps, which corresponds to domain boundaries, 1d-array
"""
from scipy.ndimage.interpolation import map_coordinates
from scipy.signal import find_peaks
#from astropy.convolution import Gaussian2DKernel,convolve
dim = np.shape(distmap)[0]
# genrate coordinates for line i+x, i+x/2 which arrow edges align:
start_ind = np.arange(-int(dim / 2), dim)
coord_list = [
np.stack([
np.arange(np.abs(i), dim),
max(0, i) / 2 + np.arange(max(0, i), dim + min(0, i)) / 2
]) for i in start_ind
]
# set gaussian kernel
#kernel = Gaussian2DKernel(x_stddev=gaussian_size)
# initialize feature ids
feature_list = []
for feature_id in range(2):
# gaussian filter this map
if gaussian_size:
feature_map = convolve(S_features[feature_id], kernel)
else:
feature_map = S_features[feature_id]
# extract arrow lines
arrow_lines = [
map_coordinates(feature_map, _coords) for _coords in coord_list
]
# calculate mean to find local maximum
arrow_line_means = np.array(
[np.mean(arrline) for arrline in arrow_lines])
# calculate peaks for meean behavior line
feature_line_ids = find_peaks(
arrow_line_means, distance=3,
width=2)[0] # this step is better to be more rigorious
feature_line_ids = feature_line_ids[
start_ind[feature_line_ids] > lower_ind_thres]
feature_list.append(feature_line_ids)
# plot selected lines
#plt.figure()
#plt.plot(start_ind, arrow_line_means)
#plt.plot(start_ind[feature_line_ids], arrow_line_means[feature_line_ids], 'ro')
#plt.show()
# select shared feature_ids
selected_ids = []
for _id in feature_list[0]:
if sum(np.abs(feature_list[1] - _id) <= 1) > 0:
_local_ids = feature_list[1][np.abs(feature_list[1] - _id) <= 1]
_local_ids = np.concatenate([[_id], _local_ids])
selected_ids.append(np.min(_local_ids))
selected_ids = np.array(selected_ids)
if len(selected_ids) == 0:
return np.array([])
# selected ids plus +-1 lines
feature_map = convolve(S_features[1], kernel)
selected_coords = [
coord_list[_i]
for _i in np.unique([selected_ids, selected_ids - 1, selected_ids + 1])
]
selected_lines = [
map_coordinates(feature_map, _coords) for _coords in selected_coords
]
# call peaks
pks = [
find_peaks(_line, distance=2, width=2)[0] for _line in selected_lines
]
pk_coords = np.sort(
np.concatenate(
[_coord[0, _pk] for _coord, _pk in zip(selected_coords, pks)]))
# select into connected groups
selected_groups = []
_group = []
for _i, _c in enumerate(pk_coords):
if len(_group) == 0:
_group.append(_c)
elif sum(np.abs(np.array(_group) - _c) <= 1) >= 1:
_group.append(_c)
np.delete(pk_coords, _i)
else:
if len(_group) > 1:
selected_groups.append(_group)
_group = []
# pick from connected groups
group_size_th = 2
selected_pk_coords = np.sort([
int(np.round(np.mean(_group))) for _group in selected_groups
if len(_group) >= group_size_th
])
if make_plot:
plt.figure()
plt.imshow(distmap, cmap='seismic_r', vmin=0, vmax=1000)
plt.colorbar()
plt.title("input distance map")
edges = [0] + list(selected_pk_coords) + [dim]
for _i, _c in enumerate(edges[:-1]):
plt.plot(np.arange(_c, edges[_i + 1]),
np.ones(edges[_i + 1] - _c) * _c,
color='y',
linewidth=3.0)
plt.plot(np.ones(edges[_i + 1] - _c) * edges[_i + 1],
np.arange(_c, edges[_i + 1]),
color='y',
linewidth=3.0)
plt.xlim([0, dim])
plt.show()
return selected_pk_coords
def extrapolate(
precip,
velocity,
timesteps,
outval=np.nan,
xy_coords=None,
allow_nonfinite_values=False,
vel_timestep=1,
**kwargs,
):
"""Apply semi-Lagrangian backward extrapolation to a two-dimensional
precipitation field.
Parameters
----------
precip: array-like or None
Array of shape (m,n) containing the input precipitation field. All
values are required to be finite by default. If set to None, only the
displacement field is returned without interpolating the inputs. This
requires that return_displacement is set to True.
velocity: array-like
Array of shape (2,m,n) containing the x- and y-components of the m*n
advection field. All values are required to be finite by default.
timesteps: int or list of floats
If timesteps is integer, it specifies the number of time steps to
extrapolate. If a list is given, each element is the desired
extrapolation time step from the current time. The elements of the list
are required to be in ascending order.
outval: float, optional
Optional argument for specifying the value for pixels advected from
outside the domain. If outval is set to 'min', the value is taken as
the minimum value of precip.
Default: np.nan
xy_coords: ndarray, optional
Array with the coordinates of the grid dimension (2, m, n ).
* xy_coords[0]: x coordinates
* xy_coords[1]: y coordinates
By default, the *xy_coords* are computed for each extrapolation.
allow_nonfinite_values: bool, optional
If True, allow non-finite values in the precipitation and advection
fields. This option is useful if the input fields contain a radar mask
(i.e. pixels with no observations are set to nan).
Other Parameters
----------------
displacement_prev: array-like
Optional initial displacement vector field of shape (2,m,n) for the
extrapolation.
Default: None
n_iter: int
Number of inner iterations in the semi-Lagrangian scheme. If n_iter > 0,
the integration is done using the midpoint rule. Otherwise, the advection
vectors are taken from the starting point of each interval.
Default: 1
return_displacement: bool
If True, return the displacement between the initial input field and
the one obtained by integrating along the advection field.
Default: False
vel_timestep: float
The time step of the velocity field. It is assumed to have the same
unit as the timesteps argument. Applicable if timeseps is a list.
Default: 1.
interp_order: int
The order of interpolation to use. Default: 1 (linear). Setting this
to 0 (nearest neighbor) gives the best computational performance but
may produce visible artefacts. Setting this to 3 (cubic) gives the best
ability to reproduce small-scale variability but may significantly
increase the computation time.
Returns
-------
out: array or tuple
If return_displacement=False, return a time series extrapolated fields
of shape (num_timesteps,m,n). Otherwise, return a tuple containing the
extrapolated fields and the integrated trajectory (displacement) along
the advection field.
References
----------
:cite:`GZ2002`
"""
if precip is not None and precip.ndim != 2:
raise ValueError("precip must be a two-dimensional array")
if velocity.ndim != 3:
raise ValueError("velocity must be a three-dimensional array")
if precip is not None and not allow_nonfinite_values:
if np.any(~np.isfinite(precip)):
raise ValueError("precip contains non-finite values")
if np.any(~np.isfinite(velocity)):
raise ValueError("velocity contains non-finite values")
if isinstance(timesteps, list) and not sorted(timesteps) == timesteps:
raise ValueError("timesteps is not in ascending order")
# defaults
verbose = kwargs.get("verbose", False)
displacement_prev = kwargs.get("displacement_prev", None)
n_iter = kwargs.get("n_iter", 1)
return_displacement = kwargs.get("return_displacement", False)
interp_order = kwargs.get("interp_order", 1)
if precip is None and not return_displacement:
raise ValueError("precip is None but return_displacement is False")
if "D_prev" in kwargs.keys():
warnings.warn(
"deprecated argument D_prev is ignored, use displacement_prev instead",
)
# if interp_order > 1, apply separate masking to preserve nan and
# non-precipitation values
if precip is not None and interp_order > 1:
minval = np.nanmin(precip)
mask_min = (precip > minval).astype(float)
if allow_nonfinite_values:
mask_finite = np.isfinite(precip)
precip = precip.copy()
precip[~mask_finite] = 0.0
mask_finite = mask_finite.astype(float)
prefilter = True if interp_order > 1 else False
if isinstance(timesteps, int):
timesteps = np.arange(1, timesteps + 1)
vel_timestep = 1.0
elif np.any(np.diff(timesteps) <= 0.0):
raise ValueError(
"the given timestep sequence is not monotonously increasing")
timestep_diff = np.hstack([[timesteps[0]], np.diff(timesteps)])
if verbose:
print("Computing the advection with the semi-lagrangian scheme.")
t0 = time.time()
if precip is not None and outval == "min":
outval = np.nanmin(precip)
if xy_coords is None:
x_values, y_values = np.meshgrid(np.arange(velocity.shape[2]),
np.arange(velocity.shape[1]))
xy_coords = np.stack([x_values, y_values])
def interpolate_motion(displacement, velocity_inc, td):
coords_warped = xy_coords + displacement
coords_warped = [coords_warped[1, :, :], coords_warped[0, :, :]]
velocity_inc_x = ip.map_coordinates(
velocity[0, :, :],
coords_warped,
mode="nearest",
order=1,
prefilter=False,
)
velocity_inc_y = ip.map_coordinates(
velocity[1, :, :],
coords_warped,
mode="nearest",
order=1,
prefilter=False,
)
velocity_inc[0, :, :] = velocity_inc_x
velocity_inc[1, :, :] = velocity_inc_y
if n_iter > 1:
velocity_inc /= n_iter
velocity_inc *= td / vel_timestep
precip_extrap = []
if displacement_prev is None:
displacement = np.zeros((2, velocity.shape[1], velocity.shape[2]))
velocity_inc = velocity.copy() * timestep_diff[0] / vel_timestep
else:
displacement = displacement_prev.copy()
velocity_inc = np.empty(velocity.shape)
interpolate_motion(displacement, velocity_inc, timestep_diff[0])
for ti, td in enumerate(timestep_diff):
if n_iter > 0:
for k in range(n_iter):
interpolate_motion(displacement - velocity_inc / 2.0,
velocity_inc, td)
displacement -= velocity_inc
interpolate_motion(displacement, velocity_inc, td)
else:
if ti > 0 or displacement_prev is not None:
interpolate_motion(displacement, velocity_inc, td)
displacement -= velocity_inc
coords_warped = xy_coords + displacement
coords_warped = [coords_warped[1, :, :], coords_warped[0, :, :]]
if precip is not None:
precip_warped = ip.map_coordinates(
precip,
coords_warped,
mode="constant",
cval=outval,
order=interp_order,
prefilter=prefilter,
)
if interp_order > 1:
mask_warped = ip.map_coordinates(
mask_min,
coords_warped,
mode="constant",
cval=0,
order=1,
prefilter=False,
)
precip_warped[mask_warped < 0.5] = minval
if allow_nonfinite_values:
mask_warped = ip.map_coordinates(
mask_finite,
coords_warped,
mode="constant",
cval=0,
order=1,
prefilter=False,
)
precip_warped[mask_warped < 0.5] = np.nan
precip_extrap.append(np.reshape(precip_warped, precip.shape))
if verbose:
print("--- %s seconds ---" % (time.time() - t0))
if precip is not None:
if not return_displacement:
return np.stack(precip_extrap)
else:
return np.stack(precip_extrap), displacement
else:
return None, displacement
def interpolate(self,
l,
m,
time=None,
freq=None,
freqaxis=None,
output=None):
"""Interpolates l/m coordinates in the beam.
l,m may be arrays (both must be the same shape, or will be promoted to the same shape)
If beam has a freq dependence, then an array of frequency coordinates (freq) must be given,
and freqaxis must be set to the number of the frequency axis. Then the following
possibilities apply:
(A) len(freq)==1 (freqaxis need not be set)
l/m is interpolated at the same frequency point.
