给定规定直方图如下:
| $z_q$ | $p_z(z_q)$ | $G(z_q)=\sum_{j = 0}^{q}p_z(z_j)$ |
| --- | --- | --- |
| $r_0 = 0$ | 0.000 | 0.000 |
| $r_1 = 1$ | 0.000 | 0.000 |
| $r_2 = 2$ | 0.000 | 0.000 |
| $r_3 = 3$ | 0.151 | 0.151 |
| $r_4 = 4$ | 0.202 | 0.353 |
| $r_5 = 5$ | 0.305 | 0.658 |
| $r_6 = 6$ | 0.206 | 0.864 |
| $r_7 = 7$ | 0.157 | 1.021 (近似为 1) |
假设存在一个输入图像,其直方图分布需要与上述规定直方图进行匹配。这里以一个简单的图像数据为例说明,假设输入图像的像素值如下(为简化,假设图像为 4x4 的灰度图像):
```plaintext
[
[3, 4, 3, 5],
[4, 5, 6, 3],
[5, 6, 7, 4],
[6, 7, 3, 5]
]
```
以下是使用 Python 实现直方图匹配的代码示例:
```python
import numpy as np
import cv2
import matplotlib.pyplot as plt
# 输入图像数据
input_image = np.array([
[3, 4, 3, 5],
[4, 5, 6, 3],
[5, 6, 7, 4],
[6, 7, 3, 5]
], dtype=np.uint8)
# 规定直方图
specified_hist = np.array([0.000, 0.000, 0.000, 0.151, 0.202, 0.305, 0.206, 0.157])
# 计算输入图像的直方图
hist_input = cv2.calcHist([input_image], [0], None, [8], [0, 8])
hist_input = hist_input.flatten() / (input_image.shape[0] * input_image.shape[1])
# 计算输入图像的累积分布函数 (CDF)
cdf_input = np.cumsum(hist_input)
# 计算规定直方图的累积分布函数 (CDF)
cdf_specified = np.cumsum(specified_hist)
# 创建映射表
mapping = np.zeros(8, dtype=np.uint8)
for i in range(8):
diff = np.abs(cdf_input[i] - cdf_specified)
mapping[i] = np.argmin(diff)
# 应用映射表到输入图像
matched_image = mapping[input_image]
# 输出结果
print("输入图像:")
print(input_image)
print("匹配后的图像:")
print(matched_image)
# 绘制直方图
plt.figure(figsize=(12, 4))
plt.subplot(131)
plt.bar(range(8), hist_input)
plt.title('Input Image Histogram')
plt.subplot(132)
plt.bar(range(8), specified_hist)
plt.title('Specified Histogram')
plt.subplot(133)
hist_matched = cv2.calcHist([matched_image], [0], None, [8], [0, 8])
hist_matched = hist_matched.flatten() / (matched_image.shape[0] * matched_image.shape[1])
plt.bar(range(8), hist_matched)
plt.title('Matched Image Histogram')
plt.show()
```
上述代码中,首先定义了输入图像和规定直方图。然后计算输入图像的直方图以及输入图像和规定直方图的累积分布函数(CDF)。接着,创建一个映射表,将输入图像的每个灰度级映射到规定直方图中最接近的灰度级。最后,应用这个映射表到输入图像上,得到匹配后的图像,并绘制输入图像、规定直方图和匹配后图像的直方图,以便直观观察匹配效果。