def centerOfMass(img, yx, window=5):
"""
find peak by center of mass in a 2D image
img: a 2D image array
yx: (y,x) in the image
window: a window where CM calculation is performed on
return yx
"""
# prepare small image
s = N.array([window, window])
c = s / 2.
yx = N.round_(yx)
yx -= c
yi, xi = N.indices(s)
yi += yx[0]
xi += yx[1]
cc = img[yi, xi]
# calculate center of mass
yxi = N.indices(s)
yxi *= cc
yxi = yxi.T
vv = N.sum(yxi, axis=0)
vv = N.sum(vv, axis=0)
yxs = vv / float(N.sum(cc))
yxs += yx
return yxs
def cutOutCenter(arr, windowSize, sectWise=None, interpolate=True):
"""
windowSize: scalar (in pixel or as percent < 1.) or ((z,)y,x)
sectWise: conern only XY of windowSize
"""
shape = N.array(arr.shape)
center = shape / 2.
return pointsCutOutND(arr, [center], windowSize, sectWise, interpolate)[0]
def paddingFourier(arr, shape, value=0, interpolate=True):
"""
arr: assuming origin at 0, rfft product (half x size), up to 3D
shape: target shape
value: the value to fill in empty part
interpolate: shift by interpolation if necessary
return array with target shape
"""
# prepare buffer
dtype = arr.dtype.type
canvas = N.empty(shape, dtype)
canvas[:] = value
# calc and shift
shapeS = N.array(arr.shape)
shapeL = N.asarray(shape)
halfS = shapeS / 2.
subpx_shift = halfS % 1
if interpolate and N.sometrue(subpx_shift):
arr = U.nd.shift(arr, subpx_shift)
# create empty list for slices
nds = arr.ndim - 1
choices = ['slice(halfS[%i])', 'slice(-halfS[%i], None)']
nchoices = len(choices)
nds2 = nds**2
slcs = []
for ns in range(nds2):
slcs.append([])
for n in range(nchoices * nds):
slcs[ns].append(
[Ellipsis]) # Ellipsis help to make arbitray number of list
# fill the empty list by slice (here I don't know how to use 4D..)
for i in range(nds2):
for d in range(nds):
for x in range(nds):
for c, choice in enumerate(choices):
if d == 0 and x == 0:
idx = x * (nchoices) + c
else: # how can I use 4D??
idx = x * (nchoices) + (nchoices - 1) - c
exec('content=' + choice % d)
slcs[i][idx] += [content]
# cutout and paste
for slc in slcs:
for s in slc:
s.append(slice(shapeS[-1]))
#print s
canvas[s] = arr[s]
return canvas
def radialaverage(data, center=None, useMaxShape=False):
"""
data: ND array
center: coordinate of center of radii
useMinShape: the output uses the maximum shape available
return 1D array
"""
if center is None:
center = N.array(data.shape) // 2
if len(center) != data.ndim:
raise ValueError, 'dimension of center (%i) does not match the dimension of data (%i)' % (
len(center), data.ndim)
zyx = N.indices((data.shape))
r = N.zeros(data.shape, N.float32)
for i, t in enumerate(zyx):
r += (t - center[i])**2
r = N.sqrt(r)
#y, x = N.indices((data.shape))
#r = N.sqrt((x - center[0])**2 + (y - center[1])**2) # distance from the center
r = r.astype(N.int)
if data.dtype.type in (N.complex64, N.complex128):
rbin = N.bincount(r.ravel(), data.real.ravel())
ibin = N.bincount(r.ravel(), data.imag.ravel())
tbin = N.empty(rbin.shape, data.dtype.type)
tbin.real = rbin
tbin.imag = ibin
else:
tbin = N.bincount(r.ravel(), data.ravel())
nr = N.bincount(r.ravel())
radialprofile = tbin / nr.astype(N.float32)
if not useMaxShape:
minShape = min(list(N.array(data.shape) - center) + list(center))
radialprofile = radialprofile[:minShape]
return radialprofile
def _smoothBorder(arr, start, stop, smooth, value):
"""
start, stop: [z,y,x]
"""
# prepare coordinates
shape = N.array(arr.shape)
start = N.ceil(start).astype(N.int16)
stop = N.ceil(stop).astype(N.int16)
smooth_start = start - smooth
smooth_stop = stop + smooth
smooth_start = N.where(smooth_start < 0, 0, smooth_start)
smooth_stop = N.where(smooth_stop > shape, shape, smooth_stop)
#print smooth_start, smooth_stop
import copy
sliceTemplate = [slice(None, None, None)] * arr.ndim
shapeTemplate = list(shape)
for d in range(arr.ndim):
smooth_shape = shapeTemplate[:d] + shapeTemplate[d + 1:]
# make an array containing the edge value
edges = N.empty([2] + smooth_shape, N.float32)
# start side
slc = copy.copy(sliceTemplate)
slc[d] = slice(start[d], start[d] + 1, None)
edges[0] = arr[slc].reshape(smooth_shape)
# stop side
slc = copy.copy(sliceTemplate)
slc[d] = slice(stop[d] - 1, stop[d], None)
edges[1] = arr[slc].reshape(smooth_shape)
edges = (edges - value) / float(
smooth + 1) # this value can be array??
