Sliding window histogram¶
Histogram matching can be used for object detection in images 1. This
example extracts a single coin from the
skimage.data.coins image and uses
histogram matching to attempt to locate it within the original image.
First, a box-shaped region of the image containing the target coin is extracted and a histogram of its greyscale values is computed.
Next, for each pixel in the test image, a histogram of the greyscale values in
a region of the image surrounding the pixel is computed.
skimage.filters.rank.windowed_histogram is used for this task, as it employs
an efficient sliding window based algorithm that is able to compute these
histograms quickly 2. The local histogram for the region surrounding each
pixel in the image is compared to that of the single coin, with a similarity
measure being computed and displayed.
The histogram of the single coin is computed using
numpy.histogram on a box
shaped region surrounding the coin, while the sliding window histograms are
computed using a disc shaped structural element of a slightly different size.
This is done in aid of demonstrating that the technique still finds similarity
in spite of these differences.
To demonstrate the rotational invariance of the technique, the same test is performed on a version of the coins image rotated by 45 degrees.
Porikli, F. “Integral Histogram: A Fast Way to Extract Histograms in Cartesian Spaces” CVPR, 2005. Vol. 1. IEEE, 2005
S.Perreault and P.Hebert. Median filtering in constant time. Trans. Image Processing, 16(9):2389-2394, 2007.
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:coin_coords, coin_coords:coin_coords] # 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) # 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) 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()
Total running time of the script: ( 0 minutes 2.146 seconds)