Output array is same shape as l/m.
(B) len(freq)>1 and l.shape[freqaxis] == 1:
The same l/m is interpolated at every point in freq.
Output array is same shape as l/m, plus an extra frequency axis (number freqaxis)
(C) len(freq)>1 and l.shape[freqaxis] == len(freq)
l/m has its own freq dependence, so a different l/m/freq is interpolated at every point.
Output array is same shape as l/m.
And finally (D):
(D) No dependence on frequency in the beam.
We simply interpolate every l/m value as is. Output array is same shape as l/m.
'time' is currently ignored -- provided for later compatibility (i.e. beams with time planes)
"""
# make sure inputs are arrays
l = numpy.array(l) + self.l0
m = numpy.array(m) + self.m0
freq = numpy.array(freq)
# promote l,m to the same shape
l, m = unite_shapes(l, m)
dprint(3, "input l/m is", l, m)
l, m = self.beam.lmToBeam()
dprint(3, "in beam coordinates this is", l, m)
# now we make a 2xN coordinate array for map_coordinates
# lm[0,:] will be flattened L array, lm[1,:] will be flattened M array
# lm[2,:] will be flattened freq array (if we have a freq dependence)
# Do we have a frequency axis in the beam? (case A,B,C):
if self.beam.hasFrequencyAxis():
if freq is None:
raise ValueError, "frequencies not specified, but beam has a frequency dependence"
freq = numpy.array(freq)
if not freq.ndim:
freq = freq.reshape(1)
print freq
freq = self.beam.freqToBeam(freq)
# case (A): reuse same frequency for every l/m point
if len(freq) == 1:
lm = numpy.vstack((l.ravel(), m.ravel(), [freq[0]] * l.size))
# case B/C:
else:
# first turn freq vector into an array of the proper shape
if freqaxis is None:
raise ValueError, "frequency axis not specified, but beam has a frequency dependence"
freqshape = [1] * (freqaxis + 1)
freqshape[freqaxis] = len(freq)
freq = freq.reshape(freqshape)
# now promote freq to same shape as l,m. This takes care of cases B and C.
# (the freq axis of l/m will be expanded, and other axes of freq will be expanded)
l, freq = unite_shapes(l, freq)
m, freq = unite_shapes(m, freq)
lm = numpy.vstack((l.ravel(), m.ravel(), freq.ravel()))
# case (D): no frequency dependence in the beam
else:
lm = numpy.vstack((l.ravel(), m.ravel()))
# interpolate and reshape back to shape of L
if output is None:
output = numpy.zeros(l.shape, complex)
elif output.shape != l.shape:
output.resize(l.shape)
self.beam.interpolate(output, lm)
return output
output.real = interpolation.map_coordinates(
self._beam_real,
lm,
order=self._spline_order,
prefilter=(self._spline_order == 1)).reshape(l.shape)
output.imag = interpolation.map_coordinates(
self._beam_imag,
lm,
order=self._spline_order,
prefilter=(self._spline_order == 1)).reshape(l.shape)
if not self._beam_ampl is None:
output_ampl = interpolation.map_coordinates(
self._beam_ampl,
lm,
order=self._spline_order,
prefilter=(self._spline_order == 1)).reshape(l.shape)
phase_array = numpy.arctan2(output.imag, output.real)
output.real = output_ampl * numpy.cos(phase_array)
output.imag = output_ampl * numpy.sin(phase_array)
dprint(3, "interpolated value is", output)
return output
def get_unknown_uncertainty(cloud_distances, transmission_values):
"""Calculates the unknown uncertainty term, which is part of the surface
temperature uncertainty estimation.
Args:
cloud_distances <numpy.2darray>: distances to nearest cloud
transmission_values <numpy.2darray>: transmission
Returns:
unknown_uncertainty <numpy.2darray>: interpolated unknown uncertainty
"""
# Flatten the inputs.
flat_cloud_distances = cloud_distances.flatten()
flat_transmission_values = transmission_values.flatten()
# Matrix of "unknown errors," which was calculated from observed and
# predicted ST errors from the L7 global validation study.
unknown_error_matrix = np.array([[2.3749, 2.6962, 2.5620, 2.1131],
[1.9912, 1.6789, 1.4471, 1.2739],
[1.7925, 1.0067, 0.9143, 0.6366],
[1.9416, 1.3558, 0.7604, 0.6682],
[1.3861, 0.8269, 0.7404, 0.3125]])
# tau bins are 0.3 - 0.55, 0.55 - 0.7, 0.7 - 0.85, 0.85 - 1.0
# cloud bins are 0 - 1 km, 1 - 5 km, 5 - 10 km, 10 - 40 km, 40 - inf
#
# tau_interp and cloud_interp should be a vector of the center values
# for each bin, but we also want anything outside the entire range to be
# equal to the nearest value from the unknown matrix.
tau_interp = np.array([0.0, 0.425, 0.625, 0.775, 0.925, 1.0])
cld_interp = np.array([0, 0.5, 3.0, 7.5, 25.0, 82.5, 200.0])
# Define the highest values in the vectors. These are the last values.
tau_highest = tau_interp[-1]
cld_highest = cld_interp[-1]
# From input transmission values, find closest indices from tau_interp
# vector, calculate step in vector, then calculate fractional tau index.
tau_close_index = np.searchsorted(tau_interp,
flat_transmission_values,
side='right')
tau_close_index = tau_close_index - 1
tau_step = tau_interp[tau_close_index + 1] - tau_interp[tau_close_index]
tau_frac_index = tau_close_index + (
(flat_transmission_values - tau_interp[tau_close_index]) / tau_step)
one_locations = np.where(tau_frac_index == tau_highest)
tau_frac_index[one_locations] = len(tau_interp) - 1
# Memory cleanup
del tau_interp
del tau_close_index
del tau_step
del one_locations
# From input cloud distance values, find closest indices from cld_interp
# vector, calculate step in vector, then calculate fractional cloud index.
cld_close_index = np.searchsorted(cld_interp,
flat_cloud_distances,
side='right')
cld_close_index = cld_close_index - 1
cld_step = cld_interp[cld_close_index + 1] - cld_interp[cld_close_index]
cld_frac_index = cld_close_index + (
(flat_cloud_distances - cld_interp[cld_close_index]) / cld_step)
two_hundred_locations = np.where(cld_frac_index == cld_highest)
cld_frac_index[two_hundred_locations] = len(cld_interp) - 1
# Memory cleanup
del cld_interp
del cld_close_index
del cld_step
del two_hundred_locations
# Merge the arrays so they represent coordinates in the unknown_error_matrix
# grid to map_coordinates.
coordinates = np.row_stack((cld_frac_index, tau_frac_index))
# Memory cleanup
del tau_frac_index
del cld_frac_index
# Interpolate the results at the specified coordinates.
unknown_uncertainty = map_coordinates(unknown_error_matrix,
coordinates,
order=1,
mode='nearest')
# Memory cleanup
del unknown_error_matrix
del coordinates
return unknown_uncertainty
def elastic_transform_nd(image,
alpha,
sigma,
random_state=None,
order=1,
lazy=False):
"""Expects data to be (nx, ny, n1 ,..., nm)
params:
------
alpha:
the scaling parameter.
E.g.: alpha=2 => distorts images up to 2x scaling
sigma:
standard deviation of gaussian filter.
E.g.
low (sig~=1e-3) => no smoothing, pixelated.
high (1/5 * imsize) => smooth, more like affine.
very high (1/2*im_size) => translation
"""
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape
imsize = shape[:2]
dim = shape[2:]
# Random affine
blur_size = int(4 * sigma) | 1
dx = cv2.GaussianBlur(random_state.rand(*imsize) * 2 - 1,
ksize=(blur_size, blur_size),
sigmaX=sigma) * alpha
dy = cv2.GaussianBlur(random_state.rand(*imsize) * 2 - 1,
ksize=(blur_size, blur_size),
sigmaX=sigma) * alpha
# use as_strided to copy things over across n1...nn channels
dx = as_strided(dx.astype(np.float32),
strides=(0, ) * len(dim) + (4 * shape[1], 4),
shape=dim + (shape[0], shape[1]))
dx = np.transpose(dx, axes=(-2, -1) + tuple(range(len(dim))))
dy = as_strided(dy.astype(np.float32),
strides=(0, ) * len(dim) + (4 * shape[1], 4),
shape=dim + (shape[0], shape[1]))
dy = np.transpose(dy, axes=(-2, -1) + tuple(range(len(dim))))
coord = np.meshgrid(
*[np.arange(shape_i) for shape_i in (shape[1], shape[0]) + dim])
indices = [
np.reshape(e + de, (-1, 1))
for e, de in zip([coord[1], coord[0]] + coord[2:], [dy, dx] +
[0] * len(dim))
]
if lazy:
return indices
return map_coordinates(image, indices, order=order,
mode='reflect').reshape(shape)
def applyDeformation(image,
field,
ref=None,
order=1,
mode=None,
cval=None,
premat=None):
"""Applies a :class:`DeformationField` to an :class:`.Image`.
The image is transformed into the space of the field's reference image
space. See the ``scipy.ndimage.interpolation.map_coordinates`` function
for details on the ``order``, ``mode`` and ``cval`` options.
If an alternate reference image is provided via the ``ref`` argument,
the deformation field is resampled into its space, and then applied to
the input image. It is therefore assumed that an alternate ``ref`` is
aligned in world coordinates with the field's actual reference image.
:arg image: :class:`.Image` to be transformed
:arg field: :class:`DeformationField` to use
:arg ref: Alternate reference image - if not provided, ``field.ref``
is used
:arg order: Spline interpolation order, passed through to the
``scipy.ndimage.affine_transform`` function - ``0``
corresponds to nearest neighbour interpolation, ``1``
(the default) to linear interpolation, and ``3`` to
cubic interpolation.
:arg mode: How to handle regions which are outside of the image FOV.
Defaults to `''nearest'``.
:arg cval: Constant value to use when ``mode='constant'``.
:arg premat: Optional affine transform which can be used if ``image`` is
not in the same space as ``field.src``. Assumed to transform
from ``image`` **voxel** coordinates into ``field.src``
**voxel** coordinates.
:return: ``numpy.array`` containing the transformed image data.
