def main():
"""Load image, apply filter, plot."""
img = data.camera()
# just like sobel, but no -2/+2 in the middle
prewitt_y = np.array([
[-1, -1, -1],
[0, 0, 0],
[1, 1, 1]
])
prewitt_x = np.rot90(prewitt_y) # rotates counter-clockwise
img_sx = signal.correlate(img, prewitt_x, mode="same")
img_sy = signal.correlate(img, prewitt_y, mode="same")
g_magnitude = np.sqrt(img_sx**2 + img_sy**2)
ground_truth = skifilters.prewitt(data.camera())
util.plot_images_grayscale(
[img, img_sx, img_sy, g_magnitude, ground_truth],
["Image", "Prewitt (x)", "Prewitt (y)", "Prewitt (both/magnitude)",
"Prewitt (Ground Truth)"]
)
def main():
"""Load image, apply sobel (to get x/y gradients), plot the results."""
img = data.camera()
sobel_y = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
sobel_x = np.rot90(sobel_y) # rotates counter-clockwise
# apply x/y sobel filter to get x/y gradients
img_sx = signal.correlate(img, sobel_x, mode="same")
img_sy = signal.correlate(img, sobel_y, mode="same")
# combine x/y gradients to gradient magnitude
# scikit-image's implementation divides by sqrt(2), not sure why
img_s = np.sqrt(img_sx ** 2 + img_sy ** 2) / np.sqrt(2)
# create binarized image
threshold = np.average(img_s)
img_s_bin = np.zeros(img_s.shape)
img_s_bin[img_s > threshold] = 1
# generate ground truth (scikit-image method)
ground_truth = skifilters.sobel(data.camera())
# plot
util.plot_images_grayscale(
[img, img_sx, img_sy, img_s, img_s_bin, ground_truth],
[
"Image",
"Sobel (x)",
"Sobel (y)",
"Sobel (magnitude)",
"Sobel (magnitude, binarized)",
"Sobel (Ground Truth)",
],
)
def main():
"""Load image, apply sobel (to get x/y gradients), plot the results."""
img = data.camera()
sobel_y = np.array([
[-1, -2, -1],
[0, 0, 0],
[1, 2, 1]
])
sobel_x = np.rot90(sobel_y) # rotates counter-clockwise
# apply x/y sobel filter to get x/y gradients
img_sx = signal.correlate(img, sobel_x, mode="same")
img_sy = signal.correlate(img, sobel_y, mode="same")
# combine x/y gradients to gradient magnitude
# scikit-image's implementation divides by sqrt(2), not sure why
img_s = np.sqrt(img_sx**2 + img_sy**2) / np.sqrt(2)
# create binarized image
threshold = np.average(img_s)
img_s_bin = np.zeros(img_s.shape)
img_s_bin[img_s > threshold] = 1
# generate ground truth (scikit-image method)
ground_truth = skifilters.sobel(data.camera())
# plot
util.plot_images_grayscale(
[img, img_sx, img_sy, img_s, img_s_bin, ground_truth],
["Image", "Sobel (x)", "Sobel (y)", "Sobel (magnitude)",
"Sobel (magnitude, binarized)", "Sobel (Ground Truth)"]
)
def main():
"""Load template image (needle) and the large example image (haystack),
generate matching score per pixel, plot the results."""
img_haystack = skiutil.img_as_float(data.camera()) # the image in which to search
img_needle = img_haystack[140:190, 220:270] # the template to search for
img_sad = np.zeros(img_haystack.shape) # score image
height_h, width_h = img_haystack.shape
height_n, width_n = img_needle.shape
# calculate score for each pixel
# stop iterating over pixels when the whole template cannot any more (i.e. stop
# at bottom and right border)
for y in range(height_h - height_n):
for x in range(width_h - width_n):
patch = img_haystack[y:y+height_n, x:x+width_n]
img_sad[y, x] = sad(img_needle, patch)
img_sad = img_sad / np.max(img_sad)
# add highest score to bottom and right borders
img_sad[height_h-height_n:, :] = np.max(img_sad[0:height_h, 0:width_h])
img_sad[:, width_h-width_n:] = np.max(img_sad[0:height_h, 0:width_h])
# plot results
util.plot_images_grayscale(
[img_haystack, img_needle, img_sad],
["Image", "Image (Search Template)", "Matching (darkest = best match)"]
)
def main():
"""Load image, apply filters and plot the results."""
img = data.moon()
util.plot_images_grayscale(
[img, median(img), morphological_edge(img),
erosion(img), dilation(img),
opening(img), closing(img)],
["Image", "Median", "Morphological Edge", "Erosion", "Dilation", "Opening", "Closing"]
)
def main():
"""Load image, calculate harris scores (window functions: matrix of ones, gauss)
and plot the results."""
img = data.checkerboard()
score_window = harris_ones(img, 7)
score_gauss = harris_gauss(img)
util.plot_images_grayscale(
[img, score_window, score_gauss, feature.corner_harris(img)],
["Image", "Harris-Score (ones)", "Harris-Score (gauss)", "Harris-Score (ground truth)"]
)
def main():
"""Load image, calculate optimal threshold, binarize, plot."""
