def lcn_mauch(X, kernel=None, rho=0):
"""Apply a version of local contrast normalization (LCN), inspired by
Mauch, Dixon (2009), "Approximate Note Transcription...".
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
rho : scalar
Scalar applied to the final output for heuristic range control.
Returns
-------
Z : np.ndarray
The processed output.
"""
if kernel is None:
dim0, dim1 = 15, 37
dim0_weights = np.hamming(dim0 * 2 + 1)[:dim0]
dim1_weights = np.hamming(dim1)
kernel = dim0_weights[:, np.newaxis] * dim1_weights[np.newaxis, :]
kernel /= kernel.sum()
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = hwr(X - Xh)
S = np.sqrt(
convolve2d(np.power(V, 2.0), kernel, mode='same', boundary='symm'))
S2 = np.zeros(S.shape) + S.mean()
S2[S > S.mean()] = S[S > S.mean()]
if S2.sum() == 0.0:
S2 += 1.0
return V / S2**rho
def lcn_v2(X, kernel, mean_scalar=1.0):
"""Apply an alternative version of local contrast normalization (LCN) to an
array.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = X - Xh
S = np.sqrt(convolve2d(np.power(V, 2.0),
kernel, mode='same', boundary='symm'))
thresh = np.exp(np.log(S + np.power(2.0, -5)).mean(axis=-1))
S = S*np.greater(S - thresh.reshape(-1, 1), 0)
S += 1.0*np.equal(S, 0.0)
return V / S
def lcn_mauch(X, kernel=None, rho=0):
"""Apply a version of local contrast normalization (LCN), inspired by
Mauch, Dixon (2009), "Approximate Note Transcription...".
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
rho : scalar
Scalar applied to the final output for heuristic range control.
Returns
-------
Z : np.ndarray
The processed output.
"""
if kernel is None:
dim0, dim1 = 15, 37
dim0_weights = np.hamming(dim0 * 2 + 1)[:dim0]
dim1_weights = np.hamming(dim1)
kernel = dim0_weights[:, np.newaxis] * dim1_weights[np.newaxis, :]
kernel /= kernel.sum()
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = hwr(X - Xh)
S = np.sqrt(
convolve2d(np.power(V, 2.0), kernel, mode='same', boundary='symm'))
S2 = np.zeros(S.shape) + S.mean()
S2[S > S.mean()] = S[S > S.mean()]
if S2.sum() == 0.0:
S2 += 1.0
return V / S2**rho
def lcn(X, kernel):
"""Apply Local Contrast Normalization (LCN) to an array.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = X - Xh
S = np.sqrt(
convolve2d(np.power(V, 2.0), kernel, mode='same', boundary='symm'))
S2 = np.zeros(S.shape) + S.mean()
S2[S > S.mean()] = S[S > S.mean()]
if S2.sum() == 0.0:
S2 += 1.0
return V / S2
def lcn(X, kernel):
"""Apply Local Contrast Normalization (LCN) to an array.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = X - Xh
S = np.sqrt(convolve2d(np.power(V, 2.0),
kernel, mode='same', boundary='symm'))
S2 = np.zeros(S.shape) + S.mean()
S2[S > S.mean()] = S[S > S.mean()]
if S2.sum() == 0.0:
S2 += 1.0
return V / S2
def lcn_v2(X, kernel, mean_scalar=1.0):
"""Apply an alternative version of local contrast normalization (LCN) to an
array.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
V = X - Xh
S = np.sqrt(
convolve2d(np.power(V, 2.0), kernel, mode='same', boundary='symm'))
thresh = np.exp(np.log(S + np.power(2.0, -5)).mean(axis=-1))
S = S * np.greater(S - thresh.reshape(-1, 1), 0)
S += 1.0 * np.equal(S, 0.0)
return V / S
def directionality(img):
newImg = img + 4
convV = np.zeros(newImg.shape)
convH = np.zeros(newImg.shape)
for i in range(newImg.shape[2]):
convV[:,:,i] = convolve2d(newImg[:,:,i],V,mode='same',fillvalue=1)
