def grad_gauss_energy_per_region(omega_coord, affine_omega_coord, omega_mean, omega_std, image, image_gradient):
b = 1 / (np.power(omega_std, 2))
aux = utils.evaluate_image(omega_coord, image) - omega_mean
image_gradient_by_point = b * np.array([utils.evaluate_image(omega_coord, image_gradient[0]),
utils.evaluate_image(omega_coord, image_gradient[1])])
grad = gradient_gauss_energy_for_each_vertex(aux, affine_omega_coord, image_gradient_by_point)
return grad
def get_hsi_derivatives(coordinates, image):
'''
Gets neighboring pixels of an array of pixels.
:param coordinates (numpy array):
:return returns 8 arrays of coordinate pixels:
'''
import utils
x = np.zeros([len(coordinates), 3, 3])
hsi_im = image.hsi_image[:, :, 0]
hsi_im_border = np.pad(hsi_im, (1, 1), 'reflect')
for i in xrange(-1, 2):
for j in xrange(-1, 2):
x[:, i + 1, j + 1] = directed_hue_color_distance(
utils.evaluate_image(coordinates, hsi_im, outside_value=0.),
utils.evaluate_image(coordinates + [i + 1, j + 1], hsi_im_border, outside_value=0.)
)
dx = np.array([
[-1, -2, -1],
[0, 0, 0],
[1, 2, 1]
])
dy = np.array([
[-1, 0, 1],
[-2, 0, 2],
[-1, 0, 1]
])
derivative_x = np.array([sum(sum(np.transpose(x * dx)))])
derivative_y = np.array([sum(sum(np.transpose(x * dy)))])
derivative = np.concatenate((derivative_x, derivative_y))
return derivative
def mean_energy_grad_per_region(omega_coord, affine_omega_coord, image, image_gradient):
# E_mean
omega_mean, omega_std = get_omega_mean(omega_coord, image)
aux = utils.evaluate_image(omega_coord, image, omega_mean) - omega_mean
image_gradient_by_point = [utils.evaluate_image(omega_coord, image_gradient[0], 0),
utils.evaluate_image(omega_coord, image_gradient[1], 0)]
mean_derivative = np.dot(image_gradient_by_point, affine_omega_coord) / float(len(omega_coord))
grad = gradient_energy_for_each_vertex(aux, affine_omega_coord, image_gradient_by_point, mean_derivative)
return grad # *(1/pow(omega_std, 2)) for GAUSS
def grad_gauss_energy_per_region(omega_coord,
affine_omega_coord,
gmm,
image,
image_gradient,
smallest_num=np.exp(-200)):
means = np.array([m for m in gmm.means_])
covars = np.array([v for v in gmm.covars_])
weights = np.array([w for w in gmm.weights_]).T
x_ = utils.evaluate_image(omega_coord, image)
x_m = np.transpose(np.tile(x_, (1, 1, 1)), (1, 0, 2)) - means
denom = np.linalg.inv(covars)
# x_m_denom = np.dot(x_m, denom)
# x_m_denom = np.array([x_m_denom[:, i, i, :] for i in xrange(len(weights))])
x_m_denom = np.array(
[np.dot(X, M) for M, X in zip(denom, np.transpose(x_m, (1, 0, 2)))])
aux = -np.sum(np.multiply(np.transpose(x_m_denom,
(1, 0, 2)), x_m), axis=2) / 2.
exp_x_m_denom_x_m = np.exp(aux)
k = means.shape[1]
coeff = 1 / (np.power(np.sqrt(2 * np.pi), k) *
np.sqrt(np.linalg.det(covars)))
mixt = exp_x_m_denom_x_m * coeff
unsummed_mixture_prob = mixt * weights
mixture_prob = np.sum(unsummed_mixture_prob, axis=1)
mixture_prob = avoid_zero_terms(mixture_prob, smallest_num=smallest_num)
# caluculate 1/P(x)
coeff_ = 1 / mixture_prob
denom_x_m = np.array(
[np.dot(M, X) for M, X in zip(denom, np.transpose(x_m, (1, 2, 0)))])
# x_m_denom = np.transpose(np.array([np.dot(X, M) for M, X in zip(denom, np.transpose(x_m, (1, 0, 2)))]),(0,2,1))
image_gradient_by_point = np.array([
utils.evaluate_image(omega_coord, image_gradient[0]),
utils.evaluate_image(omega_coord, image_gradient[1])
])
image_gradient_by_point = np.transpose(image_gradient_by_point, (0, 2, 1))
denom_x_m_derImage = -np.array(
[np.sum(Mx * image_gradient_by_point, axis=1)
for Mx in denom_x_m]) / 2.