# load image
img = data.coins()
height, width = img.shape
nb_pixels = height * width
# precalculate some values for speedup
# average pixel value
g_avg = np.average(img)
# P(pixel-value), i.e. #pixels-with-value / #all-pixels
p_g = [0] * 256
for g in range(0, 256):
p_g[g] = np.sum(img == g) / nb_pixels
# Otsu method
# calculations are based on standard formulas
q_best = None
threshold_best = None
img_bin_best = None
# iterate over all possible thresholds
for t in range(1, 255):
img_bin = np.zeros(img.shape)
img_bin[img >= t] = 1
p1 = np.sum(img_bin) / nb_pixels
p0 = 1 - p1
g0 = np.average(img[img_bin == 0]) if np.sum(img[img_bin == 0]) > 0 else 0
g1 = np.average(img[img_bin == 1]) if np.sum(img[img_bin == 1]) > 0 else 0
var0 = sum([(g-g0)**2 * p_g[g] for g in range(0, t+1)])
var1 = sum([(g-g1)**2 * p_g[g] for g in range(t+1, 256)])
var_between = p0 * (g0 - g_avg)**2 + p1 * (g1 - g_avg)**2
var_inner = p0 * var0**2 + p1 * var1**2
# q is the relation of variance between classes and variance within classes
q = var_between / var_inner if var_inner > 0 else 0
print(t, p0, p1, g0, g1, g_avg, var_between, var_inner, q)
if q_best is None or q_best < q:
q_best = q
threshold_best = t
img_bin_best = img <= t
# ground truth, based on scikit-image
gt_tresh = skifilters.threshold_otsu(img)
ground_truth = img <= gt_tresh
# plot
util.plot_images_grayscale(
[img, img_bin_best, ground_truth],
["Image", "Otsu", "Otsu (Ground Truth)"]
)
def main():
"""Load image, calculate optimal threshold, binarize, plot."""
# load image
img = data.coins()
height, width = img.shape
nb_pixels = height * width
# precalculate some values for speedup
# average pixel value
g_avg = np.average(img)
# P(pixel-value), i.e. #pixels-with-value / #all-pixels
p_g = [0] * 256
for g in range(0, 256):
p_g[g] = np.sum(img == g) / nb_pixels
# Otsu method
# calculations are based on standard formulas
q_best = None
threshold_best = None
img_bin_best = None
# iterate over all possible thresholds
for t in range(1, 255):
img_bin = np.zeros(img.shape)
img_bin[img >= t] = 1
p1 = np.sum(img_bin) / nb_pixels
p0 = 1 - p1
g0 = np.average(
img[img_bin == 0]) if np.sum(img[img_bin == 0]) > 0 else 0
g1 = np.average(
img[img_bin == 1]) if np.sum(img[img_bin == 1]) > 0 else 0
var0 = sum([(g - g0)**2 * p_g[g] for g in range(0, t + 1)])
var1 = sum([(g - g1)**2 * p_g[g] for g in range(t + 1, 256)])
var_between = p0 * (g0 - g_avg)**2 + p1 * (g1 - g_avg)**2
var_inner = p0 * var0**2 + p1 * var1**2
# q is the relation of variance between classes and variance within classes
q = var_between / var_inner if var_inner > 0 else 0
print(t, p0, p1, g0, g1, g_avg, var_between, var_inner, q)
if q_best is None or q_best < q:
q_best = q
threshold_best = t
img_bin_best = img <= t
# ground truth, based on scikit-image
gt_tresh = skifilters.threshold_otsu(img)
ground_truth = img <= gt_tresh
# plot
util.plot_images_grayscale([img, img_bin_best, ground_truth],
["Image", "Otsu", "Otsu (Ground Truth)"])
def main():
"""Load image, convert into graph, segment."""