convH[:,:,i] = convolve2d(newImg[:,:,i],H,mode='same',fillvalue=1)
convV[convV == 0] = 0.1
convH[convH == 0] = 0.1
theta1 = pi/2. + np.arctan(convV/convH)
theta2 = pi/2 + np.arctan(convH/convV)
return [theta1.var(),theta2.var()]
def physical_SED_model(self, bases_wave_rest, obs_wave, bases_flux, Av_star, z_star, sigma_star, Rv_coeff=3.4):
# Calculate wavelength at object z
wave_z = bases_wave_rest * (1 + z_star)
# Kernel matrix
box = int(np.ceil(max(3 * sigma_star)))
kernel_len = 2 * box + 1
kernel_range = np.arange(0, 2 * box + 1)
kernel = np.empty((1, kernel_len))
# Filling gaussian values (the norm factor is the sum of the gaussian)
kernel[0, :] = np.exp(-0.5 * (np.square((kernel_range - box) / sigma_star)))
kernel /= sum(kernel[0, :])
# Convove bases with respect to kernel for dispersion velocity calculation
basesGridConvolved = convolve2d(bases_flux, kernel, mode='same', boundary='symm')
# Interpolate bases to wavelength ranges
basesGridInterp = (interp1d(wave_z, basesGridConvolved, axis=1, bounds_error=True)(obs_wave)).T
# Generate final flux model including reddening
Av_vector = Av_star * np.ones(basesGridInterp.shape[1])
obs_wave_resam_rest = obs_wave / (1 + z_star)
Xx_redd = CCM89_Bal07(Rv_coeff, obs_wave_resam_rest)
dust_attenuation = np.power(10, -0.4 * np.outer(Xx_redd, Av_vector))
bases_grid_redd = basesGridInterp * dust_attenuation
return bases_grid_redd
def plot_data(xa,ya,za,fig,nfig,colorflag=False,convolveflag=False,
clim=None):
cmap = pylab.cm.jet
cmap.set_bad('w', 1.0)
myfilter=N.array([[0.1,0.2,0.1],[0.2,0.8,0.2],[0.1,0.2,0.1]],'d') /2.0
if convolveflag:
zout=convolve2d(za,myfilter,mode='same') #to convolve, or not to convolve...
else:
zout=za
zima = ma.masked_where(N.isnan(zout),zout)
ax=fig.add_subplot(2,2,nfig)
pc=ax.pcolormesh(xa,ya,zima,shading='interp',cmap=cmap) # working good!
# pc=ax.imshow(zima,interpolation='bilinear',cmap=cmap)
if clim is None:
clim = zima.min(),zima.max()
pc.set_clim(*clim)
if colorflag:
#g=pylab.colorbar(pc,ticks=N.arange(0,675,100))
g=pylab.colorbar(pc,ticks=N.arange(clim[0],clim[1],100))
print g
#g.ticks=None
#gax.yaxis.set_major_locator(MultipleLocator(40))
#g.ticks(N.array([0,20,40,60,80]))
return ax,g
def lcn(x):
h, w = x.shape[:2]
k = np.ones((9, 9))
k /= 81
meaned = convolve2d(x, k, mode='same')
p = np.power(x, 2.0)
s = convolve2d(p, np.ones((9, 9)), mode='same')
s = np.sqrt(s)
m = x - meaned
lcned = (m / s)
lcn_min = np.min(lcned)
lcn_max = np.max(lcned)
normed = (lcned - lcn_min) * (1 / (lcn_max - lcn_min))
return normed
def plot_data(xa, ya, za, fig, nfig, colorflag=False):
cmap = pylab.cm.jet
cmap.set_bad('w', 1.0)
myfilter = N.array([[0.1, 0.2, 0.1], [0.2, 0.8, 0.2], [0.1, 0.2, 0.1]],
'd') / 2.0
if smooth:
zout = convolve2d(za, myfilter, mode='same')
else:
zout = za
zima = ma.masked_where(N.isnan(zout), zout)
ax = fig.add_subplot(1, 1, nfig)
pc = ax.pcolormesh(xa, ya, zima, shading='interp',
cmap=cmap) # working good!
# pc=ax.imshow(zima,interpolation='bilinear',cmap=cmap)
pc.set_clim(0.0, ctop)
if colorflag:
g = pylab.colorbar(pc, ticks=N.arange(0, ctop, cstep))
print g
#g.ticks=None
#gax.yaxis.set_major_locator(MultipleLocator(40))
#g.ticks(N.array([0,20,40,60,80]))
return ax, g
def feedforward(self, inputs):
"""
Calculates output of this layer from the given input.