"""
if order is None: order = 1
if mode is None: mode = 'nearest'
if cval is None: cval = 0
if ref is None: ref = field.ref
# We need the field to contain
# absolute source image voxel
# coordinates
field = convertDeformationSpace(field, 'voxel', 'voxel')
if field.deformationType != 'absolute':
field = DeformationField(convertDeformationType(field, 'absolute'),
header=field.header,
src=field.src,
ref=field.ref,
srcSpace='voxel',
refSpace='voxel',
defType='absolute')
# If the field is not voxel-aligned
# to the reference, we need to
# resample the field itself into the
# reference image space (assumed to
# be world-aligned). If field and ref
# are not not world aligned, regions
# of the field outside of the
# reference image space will contain
# -1s, so will be detected as out of
# bounds by map_coordinates below.
#
# This will potentially result in
# truncation at the field boundaries,
# but there's nothing we can do about
# that.
src = field.src
if not field.sameSpace(ref):
field = resample.resampleToReference(field,
ref,
order=order,
mode='constant',
cval=-1)[0]
else:
field = field.data
# If the input image is in a
# different space to the field
# source space, we need to
# adjust the resampling matrix.
# We assume world-world alignment
# between the original source
# and the image to be resampled
if (premat is not None) or (not image.sameSpace(src)):
if premat is None:
premat = affine.concat(image.getAffine('world', 'voxel'),
src.getAffine('voxel', 'world'))
else:
premat = affine.invert(premat)
shape = field.shape
field = field.reshape((-1, 3))
field = affine.transform(field, premat)
field = field.reshape(shape)
field = field.transpose((3, 0, 1, 2))
return ndinterp.map_coordinates(image.data,
field,
order=order,
mode=mode,
cval=cval)
def sample_cartesian2hexa(f_cartesian, fill_value=0.):
# A square integer meshgrid converted to hexagonal coordinates results in a parallelogram-shaped section
# from the hexagonal lattice. In our hexagonal grid, the shape looks like /__/ (skewed in the x / n2 direction)
# In order to make sure no information in the image is lost, we make sure the paralellogram encloses the square.
# The height of the parallelogram (size along n1 dimension) is therefore equal to the height of the square,
# while the width of the parallelogram (at any height) is equal to the height times (1 + 1. / sqrt(3)).
# This factor can easily be seen by making a drawing and noting that the difference y between the length of the
# horizontal side of the parallelogram and the side x of the inscribed square is
# y = x / tan(pi / 3) = x / sqrt(3)
alpha = 1 + 1. / np.sqrt(3)
# Map the corners of the image (in Cartesian coordinates) to hexagonal coordinates
n1_00, n2_00 = cartesian2hexa(x=0, y=0)
n1_10, n2_10 = cartesian2hexa(x=f_cartesian.shape[-1] - 1, y=0)
n1_01, n2_01 = cartesian2hexa(x=0, y=f_cartesian.shape[-2] - 1)
n1_11, n2_11 = cartesian2hexa(x=f_cartesian.shape[-1] - 1,
y=f_cartesian.shape[-2] - 1)
min_n1 = np.floor(np.min([n1_00, n1_10, n1_01, n1_11]))
max_n1 = np.ceil(np.max([n1_00, n1_10, n1_01, n1_11]))
min_n2 = np.floor(np.min([n2_00, n2_10, n2_01, n2_11]))
max_n2 = np.ceil(np.max([n2_00, n2_10, n2_01, n2_11]))
n1 = np.arange(min_n1, max_n1 + 1)
n2 = np.arange(min_n2, max_n2 + 1)
n1, n2 = np.meshgrid(n1, n2)
"""min_n1 = np.min([n1_00, n1_10, n1_01, n1_11])
max_n1 = np.max([n1_00, n1_10, n1_01, n1_11])
min_n2 = np.min([n2_00, n2_10, n2_01, n2_11])
max_n2 = np.max([n2_00, n2_10, n2_01, n2_11])
import matplotlib.pyplot as plt
fig = plt.figure()
plt.scatter([min_n1, min_n1, max_n1, max_n1], [min_n2, max_n2, min_n2, max_n2])
n1_sz = np.ceil(max_n1 - min_n1) + 1
n1 = np.linspace(start=min_n1, stop=min_n1 + n1_sz - 1, num=n1_sz, endpoint=True)
n2_sz = np.ceil(max_n2 - min_n2)
n2 = np.linspace(start=min_n2, stop=min_n2 + n2_sz - 1, num=n2_sz, endpoint=True)
n1, n2 = np.meshgrid(n1, n2)"""
# The lower-right corner of the image (highest x and y coordinate), in hexagonal coordinates
# sz1, sz2 = cartesian2hexa(x=f_cartesian.shape[-1], y=f_cartesian.shape[-2])
# sz1 = np.ceil(alpha * f_cartesian.shape[-2])
# sz2 = f_cartesian.shape[-1]
# # n1, n2 = np.meshgrid(np.arange(0, f_cartesian.shape[-2]), np.arange(0, f_cartesian.shape[-1]))
# n1, n2 = np.meshgrid(np.arange(sz1), np.arange(sz2))
# # n1, n2 = centered_meshgrid(sz1, sz2)
x, y = hexa2cartesian(n1, n2)
# x -= sz1 - f_cartesian.shape[-2]
xi = np.c_[y[..., None], x[..., None]].astype(f_cartesian.dtype)
# f_hex = interpn(
# (np.arange(0, f_cartesian.shape[-2]), np.arange(0, f_cartesian.shape[-1])),
# f_cartesian,
# xi,
# method='nearest', # 'splinef2d',
# bounds_error=False,
# fill_value=fill_value
# )
from scipy.ndimage.interpolation import map_coordinates
f_hex = map_coordinates(input=f_cartesian,
coordinates=xi.T,
order=5,
mode='constant',
cval=fill_value).T
# return f_hex, n1, n2, x, y
return f_hex
def correct_fov_image(dax_filename, sel_channels,
load_file_lock=None,
single_im_size=_image_size, all_channels=_allowed_colors,
num_buffer_frames=10, num_empty_frames=0,
drift=None, calculate_drift=False,
drift_channel='488', ref_filename=None,
use_autocorr=True, drift_args={},
corr_channels=_corr_channels, correction_folder=_correction_folder,
warp_image=True,
hot_pixel_corr=True, hot_pixel_th=4, z_shift_corr=False,
illumination_corr=True, illumination_profile=None,
bleed_corr=True, bleed_profile=None,
chromatic_ref_channel='647', chromatic_corr=True, chromatic_profile=None,
gaussian_highpass=False, gauss_sigma=5, gauss_truncate=2,
normalization=False, output_dtype=np.uint16,
return_drift=False, verbose=True):
"""Function to correct one whole field-of-view image in proper manner
Inputs:
Outputs:
"""
## check inputs
# dax_filename
if not os.path.isfile(dax_filename):
raise IOError(f"Dax file: {dax_filename} is not a file, exit!")
if not isinstance(dax_filename, str) or dax_filename[-4:] != '.dax':
raise IOError(f"Dax file: {dax_filename} has wrong data type, exit!")
if verbose:
print(f"- correct the whole fov for image: {dax_filename}")
_total_start = time.time()
# selected channels
if isinstance(sel_channels, str) or isinstance(sel_channels, int):
sel_channels = [str(sel_channels)]
else:
sel_channels = [str(ch) for ch in sel_channels]
# shared parameters
single_im_size = np.array(single_im_size, dtype=np.int)
all_channels = [str(ch) for ch in all_channels]
num_buffer_frames = int(num_buffer_frames)
num_empty_frames = int(num_empty_frames)
# drift
if drift is None:
drift = np.zeros(len(single_im_size), dtype=np.float32)
else:
drift = np.array(drift, dtype=np.float32)
if len(drift) != len(single_im_size):
raise IndexError(f"drift should have the same dimension as single_im_size.")
## correction channels and profiles
corr_channels = [str(ch) for ch in sorted(corr_channels, key=lambda v:-int(v)) if str(ch) in all_channels]
for _ch in corr_channels:
if _ch not in all_channels:
raise ValueError(f"Wrong correction channel:{_ch}, should be within {all_channels}")
## determine loaded channels
_overlap_channels = [_ch for _ch in corr_channels if _ch in sel_channels] # channels needs be corrected by bleedthrough/chromatic
if len(_overlap_channels) > 0 and bleed_corr:
_load_channels = [_ch for _ch in corr_channels]
else:
_load_channels = []
# append sel_channels
for _ch in sel_channels:
if _ch not in _load_channels:
_load_channels.append(_ch)
# append bead_image if going to do drift corr
_drift_channel = str(drift_channel)
if _drift_channel not in all_channels:
raise ValueError(f"Wrong input of drift_channel:{_drift_channel}, should be among {all_channels}")
if calculate_drift and drift_channel not in _load_channels:
_load_channels.append(drift_channel)
## check profiles
# load illumination profiles for selected channels (should exist for all include beads)
if illumination_corr:
if illumination_profile is None:
illumination_profile = load_correction_profile('illumination',
corr_channels=_load_channels,
correction_folder=correction_folder, all_channels=all_channels,
ref_channel=chromatic_ref_channel,
im_size=single_im_size,
verbose=verbose)
else:
if not isinstance(illumination_profile, dict):
raise TypeError(f"Wrong input type of illumination_profile, should be dict!")
for _ch in _load_channels:
if _ch not in illumination_profile:
raise KeyError(f"channel:{_ch} not given in illumination_profile")
# load bleedthrough profiles if required
if bleed_corr and len(_overlap_channels) > 0:
if bleed_profile is None:
bleed_profile = load_correction_profile('bleedthrough',
corr_channels=corr_channels,
correction_folder=correction_folder, all_channels=all_channels,
ref_channel=chromatic_ref_channel, im_size=single_im_size, verbose=verbose)
else:
bleed_profile = np.array(bleed_profile, dtype=np.float32)
if bleed_profile.shape != (len(corr_channels),len(corr_channels),single_im_size[-2], single_im_size[-1]) and bleed_profile.shape != tuple([len(corr_channels),len(corr_channels)]+list(single_im_size)):
raise IndexError(f"Wrong input shape for bleed_profile: {bleed_profile.shape}, should be {(len(corr_channels),len(corr_channels),single_im_size[-2], single_im_size[-1])}")
# load chromatic or chromatic_constants depends on whether do warpping
if chromatic_corr and len(_overlap_channels) > 0:
if chromatic_profile is None:
if warp_image:
chromatic_profile = load_correction_profile('chromatic',
corr_channels=corr_channels,
correction_folder=correction_folder, all_channels=all_channels,
ref_channel=chromatic_ref_channel,
im_size=single_im_size,
verbose=verbose)
else:
chromatic_profile = load_correction_profile('chromatic_constants',
corr_channels=corr_channels,
correction_folder=correction_folder, all_channels=all_channels,
ref_channel=chromatic_ref_channel,
im_size=single_im_size,
verbose=verbose)
else:
if not isinstance(chromatic_profile, dict):
raise TypeError(f"Wrong input type of chromatic_profile, should be dict!")
