Sliding window histogram

 import numpy as np

import matplotlib import matplotlib.pyplot as plt from skimage import data, transform from skimage.util import img_as_ubyte from skimage.morphology import disk from skimage.filters import rank matplotlib.rcParams['font.size'] = 9 def windowed_histogram_similarity(image, selem, reference_hist, n_bins): # Compute normalized windowed histogram feature vector for each pixel px_histograms = rank.windowed_histogram(image, selem, n_bins=n_bins) # Reshape coin histogram to (1,1,N) for broadcast when we want to use it in # arithmetic operations with the windowed histograms from the image reference_hist = reference_hist.reshape((1, 1) + reference_hist.shape) # Compute Chi squared distance metric: sum((X-Y)^2 / (X+Y)); # a measure of distance between histograms X = px_histograms Y = reference_hist num = (X - Y) ** 2 denom = X + Y denom[denom == 0] = np.infty frac = num / denom chi_sqr = 0.5 * np.sum(frac, axis=2) # Generate a similarity measure. It needs to be low when distance is high # and high when distance is low; taking the reciprocal will do this. # Chi squared will always be >= 0, add small value to prevent divide by 0. similarity = 1 / (chi_sqr + 1.0e-4) return similarity # Load the `skimage.data.coins` image img = img_as_ubyte(data.coins()) # Quantize to 16 levels of greyscale; this way the output image will have a # 16-dimensional feature vector per pixel quantized_img = img // 16 # Select the coin from the 4th column, second row. # Co-ordinate ordering: [x1,y1,x2,y2] coin_coords = [184, 100, 228, 148] # 44 x 44 region coin = quantized_img[coin_coords[1]:coin_coords[3], coin_coords[0]:coin_coords[2]] # Compute coin histogram and normalize coin_hist, _ = np.histogram(coin.flatten(), bins=16, range=(0, 16)) coin_hist = coin_hist.astype(float) / np.sum(coin_hist) # Compute a disk shaped mask that will define the shape of our sliding window # Example coin is ~44px across, so make a disk 61px wide (2 * rad + 1) to be # big enough for other coins too. selem = disk(30) # Compute the similarity across the complete image similarity = windowed_histogram_similarity(quantized_img, selem, coin_hist, coin_hist.shape[0]) # Now try a rotated image rotated_img = img_as_ubyte(transform.rotate(img, 45.0, resize=True)) # Quantize to 16 levels as before quantized_rotated_image = rotated_img // 16 # Similarity on rotated image rotated_similarity = windowed_histogram_similarity(quantized_rotated_image, selem, coin_hist, coin_hist.shape[0]) fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10)) axes[0, 0].imshow(quantized_img, cmap='gray') axes[0, 0].set_title('Quantized image') axes[0, 0].axis('off') axes[0, 1].imshow(coin, cmap='gray') axes[0, 1].set_title('Coin from 2nd row, 4th column') axes[0, 1].axis('off') axes[1, 0].imshow(img, cmap='gray') axes[1, 0].imshow(similarity, cmap='hot', alpha=0.5) axes[1, 0].set_title('Original image with overlaid similarity') axes[1, 0].axis('off') axes[1, 1].imshow(rotated_img, cmap='gray') axes[1, 1].imshow(rotated_similarity, cmap='hot', alpha=0.5) axes[1, 1].set_title('Rotated image with overlaid similarity') axes[1, 1].axis('off') plt.tight_layout() plt.show()

Share on :

Tweet