基于Zernike矩的亚像素边缘检测 python
时间: 2023-10-14 08:07:47 浏览: 131
以下是基于Zernike矩的亚像素边缘检测的Python代码示例:
```python
import cv2
import numpy as np
from scipy.special import comb
from scipy.special import factorial
def zernike_moments(img, degree):
# 计算Zernike矩
moments = []
rows, cols = img.shape
x, y = np.meshgrid(np.arange(cols), np.arange(rows))
radius = np.sqrt((2 * x - cols + 1) ** 2 + (2 * y - rows + 1) ** 2) / rows
theta = np.arctan2(2 * y - rows + 1, 2 * x - cols + 1)
for n in range(degree + 1):
for m in range(n + 1):
if (n - m) % 2 == 0:
R_nm = np.zeros_like(radius)
R_nm[radius <= 1] = zernike_radial(n, m, radius[radius <= 1])
moments.append(np.sum(img * R_nm * np.exp(-1j * m * theta)) / np.sum(R_nm ** 2))
return moments
def zernike_radial(n, m, r):
# 计算Zernike径向函数
if (n - m) % 2 != 0 or abs(m) > n:
return np.zeros_like(r)
if n == 0:
return np.ones_like(r)
elif n == 1:
if m == 1:
return 2 * r
elif m == 0:
return np.sqrt(2) * (2 * r - 1)
else:
return np.sqrt(2) * (2 * r - 1)
else:
k = (n - m) // 2
s = 0
for i in range(k + 1):
s += ((-1) ** i * comb(n - i, k - i) * comb(n - 2 * k + i, k - i) * r ** (n - 2 * i))
return s * np.sqrt(factorial(n - m) / (factorial(n + m) * np.pi))
def subpixel_edge_detection(img, degree, threshold):
# 亚像素边缘检测
moments = zernike_moments(img, degree)
rows, cols = img.shape
x, y = np.meshgrid(np.arange(cols), np.arange(rows))
radius = np.sqrt((2 * x - cols + 1) ** 2 + (2 * y - rows + 1) ** 2) / rows
theta = np.arctan2(2 * y - rows + 1, 2 * x - cols + 1)
edges = np.zeros_like(img)
for n in range(degree + 1):
for m in range(n + 1):
if (n - m) % 2 == 0:
if abs(moments[n * (n + 1) // 2 + m]) > threshold:
R_nm = np.zeros_like(radius)
R_nm[radius <= 1] = zernike_radial(n, m, radius[radius <= 1])
edges += np.real(moments[n * (n + 1) // 2 + m] * R_nm * np.exp(1j * m * theta))
return edges / np.max(edges)
# 示例用法
img = cv2.imread('image.jpg', 0)
edges = subpixel_edge_detection(img, degree=10, threshold=0.1)
cv2.imshow('Edges', edges)
cv2.waitKey(0)
cv2.destroyAllWindows()
```
在代码中,`zernike_moments`函数用于计算Zernike矩,`zernike_radial`函数用于计算Zernike径向函数,`subpixel_edge_detection`函数用于进行亚像素边缘检测。在示例用法中,读取一张灰度图像,然后调用`subpixel_edge_detection`函数进行亚像素边缘检测。`degree`参数指定Zernike矩的阶数,`threshold`参数指定阈值,用于筛选Zernike矩。最后显示边缘检测结果。
相关推荐
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![rar](https://img-home.csdnimg.cn/images/20210720083606.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)