for _ch in _load_channels:
if _ch in corr_channels and _ch not in chromatic_profile:
raise KeyError(f"channel:{_ch} not given in chromatic_profile")
## check output data-type
# if normalization, output should be float
if normalization and output_dtype==np.uint16:
output_dtype = np.float32
# otherwise keep original dtype
else:
pass
## Load image
if verbose:
print(f"-- loading image from file:{dax_filename}", end=' ')
_load_time = time.time()
if 'DaxReader' not in locals():
from ..visual_tools import DaxReader
if 'load_file_lock' in locals() and load_file_lock is not None:
load_file_lock.acquire()
_reader = DaxReader(dax_filename, verbose=verbose)
_raw_im = _reader.loadAll()
_reader.close()
if 'load_file_lock' in locals() and load_file_lock is not None:
load_file_lock.release()
# get number of colors and frames
#from ..get_img_info import get_num_frame, split_channels
_full_im_shape, _num_color = get_num_frame(dax_filename,
frame_per_color=single_im_size[0],
buffer_frame=num_buffer_frames,
empty_frame=num_empty_frames)
_ims = split_im_by_channels(_raw_im, _load_channels, all_channels[:_num_color],
single_im_size=single_im_size,
num_buffer_frames=num_buffer_frames,
num_empty_frames=num_empty_frames, skip_frame0=False)
# clear memory
del(_raw_im)
if verbose:
print(f" in {time.time()-_load_time:.3f}s")
## hot-pixel removal
if hot_pixel_corr:
if verbose:
print(f"-- removing hot pixels for channels:{_load_channels}", end=' ')
_hot_time = time.time()
# loop through and correct
for _i, (_ch, _im) in enumerate(zip(_load_channels, _ims)):
_nim = corrections.Remove_Hot_Pixels(_im.astype(np.float32),
dtype=output_dtype, hot_th=hot_pixel_th)
_ims[_i] = _nim
if verbose:
print(f"in {time.time()-_hot_time:.3f}s")
## Z-shift correction
if z_shift_corr:
if verbose:
print(f"-- correct Z-shifts for channels:{_load_channels}", end=' ')
_z_time = time.time()
for _i, (_ch, _im) in enumerate(zip(_load_channels, _ims)):
_ims[_i] = corrections.Z_Shift_Correction(_im.astype(np.float32),
dtype=output_dtype, normalization=False)
if verbose:
print(f"in {time.time()-_z_time:.3f}s")
## bleedthrough correction
# do bleedthrough correction if there's any final required image within corr_channels
if len(_overlap_channels) > 0 and bleed_corr:
if verbose:
print(f"-- bleedthrough correction for channels: {corr_channels}", end=' ')
_bleed_time = time.time()
# extract all images within corr_channels
_bld_ims = [_ims[_load_channels.index(_ch)] for _ch in corr_channels]
# initialize list to store corrected images
_bld_corr_ims = []
for _i, _ch in enumerate(corr_channels):
# new image is the sum of all intensity contribution from images in corr_channels
_nim = np.sum([_im * bleed_profile[_i, _j]
for _j,_im in enumerate(_bld_ims)],axis=0)
_bld_corr_ims.append(_nim)
# update images
for _nim, _ch in zip(_bld_corr_ims, corr_channels):
# restore output_type
_nim[_nim > np.iinfo(output_dtype).max] = np.iinfo(output_dtype).max
_nim[_nim < np.iinfo(output_dtype).min] = np.iinfo(output_dtype).min
_ims[_load_channels.index(_ch)] = _nim.astype(output_dtype)
# clear
del(_bld_ims, _bld_corr_ims, bleed_profile)
if verbose:
print(f"in {time.time()-_bleed_time:.3f}s")
## illumination correction
if illumination_corr:
if verbose:
print(f"-- illumination correction for channels:", end=' ')
_illumination_time = time.time()
for _i, (_im,_ch) in enumerate(zip(_ims, _load_channels)):
if verbose:
print(f"{_ch}", end=', ')
_ims[_i] = (_im.astype(np.float32) / illumination_profile[_ch][np.newaxis,:]).astype(output_dtype)
# clear
del(illumination_profile)
if verbose:
print(f"in {time.time()-_illumination_time:.3f}s")
## calculate bead drift if required
if calculate_drift:
if verbose:
print(f"-- apply bead_drift calculate for channel: {_drift_channel}")
_drift_time = time.time()
if 'align_image' not in locals():
from ..correction_tools.alignment import align_image
# update drift_args
_updated_drift_args = {_k:_v for _k,_v in drift_args.items()}
_updated_drift_args.update({
'all_channels': all_channels,
'ref_all_channels': all_channels,
'drift_channel': drift_channel,
})
_drift_corr_args = {
'single_im_size': single_im_size,
'num_buffer_frames':num_buffer_frames,
'num_empty_frames':num_empty_frames,
'correction_folder':correction_folder,
}
_drift, _drift_flag = align_image(
_ims[_load_channels.index(_drift_channel)],
ref_filename,
use_autocorr=use_autocorr,
correction_args=_drift_corr_args,
verbose=verbose,
**_updated_drift_args,
)
if verbose:
print(f"--- finish drift: {np.around(_drift,2)} in {time.time()-_drift_time:.3f}s")
else:
_drift = drift.copy()
_drift_flag = 0
## chromatic abbrevation
_chromatic_channels = [_ch for _ch in corr_channels
if _ch in sel_channels and _ch != chromatic_ref_channel]
if warp_image:
if verbose:
if chromatic_corr:
print(f"-- warp image with chromatic correction for channels: {_chromatic_channels} and drift:{np.round(_drift, 2)}", end=' ')
else:
print(f"-- warp image with drift:{np.round(_drift, 2)}", end=' ')
_warp_time = time.time()
for _i, _ch in enumerate(sel_channels):
if (chromatic_corr and _ch in _chromatic_channels) or _drift.any():
if verbose:
print(f"{_ch}", end=', ')
# 0. get old image
_im = _ims[_load_channels.index(_ch)]
# 1. get coordiates to be mapped
_coords = np.meshgrid( np.arange(single_im_size[0]),
np.arange(single_im_size[1]),
np.arange(single_im_size[2]), )
# transpose is necessary
_coords = np.stack(_coords).transpose((0, 2, 1, 3))
# 2. calculate corrected coordinates if chormatic abbrev.
if chromatic_corr and _ch in _chromatic_channels:
_coords = _coords + chromatic_profile[_ch]#[:,np.newaxis,:,:] # only need this for old correction
# 3. apply drift if necessary
if _drift.any():
_coords = _coords - _drift[:, np.newaxis,np.newaxis,np.newaxis]
# 4. map coordinates
_corr_im = map_coordinates(_im,
_coords.reshape(_coords.shape[0], -1),
mode='nearest').astype(output_dtype)
_corr_im = _corr_im.reshape(np.shape(_im))
# append
_ims[_load_channels.index(_ch)] = _corr_im.copy()
# local clear
del(_coords, _im, _corr_im)
# clear
if verbose:
print(f"in {time.time()-_warp_time:.3f}s")
else:
if verbose:
if chromatic_corr:
print(f"-- generate translation function for chromatic correction for channels: {_chromatic_channels} and drift:{np.round(_drift, 2)}", end=' ')
else:
print(f"-- -- generate translation function with drift:{np.round(_drift, 2)}", end=' ')
_warp_time = time.time()
# generate mapping function for spot coordinates
from ..correction_tools.chromatic import generate_chromatic_function
# init corr functions
_warp_functions = []
for _i, _ch in enumerate(sel_channels):
# with drift in consideration
if (chromatic_corr and _ch in _chromatic_channels) or _drift.any():
# with chromatic abbrevation
if chromatic_corr and _ch in _chromatic_channels:
_func = generate_chromatic_function(chromatic_profile[_ch], _drift)
# without chromatic
else:
_func = generate_chromatic_function(None, _drift)
# no translating
else:
def _func(_spots):
return _spots
_warp_functions.append(_func)
# clear
if verbose:
print(f"in {time.time()-_warp_time:.3f}s")
## apply gaussian
if gaussian_highpass:
if verbose:
print(f"-- applying gaussian highpass filte, sigma={gauss_sigma}", end=' ')
_highpass_time = time.time()
from ..correction_tools.filter import gaussian_high_pass_filter
for _i, _im in enumerate(_ims):
_ims[_i] = gaussian_high_pass_filter(_im, gauss_sigma, gauss_truncate)
# clear
if verbose:
print(f"in {time.time()-_highpass_time:.3f}s")
## normalization
if normalization:
for _i, _im in enumerate(_ims):
_ims[_i] = _im.astype(np.float32) / np.median(_im)
## summarize and report selected_ims
_sel_ims = []
for _ch in sel_channels:
_sel_ims.append(_ims[_load_channels.index(_ch)].astype(output_dtype).copy())
# clear
del(_ims)
if verbose:
print(f"-- finish correction in {time.time()-_total_start:.3f}s")
# return
_return_args = [_sel_ims]
if not warp_image:
_return_args.append(_warp_functions)
if return_drift:
_return_args.extend([_drift, _drift_flag])
return tuple(_return_args)
## We pre-allocate the memory for the 15*15 image patches extracted
## around each corner point from both images
patch_size = 15
npts1 = x1.shape[0]
npts2 = x2.shape[0]
patches1 = np.zeros((patch_size, patch_size, npts1))
patches2 = np.zeros((patch_size, patch_size, npts2))
print(npts2)
input("aa")
## The following part extracts the patches using bilinear interpolation
k = (patch_size - 1) / 2.
xv, yv = np.meshgrid(np.arange(-k, k + 1), np.arange(-k, k + 1))
for i in range(npts1):
patch = map_coordinates(I1, (yv + y1[i], xv + x1[i]))
patches1[:, :, i] = patch
for i in range(npts2):
patch = map_coordinates(I2, (yv + y2[i], xv + x2[i]))
patches2[:, :, i] = patch
############################ SSD MEASURE ######################################
## We compute the sum of squared differences (SSD) of pixels' intensities
## for all pairs of patches extracted from the two images
distmat = np.zeros((npts1, npts2))
for i1 in range(npts1):
for i2 in range(npts2):
# Sum of Squared Differences
distmat[i1, i2] = np.sum((patches1[:, :, i1] - patches2[:, :, i2])**2)
## Next we compute pairs of patches that are mutually nearest neighbors
def extrapolate(precip,
velocity,
num_timesteps,
outval=np.nan,
xy_coords=None,
allow_nonfinite_values=False,
**kwargs):
"""Apply semi-Lagrangian extrapolation to a two-dimensional precipitation
field.
Parameters
----------
precip : array-like
Array of shape (m,n) containing the input precipitation field. All
values are required to be finite by default.
velocity : array-like
Array of shape (2,m,n) containing the x- and y-components of the m*n
advection field. All values are required to be finite by default.
num_timesteps : int
Number of time steps to extrapolate.
outval : float, optional
Optional argument for specifying the value for pixels advected from
outside the domain. If outval is set to 'min', the value is taken as
the minimum value of R.
