def immeuble(x, y_sol):
'''
Paramètres
x : abscisse du centre de l'étage
y_sol : ordonnée du sol du la rue
Cette fonction dessine un immeuble Le nombre d'étage est compris aléatoirement entre 0 et 4
La couleur de la façade et la couleur de la porte sont tirées au hasard
'''
turtle.colormode(255)
# Nombre d'étage (aléatoire)
nombre_etages=randint(0,4)
#Couleurs des éléments (aléatoire)
couleur_facade = couleur_aleatoire()
couleur_porte = couleur_aleatoire()
# Dessin du RDC
rdc(x,y_sol,couleur_facade,couleur_porte)
# Dessin des étages
for i in range (nombre_etages):
etage(x, y_sol, couleur_facade, i+1)
# Dessin du toit
toit(x, y_sol, nombre_etages)
def linear_mixture(image1,
image2,
mixing_matrix=[[1, 0.5], [0.5, 1]],
show_images=True):
"""
Function that mixes to images linearly
Parameters
----------
image1: the first image to be mixed
image2: the second image to be mixed
mixing_matrix: the matrix to which the images will be multiplied
show_images: boolean, True by default, plots the mixed images if True
Return
-----------
S: the input images, flattened and stacked
X: the mixed signals, flattened and stacked
"""
assert np.shape(mixing_matrix) == (2, 2)
n = image1.shape
source1 = image1.flatten('F') #column wise
source2 = image2.flatten('F') #column wise
source1 = source1 - np.mean(source1)
source2 = source2 - np.mean(source2)
source1 = source1 / np.linalg.norm(source1)
source2 = source2 / np.linalg.norm(source2)
S = np.stack((source1, source2))
X = np.matmul(mixing_matrix, S)
X1 = X[0, :]
X2 = X[1, :]
rdc_images = rdc(X1, X2)
print("RDC =", rdc_images)
if show_images == True:
X1 = np.reshape(X1, n)
X2 = np.reshape(X2, n)
plt.figure()
plt.imshow(X1.T, cmap='gray')
plt.title("Mixed image 1")
plt.show
plt.figure()
plt.imshow(X2.T, cmap='gray')
plt.title("Mixed image 2")
plt.show()
return S.T, X
def nonlinear_mixture(image1, image2, q1, q2, show_images=True):
"""
Function that mixes to images nonlinearly
Parameters
----------
image1: the first image to be mixed
image2: the second image to be mixed
q1: float, interference level of the first image
q2: float, interference level of the second image
show_images: boolean, True by default, plots the mixed images if True
Return
-----------
S: the input images, flattened and stacked
X: the mixed signals, flattened and stacked
"""
# mixing the images
source1 = np.matrix(image1)
source1 = source1.flatten('F') #column wise
source2 = np.matrix(image2)
source2 = source2.flatten('F') #column wise
S = np.stack((source1, source2))
rdc_images = rdc(source1.T, source2.T)
print("RDC =", rdc_images)
#X1 = np.multiply(source1, np.power((source2/255),q2))
#X2 = np.multiply(source2, np.power((source1/255),q1))
X1 = np.multiply(source1, (np.exp(
-q2 * (1 - source2)))) # if 0<intensities<255 then divide by 255
X2 = np.multiply(source2, (np.exp(-q1 * (1 - source1))))
X = np.stack((X1, X2))
# Show mixed images
if (show_images == True):
X1 = np.reshape(X1, (n, n))
X2 = np.reshape(X2, (n, n))
plt.figure()
plt.imshow(X1.T, cmap='gray')
plt.title("Mixed image 1")
plt.show
plt.figure()
plt.imshow(X2.T, cmap='gray')
plt.title("Mixed image 2")
plt.show()
return S, X
def main(datafile, outputfile):
