def set_context_frame_statistics(im,ctx):
ctx["last_frame_stats"] = {}
#this is the upper bound on acceptable noise levels
excessive_noise_th = 0.1 if "excessive_noise_th" not in ctx else ctx["excessive_noise_th"]
noise = estimate_sigma(im, multichannel=False, average_sigmas=True)
ctx["last_frame_stats"]["noise"] = noise
ctx["last_frame_stats"]["percentiles_509599"] = [round(p,3) for p in np.percentile(im, [50,95, 99])]
perc = ctx["last_frame_stats"]["percentiles_509599"][-1]
#the pseudo entropy is a measure based on summed 2d projection
analysis.log_pseudo_entropy(im,ctx)
#degeneracy checks
if perc == 1.:
ctx.log("Too much saturation, 99th percentile is 1.0 - marking frame as degenerate!", mtype="WARN")
ctx["last_frame_stats"]["is_degenerate"] = True
if noise > excessive_noise_th:
ctx.log("noise level of {:.4f} is excessive - marking frame as degenerate!".format(noise), mtype="WARN")
ctx["last_frame_stats"]["is_degenerate"] = True
ctx.log_stats({"noise":ctx["last_frame_stats"]["noise"],
"degenerate":ctx.is_frame_degenerate,
"perc": perc,
"pseudo_ent": ctx["last_frame_stats"]["pseudo_ent"],
"2dhist99post": ctx["last_frame_stats"]["2dHisto_postnorm"][-1],
"2dhist95post": ctx["last_frame_stats"]["2dHisto_postnorm"][-2],
"2dhist99pre": ctx["last_frame_stats"]["2dHisto_prenorm"][-1],
"2dhist95pre": ctx["last_frame_stats"]["2dHisto_prenorm"][-2]})
def test_estimate_sigma_color():
rstate = np.random.RandomState(1234)
# astronaut image
img = astro.copy()
sigma = 0.1
# add noise to astronaut
img += sigma * rstate.standard_normal(img.shape)
sigma_est = restoration.estimate_sigma(img, multichannel=True,
average_sigmas=True)
assert_almost_equal(sigma, sigma_est, decimal=2)
sigma_list = restoration.estimate_sigma(img, multichannel=True,
average_sigmas=False)
assert_equal(len(sigma_list), img.shape[-1])
assert_almost_equal(sigma_list[0], sigma_est, decimal=2)
# default multichannel=False should raise a warning about last axis size
assert_warns(UserWarning, restoration.estimate_sigma, img)
def test_estimate_sigma_gray():
rstate = np.random.RandomState(1234)
# astronaut image
img = astro_gray.copy()
sigma = 0.1
# add noise to astronaut
img += sigma * rstate.standard_normal(img.shape)
sigma_est = restoration.estimate_sigma(img, multichannel=False)
assert_almost_equal(sigma, sigma_est, decimal=2)
def test_estimate_sigma_masked_image():
# Verify computation on an image with a large, noise-free border.
# (zero regions will be masked out by _sigma_est_dwt to avoid returning
# sigma = 0)
rstate = np.random.RandomState(1234)
# uniform image
img = np.zeros((128, 128))
center_roi = (slice(32, 96), slice(32, 96))
img[center_roi] = 0.8
sigma = 0.1
img[center_roi] = sigma * rstate.standard_normal(img[center_roi].shape)
sigma_est = restoration.estimate_sigma(img, multichannel=False)
assert_almost_equal(sigma, sigma_est, decimal=1)
from skimage.util import random_noise
from skimage.measure import compare_psnr
original = img_as_float(data.chelsea()[100:250, 50:300])
sigma = 0.12
noisy = random_noise(original, var=sigma**2)
fig, ax = plt.subplots(nrows=2, ncols=3, figsize=(8, 5),
sharex=True, sharey=True)
plt.gray()
# Estimate the average noise standard deviation across color channels.
sigma_est = estimate_sigma(noisy, multichannel=True, average_sigmas=True)
# Due to clipping in random_noise, the estimate will be a bit smaller than the
# specified sigma.
print("Estimated Gaussian noise standard deviation = {}".format(sigma_est))
im_bayes = denoise_wavelet(noisy, multichannel=True, convert2ycbcr=True,
method='BayesShrink', mode='soft')
im_visushrink = denoise_wavelet(noisy, multichannel=True, convert2ycbcr=True,
method='VisuShrink', mode='soft',
sigma=sigma_est)
