def project_param_to_shape(self, params_vec):
"""
projects PCA params back to restore the shape and set it to given ShapeVector
:param params_vec: vector of ASM parameters
:type params_vec: numpy.ndarray
:return: vector of points (2Nx1 array)
:rtype numpy.ndarray
"""
return cv.PCABackProject(params_vec, self.pca_shape, self.eigenvectors)
def demo_reconstruction(mean, eigenvectors, test_images, test_vecs):
instructions = [
'Reconstruction from PCA',
'',
'Hit [ or ] for prev/next image',
'Hit R for random image',
'Hit ESC when done',
'',
'Hit any key to begin',
]
show_text_screen(instructions)
test_recons = cv2.PCABackProject(test_vecs, mean, eigenvectors)
idx = 0
n = len(test_images)
while True:
img_orig = test_images[idx]
img_recons = test_recons[idx]
orig = row2img(img_orig, TARGET_DISPLAY_SIZE, f'Test image {idx:04d}')
recons = row2img(img_recons, TARGET_DISPLAY_SIZE,
f'Reconstructed from {len(eigenvectors)} PCs')
err = row2img(img_orig - img_recons,
TARGET_DISPLAY_SIZE,
'Error image',
img_type='error')
display = np.hstack((orig, recons, err))
cv2.imshow(WINDOW_NAME, display)
k = cv2.waitKey(5)
if k == ord(' ') or k == ord(']'):
idx = (idx + 1) % n
elif k == ord('['):
idx = (idx + n - 1) % n
elif k == ord('r') or k == ord('R'):
idx = np.random.randint(n)
elif k == 27:
return
def pcaDistanceSegmentation(p: QPoint, model: HyperspectralImgModel, threshold,
maxComponents) -> QImage:
#zmiana rozmiaru macierzy na (dlugosc obrazu * szerokosc) x il. bandów
imgarr = model.imgArr.reshape(
(model.imgArr.shape[0] * model.imgArr.shape[1], model.imgArr.shape[2]))
#PCA
mean, eigenv = np.array(cv2.PCACompute(imgarr, mean=None))
#wybor n glownych skladowych i projekcja wsteczna
reconstructed = cv2.PCABackProject(imgarr, mean[:, 0:maxComponents],
eigenv[:, 0:maxComponents])
#zmiana rozmiaru macierzy na pierwotny
reconstructed = reconstructed.reshape(model.img.shape[0],
model.img.shape[1], maxComponents)
#metoda odleglosci dla nowej macierzy
return distanceSegmentation(
p, HyperspectralImgModel(model.img, model.sceneImg, reconstructed),
threshold)
def get_curve(data, E=0.001, s=500):
mean, px = cv2.PCACompute(data=data, mean=np.array([data.mean(axis=0)]))
new_data = cv2.PCAProject(data, mean, px)
new_data = np.array(sorted(new_data, key=lambda x: x[0]))
def dist(t1, t2, sigma):
return exp(-(t2[0] - t1[0])**2 / (2 * sigma))
left_index = 0
right_index = 0
index = 0
all_px = new_data.shape[0]
curve = []
while index < all_px:
is_ = False
while (right_index < all_px) and (dist(new_data[index],
new_data[right_index], s) > E):
right_index += 1
while (left_index < index) and (dist(new_data[index],
new_data[left_index], s) < E):
left_index += 1
up = np.sum(np.array([
x * dist(x, new_data[index], s)
for x in new_data[left_index:right_index]
]),
axis=0)
down = np.sum(np.array([
dist(x, new_data[index], s)
for x in new_data[left_index:right_index]
]),
axis=0)
res = up / down
curve.append(res)
index += 1
return cv2.PCABackProject(np.array(curve), mean, px)
def get_curve(data, E=0.001, s=200):
mean, px = cv2.PCACompute(data=data, mean=np.array([data.mean(axis=0)]))
new_data = cv2.PCAProject(data, mean, px)
new_data = np.array(sorted(new_data, key=lambda x: x[0]))
def dist(t1, t2, sigma):
return exp(-(t2 - t1)**2 / (2 * sigma))
left_index = 0
right_index = 0
all_px = new_data.shape[0]
curve = []
is_ = 0
min_, max_ = int(min(new_data[:, 0])) - 1, int(max(new_data[:, 0])) + 1
for index in range(min_, max_, 10):
is_ += 1
while (right_index < all_px) and (dist(index, new_data[right_index][0],
s) > E):
right_index += 1
while (left_index < is_) and (dist(index, new_data[left_index][0], s) <
E):
left_index += 1
up = np.sum(np.array([
x * dist(x[0], index, s) for x in new_data[left_index:right_index]