X, features = read_sah_h5(datafile, just_good=False)
result = []
progress = ProgressBar(widgets=['Computing dependencies: ', Bar('='), ETA()])
for f1, f2 in progress(list(combinations(features, 2))):
x = X[:, features.index(f1)]
y = X[:, features.index(f2)]
result.append('%s,%s,%f' % (f1, f2, rdc(x, y, n=5)))
with open(outputfile, 'w+') as f:
f.write('\n'.join(result))
def main(datafile, outputfile):
X, features = read_sah_h5(datafile, just_good=False)
result = []
progress = ProgressBar(
widgets=['Computing dependencies: ',
Bar('='), ETA()])
for f1, f2 in progress(list(combinations(features, 2))):
x = X[:, features.index(f1)]
y = X[:, features.index(f2)]
result.append('%s,%s,%f' % (f1, f2, rdc(x, y, n=5)))
with open(outputfile, 'w+') as f:
f.write('\n'.join(result))
def randomized_dependence_coefficient(series1, series2):
"""
Compute the randomized dependence coefficient between two series
Measure of nonlinear dependence between random variables based on the
Hirschfeld-Gebelein-Renyi Maximum Correlation Coefficient
Args:
series1 (numpy.ndarray): First series
series2 (numpy.ndarray): Second series
Returns:
Randomized dependence coefficient between the two series
"""
return rdc(np.array(series1), np.array(series2))
# Mixing process here
img2_gray_re = np.fliplr(img2_gray)
source1 = np.matrix(img1_gray)
source1 = source1.flatten('F') #column wise
source2 = np.matrix(img2_gray)
source2 = source2.flatten('F') #column wise
source1 = source1 - np.mean(source1)
source2 = source2 - np.mean(source2)
#source1 = source1/np.linalg.norm(source1)
#source2 = source2/np.linalg.norm(source2)
print("rdc = ", rdc(source1.T,source2.T))
source = np.stack((source1, source2))
print('Covariance matrix is: ')
print(np.matmul(source,source.T))
# randomly generated mixing matrix
#np.random.seed(0)
#mixing_matrix = np.random.randn(2,2)
#mixing_matrix = np.array([[0.36, 0.66], [0.03, 0.95]])
mixing_matrix = np.array([[1, 0.5], [0.5, 1]])
print('Mixing matrix is: ')
print(mixing_matrix)
# X = source * mixing_matrix - The mixed images
SDR_ica_imp = np.zeros((1, N_sources))
SDR_sp_imp = np.zeros((1, N_sources))
for pic_set in np.arange(N_sources):
# load images and convert them
print(pic_set)
#mixing_matrix = np.array([[0.36, 0.66], [0.03, 0.95]])
mixing_matrix = np.array([[1, 0.7], [0.02, 1]])
# mixing_matrix = np.array([[1, 0.3], [0.5, 1]])
# mixing_matrix = np.array([[0.8488177, 0.17889592], [0.05436321, 0.36153845]])
X, source = three_projection_method.import_image(pic_set, mixing_matrix)
# calculate kurtosis, if it's Gaussian distribution, then it's close to zero
k1 = kurtosis(np.squeeze(source[0, :]))
k2 = kurtosis(np.squeeze(source[1, :]))
Kur_it[0, pic_set] = np.abs(k1) + np.abs(k2)
rdc_it[0, pic_set] = rdc(source[0, :], source[1, :])
# whitening processing. It's important
X_nonwhiten = np.copy(X)
X, W = whiten_projection(np.asarray(X))
(sdr_ref, sir_ref, sar,
perm) = mmetrics.bss_eval_sources(np.asarray(source), np.asarray(X))
print(sdr_ref)
new_mix = np.dot(W, mixing_matrix)
#####################################
# Using the three projection method with different non linearity
print('Here is the first algorithm')
separation_method = 'TV'