prod_2 = coeff_ * unsummed_mixture_prob.T
prod_3 = np.multiply(prod_2, np.transpose(denom_x_m_derImage, (1, 0, 2)))
prod_4 = np.sum(prod_3, axis=1)
grad = np.dot(prod_4, affine_omega_coord).T
return grad
def grad_gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image,
image_gradient):
means = np.array([m for m in gmm.means_])
covars = np.array([v[0] for v in gmm.covars_])
weights = np.array([w for w in gmm.weights_])
x_m = utils.evaluate_image(omega_coord, image).T - means
x_m = x_m.T
# print x_m.shape
x_m_squared = x_m * x_m
denom = 2 * covars.T
exp_aux = np.exp(-x_m_squared / denom)
coeff = 1 / (np.sqrt(2 * np.pi) * np.sqrt(covars.T))
mixt = coeff * exp_aux
unsummed_mixture_prob = weights * mixt
number_of_components = len(means)
if number_of_components > 1:
mixture_prob = np.array([np.sum(unsummed_mixture_prob, axis=1)]).T
else:
mixture_prob = unsummed_mixture_prob
# Avoid logarithm of zero
mixture_prob = avoid_zero_terms(mixture_prob)
energy = np.sum(np.log(mixture_prob))
# caluculate 1/P(x)
coeff_ = 1 / mixture_prob
# calculate the derivative of the mixture
unsummed_mixture_derivative = unsummed_mixture_prob * (x_m / covars.T)
if number_of_components > 1:
mixture_derivative = np.array(
[np.sum(unsummed_mixture_derivative, axis=1)]).T
else:
mixture_derivative = unsummed_mixture_derivative
image_gradient_by_point = np.array([
utils.evaluate_image(omega_coord, image_gradient[0]),
utils.evaluate_image(omega_coord, image_gradient[1])
])
prod_2 = coeff_ * mixture_derivative
grad = gradient_gauss_energy_for_each_vertex(prod_2, affine_omega_coord,
image_gradient_by_point)
plot_grad = False
if plot_grad:
show_direction(image, prod_2, omega_coord, affine_omega_coord,
image_gradient_by_point)
return grad, energy
def grad_gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image, image_gradient, weight=[1, 1, 1]):
# E_mean
image_gradient_by_point = np.array([utils.evaluate_image(omega_coord, image_gradient[0], 0),
utils.evaluate_image(omega_coord, image_gradient[1], 0)])
omega_mean, omega_std = gmm.means_, gmm.covars_
omega_std = omega_std[0]
sigma = np.linalg.inv(omega_std)
aux = utils.evaluate_image(omega_coord, image, omega_mean)
aux -= omega_mean
sigma_aux = np.dot(sigma, aux.T)
prod_1 = np.sum(sigma_aux.T * np.transpose(image_gradient_by_point, (0, 1, 2)), axis=2)
grad = np.dot(prod_1, affine_omega_coord).T
return grad
def gauss_energy_per_region(omega_coord,
affine_omega_coord,
gmm,
image,
smallest_num=np.exp(-200)):
means = np.array([m for m in gmm.means_])
covars = np.array([v for v in gmm.covars_])
weights = np.array([w for w in gmm.weights_]).T
x_ = utils.evaluate_image(omega_coord, image)
x_m = np.transpose(np.tile(x_, (1, 1, 1)), (1, 0, 2)) - means
# print x_m.shape
denom = np.linalg.inv(covars)
# x_m_denom = np.dot(x_m, denom)
# x_m_denom = np.array([x_m_denom[:, i, i, :] for i in xrange(len(weights))])
x_m_denom = np.array(
[np.dot(X, M) for M, X in zip(denom, np.transpose(x_m, (1, 0, 2)))])
aux = -np.sum(np.multiply(np.transpose(x_m_denom,
(1, 0, 2)), x_m), axis=2) / 2.