# VisuShrink is designed to eliminate noise with high probability, but this
# results in a visually over-smooth appearance. Repeat, specifying a reduction
# in the threshold by factors of 2 and 4.
im_visushrink2 = denoise_wavelet(noisy, multichannel=True, convert2ycbcr=True,
method='VisuShrink', mode='soft',
import matplotlib.pyplot as plt
from skimage import data, img_as_float
from skimage.restoration import denoise_nl_means, estimate_sigma
from skimage.measure import compare_psnr
from skimage.util import random_noise
astro = img_as_float(data.astronaut())
astro = astro[30:180, 150:300]
sigma = 0.08
noisy = random_noise(astro, var=sigma**2)
# estimate the noise standard deviation from the noisy image
sigma_est = np.mean(estimate_sigma(noisy, multichannel=True))
print("estimated noise standard deviation = {}".format(sigma_est))
patch_kw = dict(patch_size=5, # 5x5 patches
patch_distance=6, # 13x13 search area
multichannel=True)
# slow algorithm
denoise = denoise_nl_means(noisy, h=1.15 * sigma_est, fast_mode=False,
**patch_kw)
# slow algorithm, sigma provided
denoise2 = denoise_nl_means(noisy, h=0.8 * sigma_est, sigma=sigma_est,
fast_mode=False, **patch_kw)
# fast algorithm
original = img_as_float(data.chelsea()[100:250, 50:300])
sigma = 0.12
noisy = random_noise(original, var=sigma**2)
fig, ax = plt.subplots(nrows=2,
ncols=3,
figsize=(8, 5),
sharex=True,
sharey=True)
plt.gray()
# Estimate the average noise standard deviation across color channels.
sigma_est = estimate_sigma(noisy, channel_axis=-1, average_sigmas=True)
# Due to clipping in random_noise, the estimate will be a bit smaller than the
# specified sigma.
print(f"Estimated Gaussian noise standard deviation = {sigma_est}")
im_bayes = denoise_wavelet(noisy,
channel_axis=-1,
convert2ycbcr=True,
method='BayesShrink',
mode='soft',
rescale_sigma=True)
im_visushrink = denoise_wavelet(noisy,
channel_axis=-1,
convert2ycbcr=True,
method='VisuShrink',
mode='soft',
def motor_recon_met2(TE_array, path_to_data, path_to_mask, path_to_save_data,
TR, reg_method, reg_matrix, denoise, FA_method, FA_smooth,
myelin_T2, num_cores):
# Load Data and Mask
img = nib.load(path_to_data)
data = img.get_data()
data = data.astype(np.float64, copy=False)
img_mask = nib.load(path_to_mask)
mask = img_mask.get_data()
mask = mask.astype(np.int64, copy=False)
print('--------- Data shape -----------------')
nx, ny, nz, nt = data.shape
print(data.shape)
print('--------------------------------------')
for c in xrange(nt):
data[:, :, :, c] = np.squeeze(data[:, :, :, c]) * mask
#end
# Only for testing: selects a few slices
#mask[:,:,40:-1] = 0
#mask[:,:,0:35] = 0
nEchoes = TE_array.shape[0]
tau = TE_array[1] - TE_array[0]
fM = np.zeros((nx, ny, nz))
fIE = fM.copy()
fnT = fM.copy()
fCSF = fM.copy()
T2m = fM.copy()
T2IE = fM.copy()
T2nT = fM.copy()
Ktotal = fM.copy()
FA = fM.copy()
FA_index = fM.copy()
reg_param = fM.copy()
NITERS = fM.copy()
# ==============================================================================
# Inital values for the dictionary
if reg_method == 'T2SPARC':
# Regularization matrix for method: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3568216/
#: Junyu Guo et al. 2014. Multi-slice Myelin Water Imaging for Practical Clinical Applications at 3.0 T.