# both side
for s, side in enumerate([start, stop]):
if s == 0:
rs = range(smooth_start[d], start[d])
rs.sort(reverse=True)
elif s == 1:
rs = range(stop[d], smooth_stop[d])
# smoothing
for f, i in enumerate(rs):
slc = copy.copy(sliceTemplate)
slc[d] = slice(i, i + 1, None)
edgeArr = edges[s].reshape(arr[slc].shape)
#arr[slc] += edgeArr * (smooth - f)
arr[slc] = arr[slc] + edgeArr * (smooth - f) # casting rule
arr = N.ascontiguousarray(arr)
return arr
def shiftFullFFT(arr, delta=None):
"""
returns new array: arr shifted by delta (tuple)
it uses fft (not rfft), multiplying with "shift array", ifft
delta defaults to half of arr.shape
"""
shape = arr.shape
if delta is None:
delta = N.array(shape) / 2.
elif not hasattr(delta, '__len__'):
delta = (delta, ) * len(shape)
elif len(shape) != len(delta):
raise ValueError, "shape and delta not same dimension"
return F.ifft(F.fourierShiftArr(shape, delta) * F.fft(arr))
def img2polar2D(img,
center,
final_radius=None,
initial_radius=None,
phase_width=360):
"""
img: array
center: coordinate y, x
final_radius: ending radius
initial_radius: starting radius
phase_width: npixles / circle
"""
if img.ndim > 2 or len(center) > 2:
raise ValueError, 'this function only support 2D, you entered %i-dim array and %i-dim center coordinate' % (
img.ndim, len(center))
if initial_radius is None:
initial_radius = 0
if final_radius is None:
rad0 = N.ceil(N.array(img.shape) - center)
final_radius = min((min(rad0), min(N.ceil(center))))
if phase_width is None:
phase_width = N.sum(img.shape[-2:]) * 2
theta, R = np.meshgrid(np.linspace(0, 2 * np.pi, phase_width),
np.arange(initial_radius, final_radius))
Ycart, Xcart = polar2cart2D(R, theta, center)
Ycart = N.where(Ycart >= img.shape[0], img.shape[0] - 1, Ycart)
Xcart = N.where(Xcart >= img.shape[1], img.shape[1] - 1, Xcart)
Ycart = Ycart.astype(int)
Xcart = Xcart.astype(int)
polar_img = img[Ycart, Xcart]
polar_img = np.reshape(polar_img,
(final_radius - initial_radius, phase_width))
return polar_img
def getSphericalAbbe(arr3D, kmin=2, kmax=60, plot=False):
"""
compare frequency above and below the focus
return amplitude var(above)/var(below)
"""
afz = getFourierZprofile(arr3D)
# get z profile around the reasonable frequency
aa = N.abs(N.average(afz[:, kmin:kmax], axis=1))
# previously it was N.average(N.abs(afz[:,kmin:kmax]), axis=1), but that seems wrong...
# findMax
inds = N.indices(aa.shape, dtype=N.float64)
v, _0, _1, z = U.findMax(aa)
parm, check = imgFit.fitGaussianND(aa, [z], window=len(aa))
if check == 5:
raise RuntimeError, 'Peak not found check=%i' % check
gg = imgFit.yGaussianND(parm, inds, 3)
amg = aa - gg
z0 = parm[2]
mask = (parm[-1] * 3) / 2. # sigma * 3 / 2
ms0 = N.ceil(z0 - mask)
ms1 = N.ceil(z0 + mask)
amg[ms0:ms1] = 0
below = N.var(amg[:ms0])
above = N.var(amg[ms1:])
if plot:
Y.ploty(N.array((aa, gg, amg)))
print 'below: ', below
print 'above: ', above
print ms0, ms1, z0
return above / (above + below) #above / below
def paddingValue(img, shape, value=0, shift=None, smooth=0, interpolate=True):
"""
shape: in the same dimension as img
value: value in padded region, can be scaler or array with the shape
shift: scaler or in the same dimension as img and shape (default 0)
smooth: scaler value to smoothen border (here value must be scaler)
interpolate: shift array by subpixel interpolation to adjust center
return: padded array with shape
"""
# create buffer
dtype = img.dtype.type
canvas = N.empty(shape, dtype)
canvas[:] = value
# calculate position
shape = N.array(shape)
shapeS = img.shape
center = N.divide(shape, 2)
if shift is None:
shift = 0 #[0] * len(shapeS)
shapeL = shape #N.add(shapeS, center+shift)
start, stop = (shapeL - shapeS) / 2., (shapeL + shapeS) / 2.