sigma = 1e-3
from rdc import rdc
# the signals
t = np.linspace(-np.pi, np.pi, 1000)
sine = np.sin(4 * t) #for np.sin(3*t), rdc is higher => bad performance of ICA
sawtooth = signal.sawtooth(2 * np.pi * t)
#plotting
plt.figure()
plt.plot(t, sawtooth, label='sawtooth')
plt.plot(t, sine, label='sine')
plt.legend()
plt.show
#test the independence
print("rdc = ", rdc(sine, sawtooth))
# mixing the reference sources
mixing_matrix = [[1, 0.5], [0.5, 1]]
reference_sources = np.c_[sawtooth, sine]
#sources /= sources.std(axis = 0) #standardize it
M = np.dot(reference_sources, np.transpose(mixing_matrix))
#plotting the mixtures
plt.figure()
plt.plot(t, M[:, 0], label='mixed signal1')
plt.plot(t, M[:, 1], label='mixed signal2')
plt.legend()
plt.show
# Compute ICA
# We mix them here
source1 = np.matrix(img1_gray_re)
source1 = source1.flatten('F') #column wise
source2 = np.matrix(img2_gray_re)
source2 = source2.flatten('F') #column wise
source1 = source1 - np.mean(source1)
source2 = source2 - np.mean(source2)
source1 = source1 / np.linalg.norm(source1)
source2 = source2 / np.linalg.norm(source2)
rdr_this = rdc(source1.T, source2.T)
source = np.stack((source1, source2))
# randomly generated mixing matrix
np.random.seed(0)
#mixing_matrix = np.random.rand(2,2)
mixing_matrix = np.array([[1, 0.5], [0.5, 1]])
X = np.matmul(source.T, mixing_matrix)
X1 = X[:, 0]
mx1 = np.mean(X1)
X1 = np.reshape(X1, (n, n))
#print(X1.min(), X1.max(), X1.mean())
# Mixing process here
img2_gray_re = np.fliplr(img2_gray)
source1 = np.matrix(img1_gray)
source1 = source1.flatten('F') #column wise
source2 = np.matrix(img2_gray)
source2 = source2.flatten('F') #column wise
source1 = source1 - np.mean(source1)
source2 = source2 - np.mean(source2)
#source1 = source1/np.linalg.norm(source1)
#source2 = source2/np.linalg.norm(source2)
print("rdc = ", rdc(source1.T, source2.T))
source = np.stack((source1, source2))
print('Covariance matrix is: ')
print(np.matmul(source, source.T))
# randomly generated mixing matrix
#np.random.seed(0)
#mixing_matrix = np.random.rand(2,2)
#mixing_matrix = np.array([[0.36, 0.66], [0.03, 0.95]])
mixing_matrix = np.array([[1, 0.5], [0.5, 1]])
print('Mixing matrix is: ')
print(mixing_matrix)
# X = source * mixing_matrix - The mixed images
source1, source2 = load_images('./images/set' + str(i + 1) + '_pic1.png',
'./images/set' + str(i + 1) + '_pic2.png',
n,
show_images=False)
S, X = linear_mixture(source1,
source2,
mixing_matrix=mixing_matrix,
show_images=False)
#Reference SDR
(sdr_ref, sir_ref, sar,
perm) = mmetrics.bss_eval_sources(np.asarray(S), np.asarray(X))
print('The mean value of the reference SDR is: ', np.mean(sdr_ref))
#RDC of sources
rdc_i = rdc(S[0, :], S[1, :])
all_rdc.append(rdc_i)
print("rdc of sources = ", rdc_i)
#Kurtosis of sources
kurtosis_i = mean_kurtosis(S)
all_kurtosis_sources.append(kurtosis_i)
print("mean kurtosis of sources = ", kurtosis_i)
print("kurtosis of sources = ", kurtosis(S[0, :]), kurtosis(S[1, :]))
#Skewness of sources
skewness_i = mean_skewness(S)
all_skewness_sources.append(skewness_i)
print("mean skewness of sources = ", skewness_i)
print("skewness of sources = ", skew(S[0, :]), skew(S[1, :]))