]),
axis=0)
down = np.sum(np.array(
[dist(x[0], index, s) for x in new_data[left_index:right_index]]),
axis=0)
res = up / down
curve.append(res)
index += 1
return cv2.PCABackProject(np.array(curve), mean, px)
def back_projecao_PCA(projecao, media, auto_vetores):
back_projecao = cv.PCABackProject(projecao, media, auto_vetores)
return back_projecao
def find_params_for_shape(self, vec, vec_old, fit_result_old, level):
"""
Finds b parameters of the model for given shape
:param vec: fitted shape
:type vec: ShapeVector
:param vec_old: prior shape
:type vec_old: ShapeVector
:param fit_result_old: result object of the fitting
:type fit_result_old: ASMFitResult
:param level: level of the pyramid
:type level: int
:return: fitting result with found parameters set
:rtype: ASMFitResult
"""
c = np.array([0.0005, 0.0005, 0.0005])
vec_t = ShapeVector()
vec_t.set_from_vector(vec_old.vector)
vec_t.subtract_vector(vec)
rho2 = c[level] * vec_t.vector.dot(vec_t.vector)
x = ShapeVector()
x_from_params = ShapeVector()
vec_repr = ShapeVector()
cur_trans = fit_result_old.similarity_trans
cur_params = np.zeros([1, self.eigenvalues_pyr[level].shape[0]])
for i in range(self.eigenvalues_pyr[level].shape[0]):
if i < fit_result_old.params.shape[1]:
cur_params[0, i] = fit_result_old.params[0, i]
else:
cur_params[0, i] = 0
ii = 0
while True:
s = cur_trans.get_scale()
last_params = cur_params.copy()
vec_r = cur_trans.inverted_transform(vec)
p = self.sigma2_pyr[level] / (self.sigma2_pyr[level] + rho2 /
(s * s))
delta2 = 1 / (1 / self.sigma2_pyr[level] + (s * s) / rho2)
x_from_params.set_from_vector(
cv.PCABackProject(cur_params, self.pca_shape_pyr[level],
self.eigenvectors_pyr[level])[0])
tmp = vec_r.vector.reshape([1, -1])
tmp_full_params = cv.PCAProject(
tmp, self.pca_full_shape['mean'],
self.pca_full_shape['eigenvectors'],
self.pca_full_shape['eigenvalues'])
vec_repr.set_from_vector(
cv.PCABackProject(tmp_full_params, self.pca_full_shape['mean'],
self.pca_full_shape['eigenvectors'],
self.pca_full_shape['eigenvalues'])[0])
x.set_from_vector(p * vec_repr.vector +
(1 - p) * x_from_params.vector)
x2 = x.vector.dot(x.vector) + (x.vector.shape[0] - 4) * delta2
tmp = x.vector.reshape([1, -1])
cur_params = cv.PCAProject(tmp, self.pca_shape_pyr[level],
self.eigenvectors_pyr[level],
self.eigenvalues_pyr[level])
for i in range(self.eigenvalues_pyr[level].shape[0]):
cur_params[0, i] *= (
self.eigenvalues[i, 0] / self.eigenvalues[i, 0] +
self.sigma2_pyr[level])
n_p = x.n_points
cur_trans.a = vec.vector.dot(x.vector) / x2
cur_trans.b = 0
for i in range(n_p):
cur_trans.b += x.get_point(i)[0] * vec.get_point(
i)[1] - x.get_point(i)[1] * vec.get_point(i)[0]
cur_trans.b /= x2
cur_trans.x_t = vec.get_x_mean()
cur_trans.y_t = vec.get_y_mean()
ii += 1
if ii == 20 or np.linalg.norm(last_params - cur_params) <= 1e-4:
break
fit_result = ASMFitResult(cur_params, cur_trans, self)
return fit_result
def fit(self, img, verbose):
"""
fits the model to given image
:param img: target image
:type img: numpy.ndarray
:param verbose: if the progress should be displayed
:type verbose: bool
:return: result of fitting
:rtype: ASMFitResult
"""
# make sure image is in greyscale
grey_img = img.copy()
if len(grey_img.shape) == 3:
grey_img = cv.cvtColor(grey_img, cv.COLOR_BGR2GRAY)
# scale down the image
ratio = math.sqrt(40000 / (grey_img.shape[0] * grey_img.shape[1]))
new_w = int(grey_img.shape[1] * ratio)
new_h = int(grey_img.shape[0] * ratio)
resized_img = cv.resize(grey_img, (new_w, new_h))
# create temporary search model image
cur_search = ModelImage()
cur_search.shape_info = self.shape_info
cur_search.image = resized_img
# create fit result object for search
params = np.zeros([1, self.eigenvalues.shape[0]])