Npc = 96
else:
Npc = 60
#end if
# -----------
T2m0 = 10.0
T2mf = myelin_T2
T2tf = 200.0
T2csf = 2000.0
T2s = np.logspace(math.log10(T2m0),
math.log10(T2csf),
num=Npc,
endpoint=True,
base=10.0)
ind_m = T2s <= T2mf # myelin
ind_t = (T2s > T2mf) & (T2s <= T2tf) # intra+extra
ind_csf = T2s >= T2tf # quasi free-water and csf
T1s = 1000.0 * np.ones_like(
T2s) # a constant T1=1000 is assumed for all compartments
# Create multi-dimensional dictionary with multiples flip_angles
#N_alphas = 91 # (steps = 1.0 degrees, from 90 to 180)
if FA_method == 'spline':
N_alphas = 91 * 3 # (steps = 0.333 degrees, from 90 to 180)
#N_alphas = 91*2 # (steps = 0.5 degrees, from 90 to 180)
#N_alphas = 91 # (steps = 1.0 degrees, from 90 to 180)
alpha_values = np.linspace(90.0, 180.0, N_alphas)
Dic_3D = create_Dic_3D(Npc, T2s, T1s, nEchoes, tau, alpha_values, TR)
#alpha_values_spline = np.round( np.linspace(90.0, 180.0, 8) )
alpha_values_spline = np.linspace(90.0, 180.0, 15)
Dic_3D_LR = create_Dic_3D(Npc, T2s, T1s, nEchoes, tau,
alpha_values_spline, TR)
#end
if FA_method == 'brute-force':
N_alphas = 91 # (steps = 1.0 degrees, from 90 to 180)
alpha_values = np.linspace(90.0, 180.0, N_alphas)
Dic_3D = create_Dic_3D(Npc, T2s, T1s, nEchoes, tau, alpha_values, TR)
#end
# Define regularization vectors for the L-curve method
num_l_laplac = 50
lambda_reg = np.zeros((num_l_laplac))
# lambda_reg[1:] = np.logspace(math.log10(1e-8), math.log10(100.0), num=num_l_laplac-1, endpoint=True, base=10.0)
lambda_reg[1:] = np.logspace(math.log10(1e-8),
math.log10(10.0),
num=num_l_laplac - 1,
endpoint=True,
base=10.0)
# --------------------------------------------------------------------------
if reg_matrix == 'I':
order = 0
Laplac = create_Laplacian_matrix(Npc, order)
elif reg_matrix == 'L1':
order = 1
Laplac = create_Laplacian_matrix(Npc, order)
elif reg_matrix == 'L2':
order = 2
Laplac = create_Laplacian_matrix(Npc, order)
elif reg_matrix == 'InvT2':
# Regularization matrix for method: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3568216/
#: Junyu Guo et al. 2014. Multi-slice Myelin Water Imaging for Practical Clinical Applications at 3.0 T.
T2s_mod = np.concatenate((np.array([T2s[0] - 1.0]),
T2s[:-1])) # add 0.0 and remove the last one
deltaT2 = T2s - T2s_mod
deltaT2[0] = deltaT2[1]
Laplac = np.diag(1. / deltaT2)
else:
print('Error: Wrong reg_matrix option!')
sys.exit()
# end if
# create 4D images
f_sol_4D = np.zeros((nx, ny, nz, T2s.shape[0]))
s_sol_4D = np.zeros((nx, ny, nz, nEchoes))
data[data < 0.0] = 0.0 # correct artifacts
number_of_cores = multiprocessing.cpu_count()
if num_cores == -1:
num_cores = number_of_cores
print('Using all CPUs: ', number_of_cores)
else:
print('Using ', num_cores, ' CPUs from ', number_of_cores)
#end if
#_______________________________________________________________________________
#_______________________________ ESTIMATION ____________________________________
#_______________________________________________________________________________
if denoise == 'TV':
print 'Step #1: Denoising using Total Variation:'
for voxelt in progressbar.progressbar(xrange(nt),
redirect_stdout=True):
print(voxelt + 1, ' volumes processed')
data_vol = np.squeeze(data[:, :, :, voxelt])
sigma_est = np.mean(estimate_sigma(data_vol, multichannel=False))
#data[:,:,:,voxelt] = denoise_tv_chambolle(data_vol, weight=1.0*sigma_est, eps=0.0002, n_iter_max=200, multichannel=False)
data[:, :, :,