img = data.camera()
# worked decently for 32x32, not so well and slow for 64x64
img = misc.imresize(img, (32, 32))
graph = image_to_graph(img)
# Merge subgraphs until convergence
converged = False
while not converged:
print("Merging (%d subgraphs left)..." % (len(graph.subgraphs)))
converged = True
merged = []
ediffs = graph.get_ediffs()
# Iterate over all pairs subgraphs that have a connecting edge
# Merge them if possible.
# Do not stop after the first merge, so that we don't have to
# recalculate the external differences between subgraphs many times
for subgraph_a, subgraph_b, ediff in ediffs:
# Try to merge the subgraphs to one subgraph
if subgraph_a not in merged and subgraph_b not in merged:
idiff_a = subgraph_a.get_internal_difference()
idiff_b = subgraph_b.get_internal_difference()
# Merge if externel difference (between two subgraphs)
# is below both internal differences
if ediff < K * idiff_a and ediff < K * idiff_b:
graph.merge_subgraphs(subgraph_a, subgraph_b)
merged.extend([subgraph_a, subgraph_b])
converged = False
print("Found %d segments" % (len(graph.subgraphs)))
# Create images of segments
subgraphs = sorted(graph.subgraphs,
key=lambda sg: len(sg.nodes),
reverse=True)
nb_segments = 8
segment_images = []
segment_titles = []
for i in range(min(nb_segments, len(subgraphs))):
segment_titles.append("Segment %d/%d" % (i, len(subgraphs)))
segment_image = np.zeros(img.shape)
for node in subgraphs[i].nodes:
segment_image[node.y, node.x] = 255
segment_images.append(segment_image)
# plot images
images = [img]
images.extend(segment_images)
titles = ["Image"]
titles.extend(segment_titles)
util.plot_images_grayscale(images, titles)
def main():
"""Load image, calculate harris scores (window functions: matrix of ones, gauss)
and plot the results."""
img = data.checkerboard()
score_window = harris_ones(img, 7)
score_gauss = harris_gauss(img)
util.plot_images_grayscale(
[img, score_window, score_gauss,
feature.corner_harris(img)], [
"Image", "Harris-Score (ones)", "Harris-Score (gauss)",
"Harris-Score (ground truth)"
])
def main():
"""Apply several gaussian filters one by one and plot the results each time."""
img = data.checkerboard()
shapes = [(5, 5), (7, 7), (11, 11), (17, 17), (31, 31)]
sigmas = [0.5, 1.0, 2.0, 4.0, 8.0]
smoothed = []
for shape, sigma in zip(shapes, sigmas):
smoothed = apply_gauss(img, gaussian_kernel(shape, sigma=sigma))
ground_truth = filters.gaussian_filter(img, sigma)
util.plot_images_grayscale([img, smoothed, ground_truth], [
"Image",
"After gauss (sigma=%.1f)" % (sigma), "Ground Truth (scipy)"
])
def main():
"""Apply several gaussian filters one by one and plot the results each time."""
img = data.checkerboard()
shapes = [(5, 5), (7, 7), (11, 11), (17, 17), (31, 31)]
sigmas = [0.5, 1.0, 2.0, 4.0, 8.0]
smoothed = []
for shape, sigma in zip(shapes, sigmas):
smoothed = apply_gauss(img, gaussian_kernel(shape, sigma=sigma))
ground_truth = filters.gaussian_filter(img, sigma)
util.plot_images_grayscale(
[img, smoothed, ground_truth],
["Image", "After gauss (sigma=%.1f)" % (sigma), "Ground Truth (scipy)"]
)
def main():
"""Load image, convert into graph, segment."""
img = data.camera()
# worked decently for 32x32, not so well and slow for 64x64
img = misc.imresize(img, (32, 32))
graph = image_to_graph(img)
# Merge subgraphs until convergence
converged = False
while not converged:
print("Merging (%d subgraphs left)..." % (len(graph.subgraphs)))
converged = True
merged = []
ediffs = graph.get_ediffs()