:param inputs: 3D or 2D numpy array, if 3D, first dimension: idx of prev
feature map, second and third dimension: image output of this feature
map, if 2D just a single image.
:return 3D numpy array, 2D numpy array output for each feature map
"""
if len(np.shape(inputs)) == 2:
inputs = np.array([inputs])
self.inputs = np.copy(inputs)
in_size = np.shape(self.inputs[0])
out_shape = (in_size[0] - self.kernel_size + 1, in_size[1] - self.kernel_size + 1)
self.outputs = np.zeros((self.num_maps, out_shape[0], out_shape[1]))
# go through all feature maps of this layer
for fm_idx in range(self.num_maps):
bias = self.biases[fm_idx]
conv_out = np.zeros(out_shape)
# convolve inputs with weights and sum the results
for prev_fm_idx in range(self.num_prev_maps):
kernel = self.weights[prev_fm_idx, fm_idx]
prev_out = self.inputs[prev_fm_idx]
conv_out += signal.convolve2d(prev_out, kernel, mode='valid')
# add bias and apply activation function for final output
self.outputs[fm_idx] = self.activation_func(conv_out + bias)
if out_shape == (1, 1):
return np.array([self.outputs[:, 0, 0]])
return self.outputs
def plot_data(xa, ya, za, fig, nfig, colorflag=False, convolveflag=False):
cmap = pylab.cm.jet
cmap.set_bad("w", 1.0)
myfilter = N.array([[0.1, 0.2, 0.1], [0.2, 0.8, 0.2], [0.1, 0.2, 0.1]], "d") / 2.0
if convolveflag:
zout = convolve2d(za, myfilter, mode="same") # to convolve, or not to convolve...
else:
zout = za
zima = ma.masked_where(N.isnan(zout), zout)
ax = fig.add_subplot(1, 1, nfig)
pc = ax.pcolormesh(xa, ya, zima, shading="interp", cmap=cmap) # working good!
# pc=ax.imshow(zima,interpolation='bilinear',cmap=cmap)
pmin = zima.min()
pmax = zima.max()
# pmin=0
# pmax=700
# pc.set_clim(0.0,660.0)
pc.set_clim(pmin, pmax)
if colorflag:
# g=pylab.colorbar(pc,ticks=N.arange(0,675,100))
g = pylab.colorbar(pc, ticks=N.arange(pmin, pmax, 100))
print g
# g.ticks=None
# gax.yaxis.set_major_locator(MultipleLocator(40))
# g.ticks(N.array([0,20,40,60,80]))
return ax, g
def plot_data(xa,ya,za,fig,nfig,colorflag=False):
cmap = pylab.cm.jet
cmap.set_bad('w', 1.0)
myfilter=N.array([[0.1,0.2,0.1],[0.2,0.8,0.2],[0.1,0.2,0.1]],'d') /2.0
if smooth:
zout=convolve2d(za,myfilter,mode='same')
else:
zout=za
zima = ma.masked_where(N.isnan(zout),zout)
ax=fig.add_subplot(1,1,nfig)
pc=ax.pcolormesh(xa,ya,zima,shading='interp',cmap=cmap) # working good!