exp_x_m_denom_x_m = np.exp(aux)
k = means.shape[1]
coeff = 1 / (np.power(np.sqrt(2 * np.pi), k) *
np.sqrt(np.linalg.det(covars)))
mixt = exp_x_m_denom_x_m * coeff
mixture_prob = mixt * weights
if len(means) > 1:
mixture_prob = np.sum(mixture_prob, axis=1)
else:
mixture_prob = mixture_prob
mixture_prob = avoid_zero_terms(mixture_prob, smallest_num=smallest_num)
energy = np.sum(np.log(mixture_prob))
return energy
def grad_gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image, image_gradient):
means = np.array([m for m in gmm.means_])
covars = np.array([v[0] for v in gmm.covars_])
weights = np.array([w for w in gmm.weights_])
x_m = utils.evaluate_image(omega_coord, image).T - means
x_m = x_m.T
# print x_m.shape
x_m_squared = x_m * x_m
denom = 2 * covars.T
exp_aux = np.exp(-x_m_squared / denom)
coeff = 1 / (np.sqrt(2 * np.pi) * np.sqrt(covars.T))
mixt = coeff * exp_aux
unsummed_mixture_prob = weights * mixt
number_of_components = len(means)
if number_of_components > 1:
mixture_prob = np.array([np.sum(unsummed_mixture_prob, axis=1)]).T
else:
mixture_prob = unsummed_mixture_prob
# Avoid logarithm of zero
mixture_prob = avoid_zero_terms(mixture_prob)
energy = np.sum(np.log(mixture_prob))
# caluculate 1/P(x)
coeff_ = 1 / mixture_prob
# calculate the derivative of the mixture
unsummed_mixture_derivative = unsummed_mixture_prob * (x_m / covars.T)
if number_of_components > 1:
mixture_derivative = np.array([np.sum(unsummed_mixture_derivative, axis=1)]).T
else:
mixture_derivative = unsummed_mixture_derivative
image_gradient_by_point = np.array([utils.evaluate_image(omega_coord, image_gradient[0]),
utils.evaluate_image(omega_coord, image_gradient[1])])
prod_2 = coeff_ * mixture_derivative
grad = gradient_gauss_energy_for_each_vertex(prod_2, affine_omega_coord, image_gradient_by_point)
plot_grad = False
if plot_grad:
show_direction(image, prod_2, omega_coord, affine_omega_coord, image_gradient_by_point)
return grad, energy
def gauss_energy_per_region(omega_coord, affine_omega_coord, image):
x_ = utils.evaluate_image(omega_coord, image)
omega_mean = np.mean(x_)
omega_std = np.std(x_)
aux = x_ - omega_mean
a = len(aux) * np.log(omega_std)
b = 1 / float(2 * np.power(omega_std, 2))
region_energy = a + np.dot(aux, np.transpose(aux)) * b
return region_energy
def gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image):
omega_mean, omega_std = gmm.means_, gmm.covars_
aux = utils.evaluate_image(omega_coord, image, omega_mean) - omega_mean
omega_std = omega_std[0]
k = len(omega_std)
term_1 = len(aux) * k * np.log(2 * np.pi)
term_2 = len(aux) * np.log(np.linalg.det(omega_std))
sigma = np.linalg.inv(omega_std)
x_sigma = np.dot(aux, sigma)
term_3 = np.multiply(x_sigma, aux)
term_3 = np.sum(term_3, axis=1)
region_energy = term_1 + term_2 + sum(term_3)
return region_energy
def gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image):
omega_mean, omega_std = gmm.means_, gmm.covars_
aux = utils.evaluate_image(omega_coord, image, omega_mean) - omega_mean
omega_std = omega_std[0]
k = len(omega_std)
term_1 = len(aux) * k * np.log(2 * np.pi)
term_2 = len(aux) * np.log(np.linalg.det(omega_std))