# Iterate over all pairs subgraphs that have a connecting edge
# Merge them if possible.
# Do not stop after the first merge, so that we don't have to
# recalculate the external differences between subgraphs many times
for subgraph_a, subgraph_b, ediff in ediffs:
# Try to merge the subgraphs to one subgraph
if subgraph_a not in merged and subgraph_b not in merged:
idiff_a = subgraph_a.get_internal_difference()
idiff_b = subgraph_b.get_internal_difference()
# Merge if externel difference (between two subgraphs)
# is below both internal differences
if ediff < K * idiff_a and ediff < K * idiff_b:
graph.merge_subgraphs(subgraph_a, subgraph_b)
merged.extend([subgraph_a, subgraph_b])
converged = False
print("Found %d segments" % (len(graph.subgraphs)))
# Create images of segments
subgraphs = sorted(graph.subgraphs, key=lambda sg: len(sg.nodes), reverse=True)
nb_segments = 8
segment_images = []
segment_titles = []
for i in range(min(nb_segments, len(subgraphs))):
segment_titles.append("Segment %d/%d" % (i, len(subgraphs)))
segment_image = np.zeros(img.shape)
for node in subgraphs[i].nodes:
segment_image[node.y, node.x] = 255
segment_images.append(segment_image)
# plot images
images = [img]
images.extend(segment_images)
titles = ["Image"]
titles.extend(segment_titles)
util.plot_images_grayscale(images, titles)
def main():
"""Initialize kernel, apply it to an image (via crosscorrelation, convolution)."""
img = data.camera()
kernel = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
cc_response = crosscorrelate(img, kernel)
cc_gt = signal.correlate(img, kernel, mode="same")
conv_response = convolve(img, kernel)
conv_gt = signal.convolve(img, kernel, mode="same")
util.plot_images_grayscale(
[img, cc_response, cc_gt, conv_response, conv_gt], [
"Image", "Cross-Correlation", "Cross-Correlation (Ground Truth)",
"Convolution", "Convolution (Ground Truth)"
])
def main():
"""Load example faces, extract principal components, create Eigenfaces from
PCs, plot results."""
# load images, resize them, convert to 1D-vectors
images_filepaths = get_images_in_directory("images/faces/")
images = [ndimage.imread(fp, flatten=True) for fp in images_filepaths]
images = [misc.imresize(image, (SCALE, SCALE)) for image in images]
images_vecs = np.array([image.flatten() for image in images])
# ------------
# Custom Implementation of PCA
# ------------
pcs, images_vecs_transformed, images_vecs_reversed = custom_pca(images_vecs, NB_COMPONENTS)
pcs = pcs.reshape((NB_COMPONENTS, SCALE, SCALE))
# plot (First example image, recovered first example image, first 8 PCs)
plots_imgs = [images[0], images_vecs_reversed[0].reshape((SCALE, SCALE))]
plots_titles = ["Image 0", "Image 0\n(reconstructed)"]
for i in range(NB_COMPONENTS):
plots_imgs.append(pcs[i])
plots_titles.append("Eigenface %d" % (i))
util.plot_images_grayscale(plots_imgs, plots_titles)
# ------------
# Using the PCA implementation from scikit
# ------------
# train PCA, embed image vectors, reverse the embedding (lossy)
pca = PCA(NB_COMPONENTS)
images_vecs_transformed = pca.fit_transform(images_vecs)
images_vecs_reversed = pca.inverse_transform(images_vecs_transformed)
# Extract Eigenfaces. The Eigenfaces are the principal components.
pcs = pca.components_.reshape((NB_COMPONENTS, SCALE, SCALE))
# plot (First example image, recovered first example image, first 8 PCs)
plots_imgs = [images[0], images_vecs_reversed[0].reshape((SCALE, SCALE))]
plots_titles = ["Image 0", "Image 0\n(reconstructed)"]
for i in range(NB_COMPONENTS):
plots_imgs.append(pcs[i])
plots_titles.append("Eigenface %d" % (i))
util.plot_images_grayscale(plots_imgs, plots_titles)
def main():
"""Create a noisy line image, recover the line via hough transform and
plot an unnoise image with that line."""
# generate example image (noisy lines)
img = np.zeros((128, 128))
for y in range(12, 120):
img[y, y] = 1
for y in range(40, 75):
img[y, 12] = 1
for x in range(16, 64):
img[int(10 + x*0.2), x] = 1
img = (img * 100) + np.random.binomial(80, 0.5, (img.shape))
accumulator, local_maxima, img_hough = hough(img, 5)
util.plot_images_grayscale(
[img, accumulator, local_maxima, img_hough],
["Image", "Accumulator content", "Local Maxima", "Line from Hough Transform"]
)
def main():
"""Create a noisy line image, recover the line via hough transform and
plot an unnoise image with that line."""