Default : np.nan
xy_coords : ndarray, optional
Array with the coordinates of the grid dimension (2, m, n ).
* xy_coords[0] : x coordinates
* xy_coords[1] : y coordinates
By default, the *xy_coords* are computed for each extrapolation.
allow_nonfinite_values : bool, optional
If True, allow non-finite values in the precipitation and advection
fields. This option is useful if the input fields contain a radar mask
(i.e. pixels with no observations are set to nan).
Other Parameters
----------------
D_prev : array-like
Optional initial displacement vector field of shape (2,m,n) for the
extrapolation.
Default : None
n_iter : int
Number of inner iterations in the semi-Lagrangian scheme.
Default : 3
inverse : bool
If True, the extrapolation trajectory is computed backward along the
flow (default), forward otherwise.
Default : True
return_displacement : bool
If True, return the total advection velocity (displacement) between the
initial input field and the advected one integrated along
the trajectory. Default : False
Returns
-------
out : array or tuple
If return_displacement=False, return a time series extrapolated fields
of shape (num_timesteps,m,n). Otherwise, return a tuple containing the
extrapolated fields and the total displacement along the advection
trajectory.
References
----------
:cite:`GZ2002` Germann et al (2002)
"""
if len(precip.shape) != 2:
raise ValueError("precip must be a two-dimensional array")
if len(velocity.shape) != 3:
raise ValueError("velocity must be a three-dimensional array")
if not allow_nonfinite_values:
if np.any(~np.isfinite(precip)):
raise ValueError("precip contains non-finite values")
if np.any(~np.isfinite(velocity)):
raise ValueError("velocity contains non-finite values")
# defaults
verbose = kwargs.get("verbose", False)
D_prev = kwargs.get("D_prev", None)
n_iter = kwargs.get("n_iter", 3)
inverse = kwargs.get("inverse", True)
return_displacement = kwargs.get("return_displacement", False)
if verbose:
print("Computing the advection with the semi-lagrangian scheme.")
t0 = time.time()
if outval == "min":
outval = np.nanmin(precip)
coeff = 1.0 if not inverse else -1.0
if xy_coords is None:
x_values, y_values = np.meshgrid(np.arange(precip.shape[1]),
np.arange(precip.shape[0]))
xy_coords = np.stack([x_values, y_values])
R_e = []
if D_prev is None:
D = np.zeros((2, velocity.shape[1], velocity.shape[2]))
else:
D = D_prev.copy()
for t in range(num_timesteps):
V_inc = np.zeros(D.shape)
for k in range(n_iter):
if t > 0 or k > 0 or D_prev is not None:
XYW = xy_coords + D - V_inc / 2.0
XYW = [XYW[1, :, :], XYW[0, :, :]]
VWX = ip.map_coordinates(velocity[0, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
VWY = ip.map_coordinates(velocity[1, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
else:
VWX = velocity[0, :, :]
VWY = velocity[1, :, :]
V_inc[0, :, :] = VWX / n_iter
V_inc[1, :, :] = VWY / n_iter
D += coeff * V_inc
XYW = xy_coords + D
XYW = [XYW[1, :, :], XYW[0, :, :]]
IW = ip.map_coordinates(precip,
XYW,
mode="constant",
cval=outval,
order=0,
prefilter=False)
R_e.append(np.reshape(IW, precip.shape))
if verbose:
print("--- %s seconds ---" % (time.time() - t0))
if not return_displacement:
return np.stack(R_e)
else:
return np.stack(R_e), D
def extrapolate(precip,
velocity,
timesteps,
outval=np.nan,
xy_coords=None,
allow_nonfinite_values=False,
vel_timestep=None,
**kwargs):
"""Apply semi-Lagrangian backward extrapolation to a two-dimensional
precipitation field.
Parameters
----------
precip : array-like
Array of shape (m,n) containing the input precipitation field. All
values are required to be finite by default.
velocity : array-like
Array of shape (2,m,n) containing the x- and y-components of the m*n
advection field. All values are required to be finite by default.
timesteps : int or list
If timesteps is integer, it specifies the number of time steps to
extrapolate. If a list is given, each element is the desired
extrapolation time step from the current time. In this case, the
vel_timestep argument must be specified.
outval : float, optional
Optional argument for specifying the value for pixels advected from
outside the domain. If outval is set to 'min', the value is taken as
the minimum value of R.
Default : np.nan
xy_coords : ndarray, optional
Array with the coordinates of the grid dimension (2, m, n ).
* xy_coords[0] : x coordinates
* xy_coords[1] : y coordinates
By default, the *xy_coords* are computed for each extrapolation.
allow_nonfinite_values : bool, optional
If True, allow non-finite values in the precipitation and advection
fields. This option is useful if the input fields contain a radar mask
(i.e. pixels with no observations are set to nan).
Other Parameters
----------------
D_prev : array-like
Optional initial displacement vector field of shape (2,m,n) for the
extrapolation.
Default : None
n_iter : int
Number of inner iterations in the semi-Lagrangian scheme. If n_iter > 0,
the integration is done using the midpoint rule. Otherwise, the advection
vectors are taken from the starting point of each interval.
Default : 1
return_displacement : bool
If True, return the total advection velocity (displacement) between the
initial input field and the advected one integrated along
the trajectory. Default : False
vel_timestep : float
The time step of the velocity field. It is assumed to have the same
unit as the timesteps argument.
Returns
-------
out : array or tuple
If return_displacement=False, return a time series extrapolated fields
of shape (num_timesteps,m,n). Otherwise, return a tuple containing the
extrapolated fields and the total displacement along the advection
trajectory.
References
----------
:cite:`GZ2002` Germann et al (2002)
"""
if len(precip.shape) != 2:
raise ValueError("precip must be a two-dimensional array")
if len(velocity.shape) != 3:
raise ValueError("velocity must be a three-dimensional array")
if not allow_nonfinite_values:
if np.any(~np.isfinite(precip)):
raise ValueError("precip contains non-finite values")
if np.any(~np.isfinite(velocity)):
raise ValueError("velocity contains non-finite values")
# defaults
verbose = kwargs.get("verbose", False)
D_prev = kwargs.get("D_prev", None)
n_iter = kwargs.get("n_iter", 1)
return_displacement = kwargs.get("return_displacement", False)
if isinstance(timesteps, int):
timesteps = np.arange(1, timesteps + 1)
vel_timestep = 1.0
elif np.any(np.diff(timesteps) <= 0.0):
raise ValueError(
"the given timestep sequence is not monotonously increasing")
timestep_diff = np.hstack([[timesteps[0]], np.diff(timesteps)])
if verbose:
print("Computing the advection with the semi-lagrangian scheme.")
t0 = time.time()
if outval == "min":
outval = np.nanmin(precip)
if xy_coords is None:
x_values, y_values = np.meshgrid(np.arange(precip.shape[1]),
np.arange(precip.shape[0]))
xy_coords = np.stack([x_values, y_values])
def interpolate_motion(D, V_inc, td):
XYW = xy_coords + D
XYW = [XYW[1, :, :], XYW[0, :, :]]
VWX = ip.map_coordinates(velocity[0, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
VWY = ip.map_coordinates(velocity[1, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
V_inc[0, :, :] = VWX
V_inc[1, :, :] = VWY
if n_iter > 1:
V_inc /= n_iter
V_inc *= td / vel_timestep
R_e = []
if D_prev is None:
D = np.zeros((2, velocity.shape[1], velocity.shape[2]))
V_inc = velocity.copy() * timestep_diff[0] / vel_timestep
else:
D = D_prev.copy()
V_inc = np.empty(velocity.shape)
interpolate_motion(D, V_inc, timestep_diff[0])
for ti, td in enumerate(timestep_diff):
if n_iter > 0:
for k in range(n_iter):
interpolate_motion(D - V_inc / 2.0, V_inc, td)
D -= V_inc
interpolate_motion(D, V_inc, td)
else:
if ti > 0 or D_prev is not None:
interpolate_motion(D, V_inc, td)
D -= V_inc
XYW = xy_coords + D
XYW = [XYW[1, :, :], XYW[0, :, :]]
IW = ip.map_coordinates(precip,
XYW,
mode="constant",
cval=outval,
order=0,
prefilter=False)
R_e.append(np.reshape(IW, precip.shape))
if verbose:
print("--- %s seconds ---" % (time.time() - t0))
if not return_displacement:
return np.stack(R_e)
else:
return np.stack(R_e), D
def project_panoramas(opt, projection_list, start_point, end_point, core):
f_handler = open(os.path.join(opt.log_folder, str(core) + '.log'), 'w')
std_f = sys.stdout
sys.stdout = f_handler
sys.stdout.write(
'start is Projection number {}, end is Projection number {}\n'.format(
start_point,
min(end_point, len(projection_list)) - 1))
sys.stdout.flush()
[tmp_xy1, m_tmp, n_tmp, _] = calculate_no_adaptive_coor(h_fov=160,
v_fov1=-45,
v_fov2=80,
mpp=0.0125 * 2)
with open(opt.panorama_rectification) as f:
rectification_results = json.load(f)
for projection_name in projection_list[start_point:end_point]:
tmp_xy = tmp_xy1.copy()
if projection_name in rectification_results:
panorama_img_name = os.path.join(
opt.pano_folder,
rectification_results[projection_name]['panoID'] + '.jpg')
projection_img_path = os.path.join(Projection_folder,
projection_name)
if os.path.exists(panorama_img_name):
if not os.path.exists(projection_img_path):
super_R = R_pitch(
rectification_results[projection_name]['pitch']).dot(
R_roll(
rectification_results[projection_name]
['roll']).dot(
R_heading(
rectification_results[projection_name]
['heading'])))
tmp_coordinates = super_R.dot(tmp_xy).T
tmp_coordinates = calculate_new_pano(
tmp_coordinates, Image.open(panorama_img_name))
tmp_coordinates = tmp_coordinates.reshape(2, m_tmp, n_tmp)
img = skimage.io.imread(panorama_img_name)
tmp_sub = np.dstack([
map_coordinates(img[:, :, 0], tmp_coordinates,
order=0),
map_coordinates(img[:, :, 1], tmp_coordinates,
order=0),
map_coordinates(img[:, :, 2], tmp_coordinates, order=0)
])
skimage.io.imsave(projection_img_path, tmp_sub)
print(projection_name + ' has been saved')
else:
print(projection_name + ' has already been saved before')
else:
print(projection_name +
' does not have corresponding panorama image')
else:
print(projection_name +
' rectification parameters are not saved before')
sys.stdout.flush()
sys.stdout.close()
sys.stdout = std_f
def _elastic_transform(self, image_in, label_in, random_state=None):
"""Elastic deformation of image_ins as described in [Simard2003]_.
.. [Simard2003] Simard, Steinkraus and Platt, "Best Practices for
Convolutional Neural Networks applied to Visual Document Analysis", in
Proc. of the International Conference on Document Analysis and
Recognition, 2003.