sigma = np.linalg.inv(omega_std)
x_sigma = np.dot(aux, sigma)
term_3 = np.multiply(x_sigma, aux)
term_3 = np.sum(term_3, axis=1)
region_energy = term_1 + term_2 + sum(term_3)
return region_energy
def grad_gauss_energy_per_region(omega_coord,
affine_omega_coord,
gmm,
image,
image_gradient,
weight=[1, 1, 1]):
# E_mean
image_gradient_by_point = np.array([
utils.evaluate_image(omega_coord, image_gradient[0], 0),
utils.evaluate_image(omega_coord, image_gradient[1], 0)
])
omega_mean, omega_std = gmm.means_, gmm.covars_
omega_std = omega_std[0]
sigma = np.linalg.inv(omega_std)
aux = utils.evaluate_image(omega_coord, image, omega_mean)
aux -= omega_mean
sigma_aux = np.dot(sigma, aux.T)
prod_1 = np.sum(sigma_aux.T * np.transpose(image_gradient_by_point,
(0, 1, 2)),
axis=2)
grad = np.dot(prod_1, affine_omega_coord).T
return grad
def get_hsi_derivatives(coordinates, image):
'''
Gets neighboring pixels of an array of pixels.
:param coordinates (numpy array):
:return returns 8 arrays of coordinate pixels:
'''
import utils
x = np.zeros([len(coordinates), 3, 3])
hsi_im = image.hsi_image[:, :, 0]
hsi_im_border = np.pad(hsi_im, (1, 1), 'reflect')
for i in xrange(-1, 2):
for j in xrange(-1, 2):
x[:, i + 1, j + 1] = directed_hue_color_distance(
utils.evaluate_image(coordinates, hsi_im, outside_value=0.),
utils.evaluate_image(coordinates + [i + 1, j + 1],
hsi_im_border,
outside_value=0.))
dx = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
dy = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])
derivative_x = np.array([sum(sum(np.transpose(x * dx)))])
derivative_y = np.array([sum(sum(np.transpose(x * dy)))])
derivative = np.concatenate((derivative_x, derivative_y))
return derivative
def gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image):
means = np.array([m for m in gmm.means_])
covars = np.array([v for v in gmm.covars_])
weights = np.array([np.round(w) for w in gmm.weights_])
x_m = utils.evaluate_image(omega_coord, image) - means
x_m = x_m.T
x_m_squared = x_m * x_m
denom = 2 * covars
exp_aux = np.exp(-x_m_squared / denom)
coeff = 1 / (np.sqrt(2 * np.pi) * np.sqrt(covars))
mixt = coeff * exp_aux
mixture_prob = weights * mixt
# Avoid logarithm of zero
mixture_prob = avoid_zero_terms(mixture_prob)
energy = np.sum(np.log(mixture_prob))
return energy
def gauss_energy_per_region(omega_coord, affine_omega_coord, gmm, image):
means = np.array([m for m in gmm.means_])
covars = np.array([v for v in gmm.covars_])
weights = np.array([np.round(w) for w in gmm.weights_])
x_m = utils.evaluate_image(omega_coord, image) - means
x_m = x_m.T
x_m_squared = x_m * x_m
denom = 2 * covars
exp_aux = np.exp(-x_m_squared / denom)
coeff = 1 / (np.sqrt(2 * np.pi) * np.sqrt(covars))
mixt = coeff * exp_aux
mixture_prob = weights * mixt
# Avoid logarithm of zero
mixture_prob = avoid_zero_terms(mixture_prob)
energy = np.sum(np.log(mixture_prob))
return energy
def mean_energy_per_region(omega_coord, affine_omega_coord, image):
omega_mean, omega_std = get_omega_mean(omega_coord, image)
aux = utils.evaluate_image(omega_coord, image, omega_mean) - omega_mean
return np.dot(aux, np.transpose(aux))