# generate example image (noisy lines)
img = np.zeros((128, 128))
for y in range(12, 120):
img[y, y] = 1
for y in range(40, 75):
img[y, 12] = 1
for x in range(16, 64):
img[int(10 + x * 0.2), x] = 1
img = (img * 100) + np.random.binomial(80, 0.5, (img.shape))
accumulator, local_maxima, img_hough = hough(img, 5)
util.plot_images_grayscale([img, accumulator, local_maxima, img_hough], [
"Image", "Accumulator content", "Local Maxima",
"Line from Hough Transform"
])
def main():
"""Load image, compute derivatives, plot."""
img = data.camera()
imgy_np, imgx_np = np.gradient(img)
imgx_ski, imgy_ski = _compute_derivatives(img)
# dx
util.plot_images_grayscale(
[img, dx_symmetric(img), dx_forward(img), dx_backward(img), imgx_np, imgx_ski],
["Image", "dx (symmetric)", "dx (forward)", "dx (backward)",
"Ground Truth (numpy)", "Ground Truth (scikit-image)"]
)
# dy
util.plot_images_grayscale(
[img, dy_symmetric(img), dy_forward(img), dy_backward(img), imgy_np, imgy_ski],
["Image", "dy (symmetric)", "dy (forward)", "dy (backward)",
"Ground Truth (numpy)", "Ground Truth (scikit-image)"]
)
def main():
"""Initialize kernel, apply it to an image (via crosscorrelation, convolution)."""
img = data.camera()
kernel = np.array([
[-1, -2, -1],
[0, 0, 0],
[1, 2, 1]
])
cc_response = crosscorrelate(img, kernel)
cc_gt = signal.correlate(img, kernel, mode="same")
conv_response = convolve(img, kernel)
conv_gt = signal.convolve(img, kernel, mode="same")
util.plot_images_grayscale(
[img, cc_response, cc_gt, conv_response, conv_gt],
["Image", "Cross-Correlation", "Cross-Correlation (Ground Truth)", "Convolution", "Convolution (Ground Truth)"]
)
def main():
"""Main function."""
img = np.zeros((128, 128), dtype=np.uint8)
img[0, 0:15] = 255
img[5:10, 5:10] = 255
img[64:71, 64:71] = 255
img[72:75, 72] = 255
img[91:95, 24:29] = 255
img[91:92, 29:31] = 255
img[30:60, 40:80] = 255
img[10:70, 100:102] = 255
img[50:60, 98:100] = 255
img[15, 20:100] = 255
img[90:110, 80:120] = 255
img[80:120, 90:110] = 255
img[100:105, 100:105] = 0
util.plot_images_grayscale(
[img, dilation(img), erosion(img), opening(img), closing(img)],
["Binary Image", "Binary Dilation", "Binary Erosion", "Binary Opening", "Binary Closing"]
)
def main():
"""Load image, apply Canny, plot."""
img = skiutil.img_as_float(data.camera())
img = filters.gaussian_filter(img, sigma=1.0)
sobel_y = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
sobel_x = np.rot90(sobel_y) # rotates counter-clockwise
img_sx = signal.correlate(img, sobel_x, mode="same")
img_sy = signal.correlate(img, sobel_y, mode="same")
g_magnitudes = np.sqrt(img_sx ** 2 + img_sy ** 2) / np.sqrt(2)
g_orientations = np.arctan2(img_sy, img_sx)
g_mag_nonmax = non_maximum_suppression(g_magnitudes, g_orientations)
canny = hysteresis(g_mag_nonmax, 0.35, 0.05)
ground_truth = feature.canny(data.camera())
util.plot_images_grayscale(
[img, g_magnitudes, g_mag_nonmax, canny, ground_truth],
["Image", "After Sobel", "After nonmax", "Canny", "Canny (Ground Truth)"],
)
def main():
"""Load image, apply Canny, plot."""
img = skiutil.img_as_float(data.camera())
img = filters.gaussian_filter(img, sigma=1.0)
sobel_y = np.array([[-1, -2, -1], [0, 0, 0], [1, 2, 1]])
sobel_x = np.rot90(sobel_y) # rotates counter-clockwise
img_sx = signal.correlate(img, sobel_x, mode="same")
img_sy = signal.correlate(img, sobel_y, mode="same")
g_magnitudes = np.sqrt(img_sx**2 + img_sy**2) / np.sqrt(2)
g_orientations = np.arctan2(img_sy, img_sx)
g_mag_nonmax = non_maximum_suppression(g_magnitudes, g_orientations)
canny = hysteresis(g_mag_nonmax, 0.35, 0.05)
ground_truth = feature.canny(data.camera())
util.plot_images_grayscale(
[img, g_magnitudes, g_mag_nonmax, canny, ground_truth], [
"Image", "After Sobel", "After nonmax", "Canny",
"Canny (Ground Truth)"
])