"""
alpha = np.random.uniform(0, self.alpha_range)
if random_state is None:
random_state = np.random.RandomState(None)
shape = image_in.shape[1:]
# shape = image_in.shape
dx = gaussian_filter((random_state.rand(*shape) * 2 - 1),
self.sigma,
mode='constant',
cval=0) * alpha
dy = gaussian_filter((random_state.rand(*shape) * 2 - 1),
self.sigma,
mode='constant',
cval=0) * alpha
x, y = np.meshgrid(np.arange(shape[0]),
np.arange(shape[1]),
indexing='ij')
indices = np.reshape(x + dx, (-1, 1)), np.reshape(y + dy, (-1, 1))
if self.use_mp:
image_out = np.concatenate(self.parallel(
delayed(self._map)(input, indices, shape)
for input in image_in),
axis=0)
else:
# image_out = map_coordinates(image_in, indices, order=1).reshape(shape)
image_out = []
for input in image_in:
image_out.append(
np.expand_dims(map_coordinates(input, indices,
order=1).reshape(shape),
axis=0))
image_out = np.concatenate(image_out, axis=0)
# image_out = []
# for input in image_in:
# image_out.append(np.expand_dims(map_coordinates(input, indices, order=1).reshape(shape), axis=0))
# image_out = np.concatenate(image_out, axis=0)
if self.use_mp:
label_out = []
for sub_vol in label_in:
results = np.concatenate(self.parallel(
delayed(self._map)(input, indices, shape)
for input in sub_vol),
axis=0)
label_out.append(np.expand_dims(results, axis=0))
label_out = np.concatenate(label_out, axis=0)
else:
label_out = map_coordinates(label_in, indices,
order=1).reshape(shape)
# label_out = []
# for sub_vol in label_in:
# results = []
# for input in sub_vol:
# results.append(np.expand_dims(map_coordinates(input, indices, order=1).reshape(shape), axis=0))
# label_out.append(np.expand_dims(np.concatenate(results, axis=0), axis=0))
# label_out = np.concatenate(label_out, axis=0)
image_out = self._shave(image_out, [self.shave, self.shave])
label_out = self._shave(label_out, [self.shave, self.shave])
return image_out, label_out
def extrapolate(R, V, num_timesteps, outval=np.nan, **kwargs):
"""Apply semi-Lagrangian extrapolation to a two-dimensional precipitation
field.
Parameters
----------
R : array-like
Array of shape (m,n) containing the input precipitation field. All
values are required to be finite.
V : array-like
Array of shape (2,m,n) containing the x- and y-components of the m*n
advection field. All values are required to be finite.
num_timesteps : int
Number of time steps to extrapolate.
outval : float
Optional argument for specifying the value for pixels advected from
outside the domain. If outval is set to 'min', the value is taken as
the minimum value of R.
Default : np.nan
Optional kwargs:
---------------
D_prev : array-like
Optional initial displacement vector field of shape (2,m,n) for the
extrapolation.
Default : None
n_iter : int
Number of inner iterations in the semi-Lagrangian scheme.
Default : 3
inverse : bool
If True, the extrapolation trajectory is computed backward along the
flow (default), forward otherwise.
Default : True
return_displacement : bool
If True, return the total advection velocity (displacement) between the
initial input field and the advected one integrated along the trajectory.
Default : False
Returns
-------
out : array or tuple
If return_displacement=False, return a time series extrapolated fields of
shape (num_timesteps,m,n). Otherwise, return a tuple containing the
extrapolated fields and the total displacement along the advection trajectory.
"""
if len(R.shape) != 2:
raise ValueError("R must be a two-dimensional array")
if len(V.shape) != 3:
raise ValueError("V must be a three-dimensional array")
if np.any(~np.isfinite(R)):
raise ValueError("R contains non-finite values")
if np.any(~np.isfinite(V)):
raise ValueError("V contains non-finite values")
# defaults
verbose = kwargs.get("verbose", False)
D_prev = kwargs.get("D_prev", None)
n_iter = kwargs.get("n_iter", 3)
inverse = kwargs.get("inverse", True)
return_displacement = kwargs.get("return_displacement", False)
if verbose:
print("Computing the advection with the semi-lagrangian scheme.")
t0 = time.time()
if outval == "min":
outval = np.nanmin(R)
coeff = 1.0 if not inverse else -1.0
X, Y = np.meshgrid(np.arange(V.shape[2]), np.arange(V.shape[1]))
XY = np.stack([X, Y])
R_e = []
if D_prev is None:
D = np.zeros((2, V.shape[1], V.shape[2]))
else:
D = D_prev.copy()
for t in range(num_timesteps):
V_inc = np.zeros(D.shape)
for k in range(n_iter):
if t > 0 or k > 0 or D_prev is not None:
XYW = XY + D - V_inc / 2.0
XYW = [XYW[1, :, :], XYW[0, :, :]]
VWX = ip.map_coordinates(V[0, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
VWY = ip.map_coordinates(V[1, :, :],
XYW,
mode="nearest",
order=0,
prefilter=False)
else:
VWX = V[0, :, :]
VWY = V[1, :, :]
V_inc[0, :, :] = VWX / n_iter
V_inc[1, :, :] = VWY / n_iter
D += coeff * V_inc
XYW = XY + D
XYW = [XYW[1, :, :], XYW[0, :, :]]
IW = ip.map_coordinates(R,
XYW,
mode="constant",
cval=outval,
order=0,
prefilter=False)
R_e.append(np.reshape(IW, R.shape))
if verbose:
print("--- %s seconds ---" % (time.time() - t0))
if not return_displacement:
return np.stack(R_e)
else:
return np.stack(R_e), D
def interpolate_intensity(self, j, w, t, r, s):
"""Returns integrated intensity in [K km/s]. Width is not FWHM."""
idxs = self.indices(j, self.fwhm * w, t, r, s)
inten = map_coordinates(self.grid[j, 0], idxs, order=1, mode='nearest')
return inten * w * np.sqrt(2. * np.pi)
def measureVcut(img_masked, line, img_unmasked=None, img_bg=None,
max_width=101,
mask_is_dark=False,
v_isDark=None):
'''
img_masked ... image with v-cut mask
img_unmasked ... image without v-cut mask
img_bg - either average background level or background (or dark current) image
line = (x0,y0,x1,y1) - line from a place within the gap untill a place behind
the v-cut intersection
line points do not have to be precise
v_isDark - whether v-cut mask is dark - if None, value is determined from image intensities at line start/end
mask_is_dark - whether mask used to build V is absolutely dark (0)
'''
if img_unmasked is not None:
img_unmasked = img_unmasked.astype(float)
img_masked = img_masked.astype(float)
if img_bg is not None:
img_unmasked = img_unmasked - img_bg
img_masked = img_masked - img_bg
s0, s1 = img_masked.shape
poly = ((0, 0), (s1, 0), (s1, s0), (0, s0), (0, 0))
line = cutToFitIntoPolygon(line, poly)
# rectify image to given line: (this is not necassarily precise)
if img_unmasked is not None:
sub_img_unmasked = alignImageAlongLine(img_unmasked, line, max_width)
sub_img_masked = alignImageAlongLine(img_masked, line, max_width)
if not mask_is_dark:
# assume mtf being 0 at given end value
offs = sub_img_masked[-1].mean()
sub_img_masked -= offs
if img_unmasked is not None:
sub_img_unmasked -= offs
# create 0...1 scaled contrast image:
if img_unmasked is None:
contrast_img = sub_img_masked
else:
# make relative
contrast_img = (sub_img_unmasked - sub_img_masked) / (sub_img_unmasked + sub_img_masked)
if v_isDark is None:
# determine whether vmask is dark from eval sub_img_masked intensities at x=0
# if mid brighter than corner:
if contrast_img[contrast_img.shape[0] // 2].mean() > contrast_img[0].mean():
v_isDark = True
if not v_isDark:
contrast_img = 1 - contrast_img
s0, s1 = contrast_img.shape
x = np.arange(s1, dtype=int)
dsub = cv2.Sobel(contrast_img, cv2.CV_64F, 0, 1, ksize=5)
# FIND LINES: (precise)
line1 = np.argmin(dsub, axis=0)
line3 = np.argmax(dsub, axis=0)
line2 = 0.5 * (line1 + line3)
xx = x
# find out where V ends:
i = np.argmax(contrast_img[line2.round().astype(int), x] < 0.22)
if i:
s1 = i
xx = x[:i]
line1 = line1[:i]
line2 = line2[:i]
line3 = line3[:i]
# FIT LINEAR LINES:
m1, n1 = robustLinregress(xx, line1)[:2] # upper edge
m3, n3 = robustLinregress(xx, line3)[:2] # lower edge
l1 = fromFn(m1, n1)
l3 = fromFn(m3, n3)
# lines y-pos:
fitline1 = x * m1 + n1 # REMOVE NOT NEEDED
fitline3 = x * m3 + n3 # R..
fitline2 = 0.5 * (fitline1 + fitline3) # middle line
y = map_coordinates(contrast_img, [fitline2, x], order=2)
try:
# Intersection of detected v-cut lines:
i0, i1 = intersection(l1, l3)
except TypeError:
raise Exception('no intersection found')
# Angle of intersection:
angle = abs(angle2(l1, l3))
dx = np.asfarray(x) - i0
dy = fitline2 - i1
# radii from intersection:
r = np.hypot(dx, dy)
# print(dx, i0, i1)
# exclude area behind intersection:
behind_intersection = np.argmax(dx > 0)
if behind_intersection:
# print(behind_intersection)
# import pylab as plt
# plt.imshow(contrast_img)
# plt.show()
# plt.plot(r, y)
# plt.plot(r[behind_intersection:], y[behind_intersection:])
#
# plt.show()
r = r[behind_intersection:]
y = y[behind_intersection:]
if img_unmasked is None:
# only one masked image avail. normalize y 0...1:
mx = y.max()
mn = y.min()
mean = y.mean()
t0 = 0.7 * mx - 0.3 * mean
t1 = 0.7 * mn + 0.3 * mean
low = np.median(y[y < t1])
high = np.median(y[y > t0])
y -= low
y /= (high - low)
return (r, y, angle), (fitline1, fitline2, fitline3), (contrast_img, dsub)
def _elastic_deformation(self,
image,
output,
alpha,
sigma,
random_state=None):
import cv2
"""Elastic deformation of images as described in [Simard2003]_.
.. [Simard2003] Simard, Steinkraus and Platt, "Best Practices for
Convolutional Neural Networks applied to Visual Document Analysis", in
Proc. of the International Conference on Document Analysis and
Recognition, 2003.