slc = [slice(start[d], stop[d], None) for d in range(img.ndim)]
#print slc, shapeS, shapeL
# shift if necessary
if interpolate:
subpx_shift = start % 1 # should be 0.5 or 0
if N.sometrue(subpx_shift):
img = U.nd.shift(img, subpx_shift)
# padding
canvas[slc] = img
if smooth:
canvas = _smoothBorder(canvas, start, stop, smooth, value)
canvas = N.ascontiguousarray(canvas)
#print shapeS, shapeL, slc
return canvas
def mask_gaussianND(arr, zyx, v, sigma=2., ret=None, rot=0, clipZero=True):
'''
subtract elliptical gaussian at y,x with peakVal v
if ret, return arr, else, arr itself is edited
'''
import imgGeo
zyx = N.asarray(zyx)
ndim = arr.ndim
shape = N.array(arr.shape)
try:
if len(sigma) != ndim:
raise ValueError, 'len(sigma) must be the same as len(shape)'
else:
sigma = N.asarray(sigma)
except TypeError: #(TypeError, ValueError):
sigma = N.asarray([sigma] * ndim)
# prepare small window
slc = imgGeo.nearbyRegion(shape, N.floor(zyx), sigma * 10)
inds, LD = imgFit.rotateIndicesND(slc, dtype=N.float32, rot=rot)
param = (
0,
v,
) + tuple(zyx) + tuple(sigma)
sidx = 2 + ndim
g = imgFit.yGaussianND(N.asarray(param), inds, sidx).astype(arr.dtype.type)
roi = arr[slc]
if clipZero:
g = N.where(g > roi, roi, g)
if ret:
e = N.zeros_like(arr)
e[slc] = g # this may be faster than copy()
return arr - e
else:
arr[slc] -= g
def pointsCutOutND(arr,
posList,
windowSize=100,
sectWise=None,
interpolate=True):
"""
array: nd array
posList: ([(z,)y,x]...)
windowSize: scalar (in pixel or as percent < 1.) or ((z,)y,x)
if arr.ndim > 2, and len(windowSize) == 2, then
cut out section-wise (higher dimensions stay the same)
sectWise: conern only XY of windowSize (higher dimensions stay the same)
interpolate: shift array by subpixel interpolation to adjust center
return: list of array centered at each pos in posList
"""
shape = N.array(arr.shape)
center = shape / 2.
# prepare N-dimensional window size
try:
len(windowSize) # seq
if sectWise:
windowSize = windowSize[-2:]
if len(windowSize) != arr.ndim:
dim = len(windowSize)
windowSize = tuple(shape[:-dim]) + tuple(windowSize)
except TypeError: # scaler
if windowSize < 1 and windowSize > 0: # percentage
w = shape * windowSize
if sectWise:
w[:-2] = shape[:-2]
windowSize = w.astype(N.uint16)
else:
windowSize = N.where(shape >= windowSize, windowSize, shape)
if sectWise:
windowSize = arr.shape[:-2] + windowSize[-2:]
windowSize = N.asarray(windowSize)
# cutout individual position
arrList = []
for pos in posList:
# prepare N-dimensional coordinate
n = len(pos)
if n != len(windowSize):
temp = center.copy()
center[-n:] = pos
pos = center
# calculate idx
ori = pos - (windowSize / 2.) # float value
oidx = N.ceil(ori) # idx
subpxl = oidx - ori # subpixel mod
if interpolate and N.sometrue(subpxl): # comit to make shift
SHIFT = 1
else:
SHIFT = 0
# prepare slice
# when comitted to make shift, first cut out window+1,
# then make subpixle shift, and then cutout 1 edge
slc = [Ellipsis] # Ellipsis is unnecessary, just in case...
slc_edge = [slice(1, -1, None)] * arr.ndim
for d in range(arr.ndim):
start = oidx[d] - SHIFT
if start < 0:
start = 0
slc_edge[d] = slice(0, slc_edge[d].stop, None)
stop = oidx[d] + windowSize[d] + SHIFT
if stop > shape[d]:
stop = shape[d]
slc_edge[d] = slice(slc_edge[d].start, shape[d], None)
slc += [slice(int(start), int(stop), None)]
# cutout, shift and cutout
try:
canvas = arr[slc]
if SHIFT:
canvas = U.nd.shift(canvas, subpxl)
canvas = canvas[slc_edge]
check = 1
except IndexError:
print 'position ', pos, ' was skipped'
check = 0
raise
if check:
arrList += [N.ascontiguousarray(canvas)]
return arrList