voxelt] = denoise_tv_chambolle(data_vol,
weight=2.0 * sigma_est,
eps=0.0002,
n_iter_max=200,
multichannel=False)
#end for
outImg = nib.Nifti1Image(data, img.affine)
nib.save(outImg, path_to_save_data + 'Data_denoised.nii.gz')
elif denoise == 'NESMA':
data_den = np.zeros_like(data)
path_size = [6, 6, 6] # real-size = 2*path_size + 1
print 'Step #1: Denoising using the NESMA filter:'
for voxelx in progressbar.progressbar(xrange(nx),
redirect_stdout=True):
print(voxelx + 1, ' slices processed')
min_x = np.max([voxelx - path_size[0], 0])
max_x = np.min([voxelx + path_size[0], nx])
for voxely in xrange(ny):
min_y = np.max([voxely - path_size[1], 0])
max_y = np.min([voxely + path_size[1], ny])
for voxelz in xrange(nz):
if mask[voxelx, voxely, voxelz] == 1:
min_z = np.max([voxelz - path_size[2], 0])
max_z = np.min([voxelz + path_size[2], nz])
# -----------------------------------------
signal_path = data[min_x:max_x, min_y:max_y,
min_z:max_z, :]
dim = signal_path.shape
signal_path2D = signal_path.reshape(
(np.prod(dim[0:3]), nt))
signal_xyz = data[voxelx, voxely, voxelz]
RE = 100 * np.sum(np.abs(signal_path2D - signal_xyz),
axis=1) / np.sum(signal_xyz)
ind_valid = RE < 2.5 # (percent %)
data_den[voxelx, voxely,
voxelz] = np.mean(signal_path2D[ind_valid, :],
axis=0)
#end if
#end vz
#end vy
#end vx
data = data_den.copy()
del data_den
#end if
print 'Step #2: Estimation of flip angles:'
if FA_smooth == 'yes':
# Smoothing the data for a robust B1 map estimation
data_smooth = np.zeros((nx, ny, nz, nt))
sig_g = 2.0
for c in xrange(nt):
data_smooth[:, :, :,
c] = filt.gaussian_filter(np.squeeze(data[:, :, :, c]),
sig_g, 0)
#end for
else:
data_smooth = data.copy()
#end if
mean_T2_dist = 0
for voxelz in progressbar.progressbar(xrange(nz), redirect_stdout=True):
#print('Estimation of flip angles: slice', voxelz+1)
print(voxelz + 1, ' slices processed')
# Parallelization by rows: this is more efficient for computing a single or a few slices
mask_slice = mask[:, :, voxelz]
data_slice = data_smooth[:, :, voxelz, :]
#FA_par = Parallel(n_jobs=num_cores)(delayed(fitting_slice_FA)(mask_slice[:, voxely], data_slice[:,voxely,:], nx, Dic_3D, alpha_values) for voxely in tqdm(range(ny)))
if FA_method == 'brute-force':
FA_par = Parallel(n_jobs=num_cores, backend='multiprocessing')(
delayed(fitting_slice_FA_brute_force)
(mask_slice[:, voxely], data_slice[:, voxely, :], nx, Dic_3D,
alpha_values) for voxely in range(ny))
for voxely in xrange(ny):
FA[:, voxely, voxelz] = FA_par[voxely][0]
FA_index[:, voxely, voxelz] = FA_par[voxely][1]
Ktotal[:, voxely, voxelz] = FA_par[voxely][2]
mean_T2_dist = mean_T2_dist + FA_par[voxely][3]
#end for voxely
elif FA_method == 'spline':
FA_par = Parallel(n_jobs=num_cores, backend='multiprocessing')(
delayed(fitting_slice_FA_spline_method)
(Dic_3D_LR, Dic_3D, data_slice[:, voxely, :],
mask_slice[:, voxely], alpha_values_spline, nx, alpha_values)
for voxely in range(ny))
for voxely in xrange(ny):
FA[:, voxely, voxelz] = FA_par[voxely][0]
FA_index[:, voxely, voxelz] = FA_par[voxely][1]
Ktotal[:, voxely, voxelz] = FA_par[voxely][2]
mean_T2_dist = mean_T2_dist + FA_par[voxely][3]
#end voxely
#end if
#end voxelx
del data_smooth
# TO DO: (1) Estimate also the standard deviation of the spectrum and plot it
# (2) Estimate a different mean spectrum for each tissue type (using a segmentation from a T1, or any strategy to segment the raw MET2 data)
mean_T2_dist = mean_T2_dist / np.sum(mean_T2_dist)