"""
start = time.time()
original_shape = image.shape
original_output_shape = output.shape
image = image[:, :, 0].astype(np.float32)
#assert len(image.shape) == 2
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape
sigma = np.random.uniform(
0.08,
0.1) * shape[1] #np.random.uniform(shape[0] * 0.5, shape[1] * 0.5)
alpha = np.random.uniform(0.8, 1.0) * shape[1]
#print('Parameters: ', alpha, sigma)
blur_size = int(4 * sigma) | 1
dx = cv2.GaussianBlur((random_state.rand(*shape) * 2 - 1),
ksize=(blur_size, blur_size),
sigmaX=sigma) * alpha
dy = cv2.GaussianBlur((random_state.rand(*shape) * 2 - 1),
ksize=(blur_size, blur_size),
sigmaX=sigma) * alpha
#dx = gaussian_filter(, sigma, mode="constant", cval=0) * alpha
#dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma, mode="constant", cval=0) * alpha
dz = np.zeros_like(dx)
#x, y, z = np.meshgrid(np.arange(shape[1]), np.arange(shape[0]), np.arange(shape[2]))
#indices = np.reshape(y + dy, (-1, 1)), np.reshape(x + dx, (-1, 1)), np.reshape(z, (-1, 1))
x, y = np.meshgrid(np.arange(shape[0]),
np.arange(shape[1]),
indexing='ij')
indices = np.reshape(x + dx, (-1, 1)), np.reshape(y + dy, (-1, 1))
# Transform output
output[:, :, 0] = np.ones(output.shape[:2]) # Clear background
for label in range(1, output.shape[2]):
#segmentation = cv2.remap(output[:, :, label], dx, dy, interpolation=cv2.INTER_LINEAR).reshape(output.shape[:2])
segmentation = map_coordinates(output[:, :, label],
indices,
order=0).reshape(output.shape[:2])
output[:, :, label] = segmentation
# Remove segmentation from other labels
for label in range(1, output.shape[2]):
for label2 in range(output.shape[2]):
if label2 == label:
continue
output[output[:, :, label] == 1, label2] = 0
#input = cv2.remap(image, dx, dy, interpolation=cv2.INTER_LINEAR).reshape(original_shape)
input = map_coordinates(image, indices,
order=1).reshape(original_shape)
end = time.time()
#print('Elastic deformation time', (end - start))
return input, output
def rz2brzt(self, r_in, z_in, t_in=None):
"""calculates Br, Bz, Bt profiles
Input
----------
r_in : ndarray
R coordinates
1D, size(nr_in) or 2D, size (nt, nr_in)
z_in : ndarray
Z coordinates
1D, size(nz_in) or 2D, size (nt, nz_in)
t_in : float or 1darray
time
Output
-------
interpBr : ndarray
profile of Br on the grid
interpBz : ndarray
profile of Bz on the grid
interpBt : ndarray
profile of Bt on the grid
"""
if not self.eq_open:
return
if t_in is None:
t_in = self.t_eq
tarr = np.atleast_1d(t_in)
r_in = np.atleast_2d(r_in)
z_in = np.atleast_2d(z_in)
self._read_scalars()
self._read_profiles()
self._read_pfm()
# Poloidal current
nt = np.size(tarr)
if np.size(r_in, 0) != nt:
r_in = np.tile(r_in, (nt, 1))
if np.size(z_in, 0) != nt:
z_in = np.tile(z_in, (nt, 1))
nr_in = np.size(r_in, 1)
nz_in = np.size(z_in, 1)
interpBr = np.zeros((nt, nr_in, nz_in), dtype='single')
interpBz = np.zeros((nt, nr_in, nz_in), dtype='single')
interpBt = np.zeros((nt, nr_in, nz_in), dtype='single')
from scipy.constants import mu_0
nr, nz = len(self.Rmesh), len(self.Zmesh)
dr = (self.Rmesh[-1] - self.Rmesh[0]) / (nr - 1)
dz = (self.Zmesh[-1] - self.Zmesh[0]) / (nz - 1)
scaling = np.array([dr, dz])
offset = np.array([self.Rmesh[0], self.Zmesh[0]])
unique_idx, idx = self._get_nearest_index(tarr)
for i in unique_idx:
Phi = self.pfm[i]
Br = -np.diff(Phi, axis=1) / (self.Rmesh[:, None])
Bz = np.diff(
Phi, axis=0) / (.5 *
(self.Rmesh[1:] + self.Rmesh[:-1])[:, None])
Bt = np.interp(Phi, self.pf[:, i],
self.fpol[:, i]) * mu_0 / self.Rmesh[:, None]
jt = idx == i
r = np.tile(r_in[jt], (nz_in, 1, 1)).transpose(1, 2, 0)
z = np.tile(z_in[jt], (nr_in, 1, 1)).transpose(1, 0, 2)
coords = np.array((r, z))
index_t = ((coords.T - offset) / scaling).T
index_r = ((coords.T - offset) / scaling - np.array((0, .5))).T
index_z = ((coords.T - offset) / scaling - np.array((.5, 0))).T
interpBr[jt] = map_coordinates(Br,
index_r,
mode='nearest',
order=2,
prefilter=True)
interpBz[jt] = map_coordinates(Bz,
index_z,
mode='nearest',
order=2,
prefilter=True)
interpBt[jt] = map_coordinates(Bt,
index_t,
mode='nearest',
order=2,
prefilter=True)
return interpBr / (2 * np.pi * dz), interpBz / (
2 * np.pi * dr), interpBt / (2. * np.pi)
def refine_ellipsoid(image3d,
params,
spacing=1,
rad_range=None,
maxfit_size=2,
spline_order=3,
threshold=0.1):
""" Refines coordinates of a 3D ellipsoid, starting from given parameters.
Interpolates the image along lines perpendicular to the ellipsoid.
The maximum along each line is found using linear regression of the
descrete derivative.
Parameters
----------
image3d : 3d numpy array of numbers
Image indices are interpreted as (z, y, x)
params : tuple
zr, yr, xr, zc, yc, xc
spacing: number
spacing along radial direction
rad_range: tuple of floats
length of the line (distance inwards, distance outwards)
maxfit_size: integer
pixels around maximum pixel that will be used in linear regression
spline_order: integer
interpolation order for edge crossections
threshold: float
a threshold is calculated based on the global maximum
fitregions are rejected if their average value is lower than this
Returns
-------
- zr, yr, xr, zc, yc, xc, skew_y, skew_x
- contour coordinates at z = 0
"""
if not np.all([x > 0 for x in params]):
raise ValueError(
"All zc, yc, xc, zr, yr, xr params should be positive")
assert image3d.ndim == 3
zr, yr, xr, zc, yc, xc = params
if rad_range is None:
rad_range = (-min(zr, yr, xr) / 2, min(zr, yr, xr) / 2)
steps = np.arange(rad_range[0], rad_range[1] + 1, 1)
pos, normal = ellipsoid_grid((zr, yr, xr), (zc, yc, xc), spacing=spacing)
coords = normal[:, :, np.newaxis] * steps[np.newaxis, np.newaxis, :] + \
pos[:, :, np.newaxis]
# interpolate the image on calculated coordinates
intensity = map_coordinates(image3d, coords, order=spline_order)
# identify the regions around the max value
r_dev = max_linregress(intensity, maxfit_size, threshold)
# calculate new coords
coord_new = pos + (r_dev + rad_range[0]) * normal
coord_new = coord_new[:, np.isfinite(coord_new).all(0)]
# fit ellipsoid
radius, center, skew = fit_ellipsoid(coord_new,
mode='xy',
return_mode='skew')
return tuple(radius) + tuple(center) + tuple(skew), coord_new.T
def elastic_transform3Dv2(self,
image,
alpha,
sigma,
alpha_affine,
random_state=None):
"""Elastic deformation of images as described in [Simard2003]_ (with modifications).
.. [Simard2003] Simard, Steinkraus and Platt, "Best Practices for
Convolutional Neural Networks applied to Visual Document Analysis", in
Proc. of the International Conference on Document Analysis and
Recognition, 2003.
Based on https://gist.github.com/erniejunior/601cdf56d2b424757de5
From https://www.kaggle.com/bguberfain/elastic-transform-for-data-augmentation
"""
# affine and deformation must be slice by slice and fixed for slices
if random_state is None:
random_state = np.random.RandomState(None)
shape = image.shape # image is contatenated, the first channel [:,:,:,0] is the image, the second channel
# [:,:,:,1] is the mask. The two channel are under the same tranformation.
shape_size = shape[:-1] # z y x
# Random affine
shape_size_aff = shape[1:-1] # y x
center_square = np.float32(shape_size_aff) // 2
square_size = min(shape_size_aff) // 3
pts1 = np.float32([
center_square + square_size,
[center_square[0] + square_size, center_square[1] - square_size],
center_square - square_size
])
pts2 = pts1 + random_state.uniform(
-alpha_affine, alpha_affine, size=pts1.shape).astype(np.float32)
M = cv2.getAffineTransform(pts1, pts2)
new_img = np.zeros_like(image)
for i in range(shape[0]):
new_img[i, :, :,
0] = cv2.warpAffine(image[i, :, :, 0],
M,
shape_size_aff[::-1],
borderMode=cv2.BORDER_CONSTANT,
borderValue=0.)
for j in range(1, 10):
new_img[i, :, :,
j] = cv2.warpAffine(image[i, :, :, j],
M,
shape_size_aff[::-1],
flags=cv2.INTER_NEAREST,
borderMode=cv2.BORDER_TRANSPARENT,
borderValue=0)
dx = gaussian_filter(
(random_state.rand(*shape[1:-1]) * 2 - 1), sigma) * alpha
dy = gaussian_filter(
(random_state.rand(*shape[1:-1]) * 2 - 1), sigma) * alpha
x, y = np.meshgrid(np.arange(shape_size_aff[1]),
np.arange(shape_size_aff[0]))
indices = np.reshape(y + dy, (-1, 1)), np.reshape(x + dx, (-1, 1))
new_img2 = np.zeros_like(image)
for i in range(shape[0]):
new_img2[i, :, :,
0] = map_coordinates(new_img[i, :, :, 0],
indices,
order=1,
mode='constant').reshape(shape[1:-1])
for j in range(1, 10):
new_img2[i, :, :,
j] = map_coordinates(new_img[i, :, :, j],
indices,
order=0,
mode='constant').reshape(
shape[1:-1])
return np.array(new_img2), new_img
def actr(data,
yxguess,
asym_rad=8,
asym_size=5,
maxcounts=2,
method='gaus',
half_pix=False,
resize=False,
weights=False):
'''
Calculate the center of an input array by first switching the array into
asymmetry space and finding the minimum
This function takes in an input two dimentional array `data`, with a certain
distribution of values, such as the flux from a star. The center of this
distribution of values is based on the idea that the center will be the
point of minimum asymmetry. To convert to asymmetry space, the asymmetry of
a radial profile about a particular pixel is calculated according to
sum(var(r)*Npts(r)), the sum of the variance about a particular radius times
the number of points at that radius. The outter radius of consideration is
set by `asym_rad`. The number of points that are converted to asymmetry
space is governed by `asym_size` producing a shape `asym_size`*2+1 by
`asym_size`*2+1. This asymmetry space is recalculated and moved succesively
until the point of minimum asymmetry is in the center of the array or
`maxcounts` is reached. Traditional Gaussian or center of light centering is
then used in the asymmetry space to find the sub-pixel point of minimum
asymmetry.