# pc=ax.imshow(zima,interpolation='bilinear',cmap=cmap)
pc.set_clim(0.0,ctop)
if colorflag:
g=pylab.colorbar(pc,ticks=N.arange(0,ctop,cstep))
print g
#g.ticks=None
#gax.yaxis.set_major_locator(MultipleLocator(40))
#g.ticks(N.array([0,20,40,60,80]))
return ax,g
def directionality(img):
newImg = img + 4
convV = np.zeros(newImg.shape)
convH = np.zeros(newImg.shape)
for i in range(newImg.shape[2]):
convV[:, :, i] = convolve2d(newImg[:, :, i],
V,
mode='same',
fillvalue=1)
convH[:, :, i] = convolve2d(newImg[:, :, i],
H,
mode='same',
fillvalue=1)
convV[convV == 0] = 0.1
convH[convH == 0] = 0.1
theta1 = pi / 2. + np.arctan(convV / convH)
theta2 = pi / 2 + np.arctan(convH / convV)
return [theta1.var(), theta2.var()]
def physical_SED_model(self,
rest_wave,
obs_wave,
bases_flux,
Av_star,
z_star,
sigma_star,
Rv_coeff=3.1):
#Calculate wavelength at object z
wave_z = rest_wave * (1 + z_star)
#Compute reddening
Av_vector = Av_star * ones(bases_flux.shape[0])
Xx_redd = CCM89_Bal07(Rv_coeff, rest_wave)
#Calculate stellar broadening kernel
r_sigma = sigma_star / (wave_z[1] - wave_z[0])
box = int(3 * r_sigma) if int(3 * r_sigma) < 3 else 3
kernel_len = 2 * box + 1
kernel = zeros((1, kernel_len))
kernel_range = arange(0, 2 * box + 1)
#Generating the kernel with sigma (the norm factor is the sum of the gaussian)
kernel[0, :] = exp(-0.5 * ((square(kernel_range - box) / r_sigma)))
norm = np_sum(kernel[0, :])
kernel = kernel / norm
#Convove bases with respect to kernel for dispersion velocity calculation
bases_grid_convolve = convolve2d(bases_flux,
kernel,
mode='same',
boundary='symm')
print 'wave_z'
print wave_z.shape
print 'bases_grid_convolve'
print bases_flux.shape
#Interpolate bases to wavelength range
bases_grid_interp = (interp1d(wave_z,
bases_grid_convolve,
axis=1,
bounds_error=True)(obs_wave)).T
#Generate final flux model including dust
dust_attenuation = power(10, -0.4 * outer(Xx_redd, Av_vector))
bases_grid_redd = bases_grid_interp * dust_attenuation
return bases_grid_redd
def solve_snakes(combined):
snake = '''
#
# ## ## ###
# # # # # # '''.strip('\n')
snake = grid_to_array(snake)
filter = np.rot90(snake, 2) # convolution filter is flipped
snakelen = snake.sum()
for i in range(NUM_TRANSFORMATIONS):
d = transformations(combined, i)
cv = convolve2d(d, filter, mode='valid')
snakes = (cv == snakelen).sum()
# assumption: no overlaps
if snakes:
return d.sum() - snakes*snakelen
def patVcut(std=None, psf=None, phi=None, angle_rad=None, size=501, SNR=30):
'''
psf ... blur kernel (2d numpy array)
phi ... rotation of v-cut (phi=0 -> v-cut opening at 3:00)
angle_rad ... v-cut opening angle
size ... output image size (x,y) [px]
SNR ... signal to noise ratio
'''
assert std is not None or psf is not None, "either std or pdf have to be provided"
if psf is None:
psf = std2PSF(
std
) # obtain guassian blur kernel (=point spread function [psf] from standard deviation
if angle_rad is None:
angle_rad = randAngle_rad()
if phi is None:
phi = np.random.rand() * 2 * np.pi # random rotation of v-cut angle
c = size / 2
rel_noise = 1.0 / SNR
s = (size, size)
s2 = size * size
img_masked = np.zeros(s)
rad = 0.5 * angle_rad
# points of vCut:
p0 = c + np.sin(rad + phi) * 2 * size
p1 = c + np.cos(rad + phi) * 2 * size
p2 = c + np.sin(-rad + phi) * 2 * size
p3 = c + np.cos(-rad + phi) * 2 * size
# v-cut positions (triangle):
pts = np.array(((c, c), (p0, p1), (p2, p3)), dtype=int)
# draw vCut:
cv2.fillConvexPoly(img_masked, pts, color=1, lineType=0)
# blur:
img_masked = convolve2d(img_masked, psf, mode='same', boundary='symm')
# add noise:
img_masked += np.random.rand(s2).reshape(s) * rel_noise
img_unmasked = np.ones(s) + np.random.rand(s2).reshape(s) * rel_noise
# line indicating gap position:
line = [c, c, c + np.sin(phi) * 0.5 * size, c + np.cos(phi) * 0.5 * size]
line = resize(line, 1.2)
return img_masked, img_unmasked, line
def highpass(X, kernel):
"""Produce a highpass kernel from its lowpass complement.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
return X - Xh
def local_l2norm(X, kernel):
"""Apply local l2-normalization over an input with a given kernel.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
local_mag = np.sqrt(
convolve2d(np.power(X, 2.0), kernel, mode='same', boundary='symm'))
local_mag = local_mag + 1.0 * (local_mag == 0.0)
return X / local_mag
def highpass(X, kernel):
"""Produce a highpass kernel from its lowpass complement.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
if X.ndim != 2:
raise ValueError("Input must be a 2D matrix.")
