局部直方图均衡化

此示例使用一种称为 局部直方图均衡化 的方法来增强低对比度图像，该方法在图像中分散最频繁的强度值。

均衡化后的图像 [1] 对于每个像素邻域具有大致线性的累积分布函数。

直方图均衡化的本地版本 [2] 强调了每个局部灰度级的变化。

这些算法可以用于2D和3D图像。

参考文献

[1]

https://zh.wikipedia.org/wiki/%E7%9B%B4%E6%96%B9%E5%9B%BE%E5%9D%87%E8%A1%A1%E5%8C%96

[2]

https://en.wikipedia.org/wiki/自适应直方图均衡化

import numpy as np
import matplotlib
import matplotlib.pyplot as plt

from skimage import data
from skimage.util.dtype import dtype_range
from skimage.util import img_as_ubyte
from skimage import exposure
from skimage.morphology import disk
from skimage.morphology import ball
from skimage.filters import rank


matplotlib.rcParams['font.size'] = 9


def plot_img_and_hist(image, axes, bins=256):
    """Plot an image along with its histogram and cumulative histogram."""
    ax_img, ax_hist = axes
    ax_cdf = ax_hist.twinx()

    # Display image
    ax_img.imshow(image, cmap=plt.cm.gray)
    ax_img.set_axis_off()

    # Display histogram
    ax_hist.hist(image.ravel(), bins=bins)
    ax_hist.ticklabel_format(axis='y', style='scientific', scilimits=(0, 0))
    ax_hist.set_xlabel('Pixel intensity')

    xmin, xmax = dtype_range[image.dtype.type]
    ax_hist.set_xlim(xmin, xmax)

    # Display cumulative distribution
    img_cdf, bins = exposure.cumulative_distribution(image, bins)
    ax_cdf.plot(bins, img_cdf, 'r')

    return ax_img, ax_hist, ax_cdf


# Load an example image
img = img_as_ubyte(data.moon())

# Global equalize
img_rescale = exposure.equalize_hist(img)

# Equalization
footprint = disk(30)
img_eq = rank.equalize(img, footprint=footprint)


# Display results
fig = plt.figure(figsize=(8, 5))
axes = np.zeros((2, 3), dtype=object)
axes[0, 0] = plt.subplot(2, 3, 1)
axes[0, 1] = plt.subplot(2, 3, 2, sharex=axes[0, 0], sharey=axes[0, 0])
axes[0, 2] = plt.subplot(2, 3, 3, sharex=axes[0, 0], sharey=axes[0, 0])
axes[1, 0] = plt.subplot(2, 3, 4)
axes[1, 1] = plt.subplot(2, 3, 5)
axes[1, 2] = plt.subplot(2, 3, 6)

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img, axes[:, 0])
ax_img.set_title('Low contrast image')
ax_hist.set_ylabel('Number of pixels')

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img_rescale, axes[:, 1])
ax_img.set_title('Global equalise')

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img_eq, axes[:, 2])
ax_img.set_title('Local equalize')
ax_cdf.set_ylabel('Fraction of total intensity')


# prevent overlap of y-axis labels
fig.tight_layout()

3D 均衡

3D 体积也可以以类似的方式进行均衡化。这里，直方图是从整个 3D 图像中收集的，但仅显示单个切片以供视觉检查。

matplotlib.rcParams['font.size'] = 9


def plot_img_and_hist(image, axes, bins=256):
    """Plot an image along with its histogram and cumulative histogram."""
    ax_img, ax_hist = axes
    ax_cdf = ax_hist.twinx()

    # Display Slice of Image
    ax_img.imshow(image[0], cmap=plt.cm.gray)
    ax_img.set_axis_off()

    # Display histogram
    ax_hist.hist(image.ravel(), bins=bins)
    ax_hist.ticklabel_format(axis='y', style='scientific', scilimits=(0, 0))
    ax_hist.set_xlabel('Pixel intensity')

    xmin, xmax = dtype_range[image.dtype.type]
    ax_hist.set_xlim(xmin, xmax)

    # Display cumulative distribution
    img_cdf, bins = exposure.cumulative_distribution(image, bins)
    ax_cdf.plot(bins, img_cdf, 'r')

    return ax_img, ax_hist, ax_cdf


# Load an example image
img = img_as_ubyte(data.brain())

# Global equalization
img_rescale = exposure.equalize_hist(img)

# Local equalization
neighborhood = ball(3)
img_eq = rank.equalize(img, footprint=neighborhood)

# Display results
fig, axes = plt.subplots(2, 3, figsize=(8, 5))
axes[0, 1] = plt.subplot(2, 3, 2, sharex=axes[0, 0], sharey=axes[0, 0])
axes[0, 2] = plt.subplot(2, 3, 3, sharex=axes[0, 0], sharey=axes[0, 0])

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img, axes[:, 0])
ax_img.set_title('Low contrast image')
ax_hist.set_ylabel('Number of pixels')

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img_rescale, axes[:, 1])
ax_img.set_title('Global equalize')

ax_img, ax_hist, ax_cdf = plot_img_and_hist(img_eq, axes[:, 2])
ax_img.set_title('Local equalize')
ax_cdf.set_ylabel('Fraction of total intensity')


# prevent overlap of y-axis labels
fig.tight_layout()
plt.show()