total_signal = 0
total_Kernel = 0
nv = 0
for voxelx in xrange(nx):
for voxely in xrange(ny):
for voxelz in xrange(nz):
if mask[voxelx, voxely, voxelz] == 1:
total_signal = total_signal + data[voxelx, voxely,
voxelz, :]
ind_xyz = np.int(FA_index[voxelx, voxely, voxelz])
total_Kernel = total_Kernel + Dic_3D[:, :, ind_xyz]
nv = nv + 1.0
#end vz
#end vy
#end vx
total_Kernel = total_Kernel / nv
total_signal = total_signal / nv
fmean1, SSE = nnls(total_Kernel, total_signal)
dist_T2_mean1 = fmean1 / np.sum(fmean1)
factor = 1.01 # smaller than 1.02 due to the low level of noise
order = 0
Id = create_Laplacian_matrix(Npc, order)
fmean2, reg_opt2, k_est = nnls_x2(total_Kernel, total_signal, Id, factor)
dist_T2_mean2 = fmean2 / np.sum(fmean2)
# Save mean_T2_dist, which is the initial value for RUMBA
fig = plt.figure('Showing results', figsize=(8, 8))
ax0 = fig.add_subplot(1, 1, 1)
im0 = plt.plot(T2s,
mean_T2_dist,
color='b',
label='Mean T2-dist from all voxels: NNLS')
im1 = plt.plot(T2s,
dist_T2_mean1,
color='g',
label='T2-dist from mean signals: NNLS')
im2 = plt.plot(T2s,
dist_T2_mean2,
color='r',
label='T2-dist from mean signals: NNLS-X2-I')
ax0.set_xscale('log')
plt.axvline(x=40.0, color='k', linestyle='--', ymin=0)
plt.title('Mean spectrum', fontsize=18)
plt.xlabel('T2', fontsize=18)
plt.ylabel('Intesity', fontsize=18)
ax0.set_xlim(T2s[0], T2s[-1])
ax0.set_ylim(0, np.max(mean_T2_dist) * 1.2)
ax0.tick_params(axis='both', which='major', labelsize=16)
ax0.tick_params(axis='both', which='minor', labelsize=14)
ax0.set_yticks([])
plt.legend()
plt.savefig(path_to_save_data + 'Mean_spectrum_unitial_iter.png', dpi=600)
plt.close('all')
# --------------------------------------------------------------------------
print 'Step #3: Estimation of T2 spectra:'
for voxelz in progressbar.progressbar(xrange(nz), redirect_stdout=True):
print(voxelz + 1, ' slices processed')
# Parallelization by rows: this is more efficient for computing a single or a few slices
mask_slice = mask[:, :, voxelz]
data_slice = data[:, :, voxelz, :]
FA_index_slice = FA_index[:, :, voxelz]
#T2_par = Parallel(n_jobs=num_cores, backend='multiprocessing')(delayed(fitting_slice_T2)(mask_slice[:, voxely], data_slice[:,voxely,:], FA_index_slice[:, voxely], nx, Dic_3D, lambda_reg, alpha_values, T2s.shape[0], nEchoes, num_l_laplac, N_alphas, reg_method, Laplac1, Laplac2, Is, Laplac_mod, mean_T2_dist, Laplac2_cp_var, W_inv_deltaT2) for voxely in range(ny))
T2_par = Parallel(n_jobs=num_cores, backend='multiprocessing')(
delayed(fitting_slice_T2)
(mask_slice[:, voxely], data_slice[:, voxely, :],
FA_index_slice[:, voxely], nx, Dic_3D, lambda_reg, T2s.shape[0],
nEchoes, reg_method, Laplac, mean_T2_dist)
for voxely in range(ny))
for voxely in xrange(ny):
f_sol_4D[:, voxely, voxelz, :] = T2_par[voxely][0]
s_sol_4D[:, voxely, voxelz, :] = T2_par[voxely][1]
reg_param[:, voxely, voxelz] = T2_par[voxely][2]
#end voxely
#end voxelx
print('Step #4: Estimation of quantitative metrics')
logT2 = np.log(T2s)
for voxelx in xrange(nx):
for voxely in xrange(ny):
for voxelz in xrange(nz):
if mask[voxelx, voxely, voxelz] > 0.0:
M = data[voxelx, voxely, voxelz, :]
x_sol = f_sol_4D[voxelx, voxely, voxelz, :]
vt = np.sum(x_sol) + epsilon
x_sol = x_sol / vt
# fill matrices
# pdb.set_trace()
fM[voxelx, voxely, voxelz] = np.sum(x_sol[ind_m])
fIE[voxelx, voxely, voxelz] = np.sum(x_sol[ind_t])
fCSF[voxelx, voxely, voxelz] = np.sum(x_sol[ind_csf])