sv = cur_search.shape_vector
sv.set_from_vector(self.project_param_to_shape(params)[0])
st = sv.get_shape_transform_fitting_size(resized_img.shape)
fit_result = ASMFitResult(params, st, self)
cur_search.build_from_shape_vector(st)
total_offset: int # sum of offsets of current iteration
shape_old = ShapeVector()
self.feature_extractor.load_image(resized_img)
if verbose:
cur_search.show(True, "resized image")
for level in range(self.pyramid_level - 1, -1, -1):
if verbose:
print(f"Pyramid level: {level}\n")
for run in range(10):
shape_old.set_from_points_array(
cur_search.points) # store old shape
total_offset = 0
best_ep = np.zeros((self.n_landmarks, 2), np.int)
# find best fit for every point
for i in range(self.n_landmarks):
if verbose:
print(f"Fitting point {i}\n")
cur_best = -1
best_i = 0
candidate_points, features = \
self.feature_extractor.get_candidates_with_feature(cur_search.points, i, level)
# select best candidate point with Mahalanobis distance
for j in range(len(candidate_points)):
x = np.zeros(len(features[j]))
for f, feature in enumerate(features[j]):
x[f] = feature
mean = self.mean_vec_pyr[level][i]
inv_cov = self.cov_mat_pyr_inv[level][i]
# ct = distance.mahalanobis(x, mean, inv_cov)
ct = cv.Mahalanobis(x, mean, inv_cov)
# if verbose:
# print(f"Mahalanobis distance: {ct}")
if ct < cur_best or cur_best < 0:
cur_best = ct
best_i = j
best_ep[i, 0] = candidate_points[j][0]
best_ep[i, 1] = candidate_points[j][1]
total_offset += abs(best_i)
# if :
# cur_search.show(True)
# modify results with factor of current pyramid level
for i in range(self.n_landmarks):
cur_search.points[i] = best_ep[i]
x = int(cur_search.points[i, 0])
cur_search.points[i, 0] = x << level
y = int(cur_search.points[i, 1])
cur_search.points[i, 1] = y << level
if level > 0:
cur_search.points[i, 0] += (1 << (level - 1))
cur_search.points[i, 1] += (1 << (level - 1))
cur_search.shape_vector.set_from_points_array(
cur_search.points)
# if verbose:
# cur_search.show(True)
# project found shape to PCA model and back to get parameters
fit_result = self.find_params_for_shape(
cur_search.shape_vector, shape_old, fit_result, level)
# apply limits to found params
for i, param in enumerate(fit_result.params[0]):
if param < self.params_limits[i, 0]:
fit_result.params[0, i] = self.params_limits[i, 0]
if param > self.params_limits[i, 1]:
fit_result.params[0, i] = self.params_limits[i, 1]
cur_search.shape_vector.set_from_vector(
cv.PCABackProject(fit_result.params,
self.pca_shape_pyr[level],
self.eigenvectors_pyr[level])[0])
cur_search.build_from_shape_vector(fit_result.similarity_trans)
avg_mov = total_offset / self.n_landmarks
if verbose:
print(f"Iteration: {run + 1}, Average offset: {avg_mov}\n")
cur_search.show(True, f"iteration {run + 1}")
if avg_mov < 1.3:
break
if verbose:
print(
f"Finished fitting after {run + 1} iterations, Average offset of last iteration: {avg_mov}\n"
)
cur_search.show(True, f"level {level} final fit")
st_ = SimilarityTransformation()
st_.a = 1 / ratio
fit_result.similarity_trans = st_.multiply(fit_result.similarity_trans)
return fit_result
# 0425.py
import cv2
import numpy as np
X = np.array([[0, 0, 0, 100, 100, 150, -100, -150],
[0, 50, -50, 0, 30, 100, -20, -100]],
dtype=np.float64)
X = X.transpose() # X = X.T
##mean = cv2.reduce(X, 0, cv2.REDUCE_AVG)
##print('mean = ', mean)
mean, eVects = cv2.PCACompute(X, mean=None)
print('mean = ', mean)
print('eVects = ', eVects)
Y = cv2.PCAProject(X, mean, eVects)
print('Y = ', Y)
X2 = cv2.PCABackProject(Y, mean, eVects)
print('X2 = ', X2)
print(np.allclose(X, X2))
cv2.waitKey()
cv2.destroyAllWindows()
def pca_reconstruct(terms, mean, eigenvecs):
return cv2.PCABackProject(terms, mean, eigenvecs.T)