Parameters
--------------
data: 2D array this is the data to be worked on, the radius of the array
should at minimum be asym_size times 2. radius being
defined as the cut size, ie data[yxguess[0]-rad:yxguess[0]
+rad+1,yxguess[1]-rad:yxguess[1]+rad+1] a recomendation
would be asym_size times 3 or 4, to account for the
searching of the algorithmu
yxguess: tuple This contains a tuple, or 1x2 array, that contains the
guess of the center, this is used as the starting location
of the transform
asym_rad: int The integer used to define the span of the radial profile
used in the asym calculation
asym_size: int This sets the radius of the asym space that is used to
determine the center. The larger the radius of the star
in flux space, the larger this variable should be
maxcounts: int An int to set the number of times the routine is allowed
to walk trying to put the point of minimum asymmetry in
the center of the array
method: string Must be "gaus" to used gaussian for sub pixel, or "col"
for center of light sub pixel
half_pix: Bool Default false, if set to true asymmetry will be calculated
for all the half pixel location between the integers
contained in the asym array. This may be more accurate,
but much slower. If set, it is recommended to use a larger
value for `asym_rad`.
resize: float Though by default False, set to a float which will be the
factor the asym the array is resized before centering.
Reccomend scale factors 5 or below. Resizeing introduces a
bit of error in the center by itself, but may be
combensated by the gains in percision. test with care.
This WILL slow the function down noticably.
weights: array This is an array the same size as the input data, each
point contains the weighting that each point should
recive. low number is less weight, should be type float,
if none is given the weights are set to one.
Returns
---------------
numpy array: A 1x2 array containing the found center of the data
numpy array: Array that contains the asymmery values calculated from
the input array
Raises
---------------
Possibly an runtime error, it the size of the radial profile is different
than a given view of the data. This is most likely due to a boundary issue,
aka the routine is trying to move out of the boundary of the input data.
This can be caused by incorrect sizes for asym_rad & asym_size, or becuase
the routine is trying to walk off the edge of data searching for the point
of minimum asymmetry. If this happens, try reducing asym_size, or maxcounts
'''
# initialize the boolean that determines if there are weights present or not
# This is used in the make asym array to square the variance, to provide
# larger contrast when using weights
w_truth = 1
# create the weights array if one is not passed in, and set w_truth to 0
if isinstance(type(weights), type(False)):
weights = np.ones(data.shape, dtype=float)
w_truth = 0
elif weights.dtype != np.dtype('float'):
# cast to a float if it is not already float
weights = np.array(weights, dtype=float)
if data.dtype != 'float64':
data = data.astype('float64')
x_guess = int(yxguess[1])
y_guess = int(yxguess[0])
# create the array indexes
ny, nx = np.indices((data.shape))
# make the view for the positions to calculate an asymmetry value, this may
# be unneeded look at removing this for optimization, save the shape for
# later shape restoration
suby = ny[y_guess - asym_size:y_guess + asym_size + 1,
x_guess - asym_size:x_guess + asym_size + 1]
shape_save = suby.shape
suby = suby.flatten()
subx = nx[y_guess - asym_size:y_guess + asym_size + 1,
x_guess - asym_size:x_guess + asym_size + 1].flatten()
# set up the range statement, to not recreate it every loop, same with len
len_y = len(suby)
itterator = np.arange(len_y)
ones_len = np.ones(len_y)
middle = (len_y - 1) / 2.
# set a counter for the number of times that the routine has moved in pixel
# space
counter = 0
# define the lambda function used to generate the views outside of the loop
view_maker = lambda frame, y_lamb, x_lamb, rng:\
frame[y_lamb-rng:y_lamb+rng+1, x_lamb-rng:x_lamb+rng+1]
# start a while loop, to be broken when the maximum number of steps is
# reached, or when the minimum asymmetry value is in the center of the array
while counter <= maxcounts:
# This will make heave use of python generators ie (x for x in
# range(10)), does not make the list all at once, but instead creates
# something that will create the each element when itterated over
# this saves memory and time, an generator needs to be recreated after
# each use however. The map function will be used alot as well. This is
# like a for loop but one which runs faster.
# create a generator for the views ahead of time that will be needed
views = (view_maker(data, suby[i], subx[i], asym_rad)
for i in itterator)
# create a generator for the view on the weights ahead of time
lb_views = (view_maker(weights, suby[i], subx[i], asym_rad)
for i in itterator)
# greate a generator duplicate for the state of w_truth
w_truth_dup = (w_truth * 1 for i in ones_len)
# now create the actual asym array
asym = np.array(map(make_asym, views, lb_views, w_truth_dup))
# need to find out if the minimum is in the center of the array if it
# is, break
if asym.argmin() == middle:
break
# if not, move the array index locations and itterate counter, the
# while loop then repeats, delete variable to make the garbage collector
# work less hard
else:
suby += (suby[asym.argmin()] - y_guess)
subx += (subx[asym.argmin()] - x_guess)
counter += 1
del views, asym
if counter <= maxcounts:
# now we must find the sub pixel persision and related options
# First reshape the array to the saved shape
asym = asym.reshape(shape_save)
# set a constant used in the center calculation, it is one if half_pix
# is unset, it becomes 2 if it is set
divisor = 1.0
# This gives the option to include the half pixel values
if half_pix:
# First create the new container array for the asymmetry, double the
# dimentions of the orrigional
new_asym = np.zeros(np.array(asym.shape) * 2, dtype=float)
# Next assign the old asym array to the be the top left corners in
# the new 4x4 pixels that represent one orrigional one
new_asym[::2, ::2] = asym.copy()
# Now create all of the edges, this represnts the upper right box in
# the 4x4, or the edges between pixels going to the right.
# create the generator for the views
views = (view_maker(data, suby[i], subx[i], asym_rad)
for i in itterator)
# create a generator for the view on the weights ahead of time
lb_views = (view_maker(weights, suby[i], subx[i], asym_rad)
for i in itterator)
# greate a generator duplicate for the state of w_truth
w_truth_dup = (w_truth * 1 for i in ones_len)
# generate the asymmetry values and save them
new_asym[::2, 1::2] = np.array(map(make_asym, views,
lb_views, w_truth_dup))\
.reshape(new_asym[::2, 1::2].shape)
# create all of the bottoms, representing the lower left box in 4x4,
# the edge between pixels going down
# create the generator for the views
views = (view_maker(data, suby[i], subx[i], asym_rad)
for i in itterator)
# create a generator for the view on the weights ahead of time
lb_views = (view_maker(weights, suby[i], subx[i], asym_rad)
for i in itterator)
# greate a generator duplicate for the state of w_truth
w_truth_dup = (w_truth for i in ones_len)
# generate the asymmetry values and save them
new_asym[1::2, ::2] = np.array(map(make_asym, views,
lb_views, w_truth_dup))\
.reshape(new_asym[1::2, ::2].shape)
# create all of the corners, like above
# create the generator for the views
views = (view_maker(data, suby[i], subx[i], asym_rad)
for i in itterator)
# create a generator for the view on the weights ahead of time
lb_views = (view_maker(weights, suby[i], subx[i], asym_rad)
for i in itterator)
# greate a generator duplicate for the state of w_truth
w_truth_dup = (w_truth for i in ones_len)
# generate the asymmetry values and save them
new_asym[1::2, 1::2] = np.array(map(make_asym, views, lb_views,
w_truth_dup))\
.reshape(new_asym[1::2, 1::2].shape)
# set the new_asym to the old one
asym = new_asym
# set the divisor varible, representing that every pixel now
# represents a half step
divisor = 2.0
# next invert the asym space so the minimum point is now the maximum
asym = -1.0 * asym
# insert any additional steps that would modify the asym array, such as
# interpolating, or adding more asym values.
if resize is not False:
fact = 1 / float(resize)
asym = map_coordinates(
asym, np.mgrid[0:asym.shape[1] - 1 + fact:fact,
0:asym.shape[1] - 1 + fact:fact])
divisor = resize
# now find the sub pixel position using the given method
if method == 'col':
return ((np.array(col(asym)))/divisor - asym_size) + \
np.array((suby[middle], subx[middle]), dtype=float)
if method == 'gaus':
return [
((np.array(fitgaussian(asym)[[1, 2]])) / divisor - asym_size) +
np.array((suby[middle], subx[middle]), dtype=float), asym
]
else:
# return this as an error code if the function waled more times than
# allowed, ie not finding a center
return np.array([-1.0, -1.0])
def warp_image(self, img, **kwargs):
assert img.shape == (self.n_pixels_r, self.n_pixels_c)
assert self.spatial_unit == 'cm'
return spndi.map_coordinates(img, self.experiment_geometry.warp_coordinates.T).reshape((self.n_pixels_r, self.n_pixels_c))
image = cv2.warpAffine(image,
M,
shape_size[::-1],
borderMode=cv2.BORDER_REFLECT_101)
dx = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma) * alpha
dy = gaussian_filter((random_state.rand(*shape) * 2 - 1), sigma) * alpha
dz = np.zeros_like(dx)
x, y, z = np.meshgrid(np.arange(shape[1]), np.arange(shape[0]),
np.arange(shape[2]))
indices = np.reshape(y + dy,
(-1, 1)), np.reshape(x + dx,
(-1, 1)), np.reshape(z, (-1, 1))
im_merge_t = map_coordinates(image, indices, order=1,
mode='reflect').reshape(shape)
# im_t = map_coordinates(image, indices, order=1, mode='reflect').reshape(shape)
# mask_t = map_coordinates(mask_, indices, order=1, mode='reflect').reshape(shape)
im_t = im_merge_t[..., 0:3]
# imshow(im_t)
# plt.show()
mask_t = im_merge_t[..., 3:6]
mask_t = cv2.cvtColor(mask_t, cv2.COLOR_RGB2GRAY)
# imshow(mask_t)
# plt.show()
new_id = 'elastic' + id_[7:]
os.mkdir(TRAIN_PATH + new_id)
os.mkdir(TRAIN_PATH + new_id + '/images/')
def _mask_transform(mask, coordinates):
mask_trans = map_coordinates(np.squeeze(mask),
coordinates,
order=0,
mode='reflect')
return np.expand_dims(mask_trans, axis=-1)
def elastic_distortion(image, alpha, sigma):
s = image.shape
dx = gaussian_filter(random_state.rand(*s) * 2 - 1, sigma, mode="constant", cval=0) * alpha
dy = gaussian_filter(random_state.rand(*s) * 2 - 1, sigma, mode="constant", cval=0) * alpha
x, y = np.meshgrid(np.arange(s[0]), np.arange(s[1]))
indices = np.reshape(y+dy, (-1, 1)), np.reshape(x+dx, (-1, 1))
return map_coordinates(image, indices, order=1).reshape(s)