# ------ T2m
# Aritmetic mean
# T2m [voxelx, voxely, voxelz] = np.sum(x_sol[ind_m] * T2s[ind_m])/(np.sum(x_sol[ind_m]) + epsilon)
# Geometric mean: see Bjarnason TA. Proof that gmT2 is the reciprocal of gmR2. Concepts Magn Reson 2011; 38A: 128– 131.
T2m[voxelx, voxely, voxelz] = np.exp(
np.sum(x_sol[ind_m] * logT2[ind_m]) /
(np.sum(x_sol[ind_m]) + epsilon))
# ------ T2IE0
# Aritmetic mean
# T2IE[voxelx, voxely, voxelz] = np.sum(x_sol[ind_t] * T2s[ind_t])/(np.sum(x_sol[ind_t]) + epsilon)
# Geometric mean: see Bjarnason TA. Proof that gmT2 is the reciprocal of gmR2. Concepts Magn Reson 2011; 38A: 128– 131.
T2IE[voxelx, voxely, voxelz] = np.exp(
np.sum(x_sol[ind_t] * logT2[ind_t]) /
(np.sum(x_sol[ind_t]) + epsilon))
Ktotal[voxelx, voxely, voxelz] = vt
# end if
#end for z
# end for y
# end for x
# -------------------------- Save all datasets -----------------------------
outImg = nib.Nifti1Image(fM, img.affine)
nib.save(outImg, path_to_save_data + 'MWF.nii.gz')
outImg = nib.Nifti1Image(fIE, img.affine)
nib.save(outImg, path_to_save_data + 'IEWF.nii.gz')
outImg = nib.Nifti1Image(fCSF, img.affine)
nib.save(outImg, path_to_save_data + 'FWF.nii.gz')
outImg = nib.Nifti1Image(T2m, img.affine)
nib.save(outImg, path_to_save_data + 'T2_M.nii.gz')
outImg = nib.Nifti1Image(T2IE, img.affine)
nib.save(outImg, path_to_save_data + 'T2_IE.nii.gz')
outImg = nib.Nifti1Image(Ktotal, img.affine)
nib.save(outImg, path_to_save_data + 'TWC.nii.gz')
outImg = nib.Nifti1Image(FA, img.affine)
nib.save(outImg, path_to_save_data + 'FA.nii.gz')
outImg = nib.Nifti1Image(f_sol_4D, img.affine)
nib.save(outImg, path_to_save_data + 'fsol_4D.nii.gz')
outImg = nib.Nifti1Image(s_sol_4D, img.affine)
nib.save(outImg, path_to_save_data + 'Est_Signal.nii.gz')
outImg = nib.Nifti1Image(reg_param, img.affine)
nib.save(outImg, path_to_save_data + 'reg_param.nii.gz')
#end if
print('Done!')
def image_noise(path = None, image = None):
#converts to an opencv image object
if image == None:
image = cv2.imread(path)
return estimate_sigma(image, multichannel=True, average_sigmas=True)
def estimate_noise_sd(self):
if self._noise_sd < 0.0:
self._noise_sd = estimate_sigma(self._image)
return self._noise_sd
img = cv2.imread('..//images//tes.jpg', 0)
blocks = []
variances = []
imgwidth, imgheight = img.shape[0:2]
blockSize = 64
print(img.shape)
#break up image into NxN blocks, N = blockSize
for j in range(0, imgheight, blockSize):
for i in range(0, imgwidth, blockSize):
a = img
if (i + blockSize > imgwidth and j + blockSize > imgheight):
a = img[i:, j:]
elif (i + blockSize > imgwidth):
a = img[i:, j:j + blockSize]
elif (j + blockSize > imgheight):
a = img[i:i + blockSize, j:]
else:
a = img[i:i + blockSize, j:j + blockSize]
sigma = estimate_sigma(a, multichannel=False, average_sigmas=True)
blocks.append(a)
variances.append([sigma])
print(variances)
kmeans = KMeans(n_clusters=2, random_state=0).fit(variances)
center1, center2 = kmeans.cluster_centers_
sigma = estimate_sigma(img, multichannel=False, average_sigmas=True)
print(sigma)
print(center1, center2)