Xh = convolve2d(X, kernel, mode='same', boundary='symm')
return X - Xh
def local_l2norm(X, kernel):
"""Apply local l2-normalization over an input with a given kernel.
Parameters
----------
X : np.ndarray, ndim=2
Input representation.
kernel : np.ndarray
Convolution kernel (should be roughly low-pass).
Returns
-------
Z : np.ndarray
The processed output.
"""
local_mag = np.sqrt(convolve2d(np.power(X, 2.0),
kernel, mode='same', boundary='symm'))
local_mag = local_mag + 1.0*(local_mag == 0.0)
return X / local_mag
def get_eye_mask(ball):
# Get segments of white pixels
white_pixels = (np.asarray(ball.convert("L")) == 255)
white_segments, n_labels = ndimage.label(white_pixels)
# Get border colors of each white segment
eye_labels = []
for label in range(1, n_labels + 1):
segment = white_segments == label
kernel = np.asarray([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
edges = convolve2d(segment.astype(int),
kernel.astype(int),
mode='same').astype(bool)
diff = edges ^ segment
border_colors = np.unique(np.asarray(ball)[diff == 1], axis=0)
# Check if only color white segment borders is black
if len(border_colors) == 1 and (border_colors[0]
== (0, 0, 0, 255)).all():
# If so, then it is an eye
eye_labels.append(label)
return np.isin(white_segments, eye_labels)
def filterimg(arr, mask):
return convolve2d(arr, mask)
def avg(img):
return convolve2d(img,np.ones((9,9)),'same')
def generate_synthObs(self,
bases_wave,
bases_flux,
basesCoeff,
Av_star,
z_star,
sigma_star,
resample_range=None,
resample_int=1):
'''basesWave: Bases wavelength must be at rest'''
nbases = basesCoeff.shape[0]
bases_wave_resam = arange(int(resample_range[0]),
int(resample_range[-1]),
resample_int,
dtype=float)
npix_resample = len(bases_wave_resam)
#Resampling the range
bases_flux_resam = empty((nbases, npix_resample))
for i in range(nbases):
# print bases_wave[i][0], bases_wave[i][-1]
# print bases_wave_resam[0], bases_wave_resam[-1]
bases_flux_resam[i, :] = interp1d(
bases_wave[i], bases_flux[i],
bounds_error=True)(bases_wave_resam)
#Display physical parameters
synth_wave = bases_wave_resam * (1 + z_star)
Av_vector = Av_star * ones(nbases)
Xx_redd = CCM89_Bal07(3.4, bases_wave_resam)
r_sigma = sigma_star / (synth_wave[1] - synth_wave[0])
#Defining empty kernel
box = int(3 * r_sigma) if int(3 * r_sigma) < 3 else 3
kernel_len = 2 * box + 1
kernel = zeros((1, kernel_len))
kernel_range = arange(0, 2 * box + 1)
#Generating the kernel with sigma (the norm factor is the sum of the gaussian)
kernel[0, :] = exp(-0.5 * ((square(kernel_range - box) / r_sigma)))
norm = np_sum(kernel[0, :])
kernel = kernel / norm
#Convove bases with respect to kernel for dispersion velocity calculation
bases_grid_convolve = convolve2d(bases_flux_resam,
kernel,
mode='same',
boundary='symm')
#Interpolate bases to wavelength range
interBases_matrix = (interp1d(bases_wave_resam,
bases_grid_convolve,
axis=1,
bounds_error=True)(bases_wave_resam)).T
#Generate final flux model including dust
dust_attenuation = power(10, -0.4 * outer(Xx_redd, Av_vector))
bases_grid_model = interBases_matrix * dust_attenuation
#Generate combined flux
synth_flux = np_sum(basesCoeff.T * bases_grid_model, axis=1)
return synth_wave, synth_flux