Python 2.x 中两个图像的直方图匹配？

Question

我正在尝试匹配两个图像的直方图（在 MATLAB 中，这可以使用 imhistmatch 完成）。标准 Python 库是否提供等效函数？我看过 OpenCV、scipy 和 numpy，但没有看到任何类似的功能。

Answer 1

我之前写了一个答案here，解释了如何对图像直方图进行分段线性插值，以强制执行特定的高光/中间调/阴影比率。

两个图像之间的histogram matching 具有相同的基本原则。本质上，您计算源图像和模板图像的累积直方图，然后进行线性插值以找到模板图像中与源图像中唯一像素值的分位数最接近的唯一像素值：

import numpy as np

def hist_match(source, template):
    """
    Adjust the pixel values of a grayscale image such that its histogram
    matches that of a target image

    Arguments:
    -----------
        source: np.ndarray
            Image to transform; the histogram is computed over the flattened
            array
        template: np.ndarray
            Template image; can have different dimensions to source
    Returns:
    -----------
        matched: np.ndarray
            The transformed output image
    """

    oldshape = source.shape
    source = source.ravel()
    template = template.ravel()

    # get the set of unique pixel values and their corresponding indices and
    # counts
    s_values, bin_idx, s_counts = np.unique(source, return_inverse=True,
                                            return_counts=True)
    t_values, t_counts = np.unique(template, return_counts=True)

    # take the cumsum of the counts and normalize by the number of pixels to
    # get the empirical cumulative distribution functions for the source and
    # template images (maps pixel value --> quantile)
    s_quantiles = np.cumsum(s_counts).astype(np.float64)
    s_quantiles /= s_quantiles[-1]
    t_quantiles = np.cumsum(t_counts).astype(np.float64)
    t_quantiles /= t_quantiles[-1]

    # interpolate linearly to find the pixel values in the template image
    # that correspond most closely to the quantiles in the source image
    interp_t_values = np.interp(s_quantiles, t_quantiles, t_values)

    return interp_t_values[bin_idx].reshape(oldshape)

例如：

from matplotlib import pyplot as plt
from scipy.misc import lena, ascent

source = lena()
template = ascent()
matched = hist_match(source, template)

def ecdf(x):
    """convenience function for computing the empirical CDF"""
    vals, counts = np.unique(x, return_counts=True)
    ecdf = np.cumsum(counts).astype(np.float64)
    ecdf /= ecdf[-1]
    return vals, ecdf

x1, y1 = ecdf(source.ravel())
x2, y2 = ecdf(template.ravel())
x3, y3 = ecdf(matched.ravel())

fig = plt.figure()
gs = plt.GridSpec(2, 3)
ax1 = fig.add_subplot(gs[0, 0])
ax2 = fig.add_subplot(gs[0, 1], sharex=ax1, sharey=ax1)
ax3 = fig.add_subplot(gs[0, 2], sharex=ax1, sharey=ax1)
ax4 = fig.add_subplot(gs[1, :])
for aa in (ax1, ax2, ax3):
    aa.set_axis_off()

ax1.imshow(source, cmap=plt.cm.gray)
ax1.set_title('Source')
ax2.imshow(template, cmap=plt.cm.gray)
ax2.set_title('template')
ax3.imshow(matched, cmap=plt.cm.gray)
ax3.set_title('Matched')

ax4.plot(x1, y1 * 100, '-r', lw=3, label='Source')
ax4.plot(x2, y2 * 100, '-k', lw=3, label='Template')
ax4.plot(x3, y3 * 100, '--r', lw=3, label='Matched')
ax4.set_xlim(x1[0], x1[-1])
ax4.set_xlabel('Pixel value')
ax4.set_ylabel('Cumulative %')
ax4.legend(loc=5)

对于一对 RGB 图像，您可以将此函数分别应用于每个通道。根据您要达到的效果，您可能希望首先将图像转换为不同的色彩空间。例如，你可以转换成HSV space，然后如果你想匹配亮度而不是色调或饱和度，则只在V通道上进行匹配。

Answer 2

我想对上面写的两个解决方案添加一个小的补充。如果有人打算将其作为全局函数（例如灰度图像），最好将最终匹配的数组转换为其相应的格式（numpy.uint8）。这可能有助于将来的图像转换而不会产生冲突。

def hist_norm(source, template):

    olddtype = source.dtype
    oldshape = source.shape
    source = source.ravel()
    template = template.ravel()

    s_values, bin_idx, s_counts = np.unique(source, return_inverse=True,
                                            return_counts=True)
    t_values, t_counts = np.unique(template, return_counts=True)
    s_quantiles = np.cumsum(s_counts).astype(np.float64)
    s_quantiles /= s_quantiles[-1]
    t_quantiles = np.cumsum(t_counts).astype(np.float64)
    t_quantiles /= t_quantiles[-1]
    interp_t_values = np.interp(s_quantiles, t_quantiles, t_values)
    interp_t_values = interp_t_values.astype(olddtype)

    return interp_t_values[bin_idx].reshape(oldshape)

Answer 3

这是另一个基于this 和scikit-image exposure 的cumulative_distribution 函数的实现，它使用np.interp，类似于ali_m 的实现。假设输入和模板图像是灰度的，像素值是 [0,255] 中的整数。

from skimage.exposure import cumulative_distribution
import matplotlib.pylab as plt
import numpy as np

def cdf(im):
 '''
 computes the CDF of an image im as 2D numpy ndarray
 '''
 c, b = cumulative_distribution(im) 
 # pad the beginning and ending pixels and their CDF values
 c = np.insert(c, 0, [0]*b[0])
 c = np.append(c, [1]*(255-b[-1]))
 return c

def hist_matching(c, c_t, im):
 '''
 c: CDF of input image computed with the function cdf()
 c_t: CDF of template image computed with the function cdf()
 im: input image as 2D numpy ndarray
 returns the modified pixel values
 ''' 
 pixels = np.arange(256)
 # find closest pixel-matches corresponding to the CDF of the input image, given the value of the CDF H of   
 # the template image at the corresponding pixels, s.t. c_t = H(pixels) <=> pixels = H-1(c_t)
 new_pixels = np.interp(c, c_t, pixels) 
 im = (np.reshape(new_pixels[im.ravel()], im.shape)).astype(np.uint8)
 return im

输出如下图：