滑动窗口直方图

直方图匹配可以用于图像中的目标检测 [1]。这个例子从 skimage.data.coins 图像中提取一枚硬币，并使用直方图匹配尝试在原始图像中定位它。

首先，提取图像中包含目标硬币的矩形区域，并计算其灰度值的直方图。

接下来，对于测试图像中的每个像素，计算围绕该像素的图像区域中的灰度值直方图。skimage.filters.rank.windowed_histogram 用于此任务，因为它采用基于高效滑动窗口的算法，能够快速计算这些直方图 [2]。图像中每个像素周围的局部直方图与单个硬币的直方图进行比较，计算并显示相似度度量。

单个硬币的直方图是使用 numpy.histogram 在一个围绕硬币的矩形区域内计算的，而滑动窗口直方图则是使用一个稍有不同大小的圆形结构元素计算的。这样做是为了证明尽管存在这些差异，该技术仍然能找到相似性。

为了演示该技术的旋转不变性，对旋转了45度的硬币图像版本进行了相同的测试。

参考文献

[1]

Porikli, F. “积分直方图：在笛卡尔空间中提取直方图的快速方法” CVPR, 2005. 第1卷. IEEE, 2005

[2]

S.Perreault 和 P.Hebert. 恒定时间的中值滤波。图像处理汇刊, 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, footprint, reference_hist, n_bins):
    # Compute normalized windowed histogram feature vector for each pixel
    px_histograms = rank.windowed_histogram(image, footprint, 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.inf
    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 grayscale; 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.
# Coordinate 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.
footprint = disk(30)

# Compute the similarity across the complete image
similarity = windowed_histogram_similarity(
    quantized_img, footprint, 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, footprint, 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()