python高斯核函数_python 实现高斯核与卷积过程

1. 二维高斯核函数

参考链接：https://blog.csdn.net/qq_16013649/article/details/78784791

g(x, y, sigma) = exp(-(x**2+y**2)/(2*sigma**2))

2. 卷积过程

高斯模糊：

G(xi, yi, sigma）= img*kernel

3. code

# 高斯核函数

import numpy as np

def gauss(kernel_size, sigma):

kernel = np.zeros((kernel_size, kernel_size))

center = kernel_size//2

if sigma<=0:

sigma = ((kernel_size-1)*0.5-1)*0.3+0.8

s = sigma**2

sum_val = 0

for i in range(kernel_size):

for j in range(kernel_size):

x, y = i-center, j-center

kernel[i, j] = np.exp(-(x**2+y**2)/2*s)

sum_val += kernel[i, j]

kernel = kernel/sum_val

return kernel

gauss_kernel = gauss(3, 2)

import matplotlib.pyplot as plt

plt.imshow(gauss_kernel)

# cv2 filter

img = np.random.random([5,5])

import cv2

fl_cv = cv2.filter2D(img, -1, gauss_kernel)

plt.imshow(fl_cv)

# python

def conv_2d(kernel, img, mode='fill'):

if mode =='fill':

h = kernel.shape[0]//2

w = kernel.shape[1]//2

# opencv filter2d 默认采用reflect填充方式

# 前面测试了constant edge都不符合

img = np.pad(img, (h,w), 'reflect')

res_h = img.shape[0]-kernel.shape[0]+1

res_w = img.shape[1]-kernel.shape[1]+1

res = np.zeros((res_h, res_w))

dh = kernel.shape[0]

dw = kernel.shape[1]

for i in range(res_h):

for j in range(res_w):

res[i,j] = np.sum(img[i:i+dh, j:j+dw]*kernel)

return res

fl_py = conv_2d(gauss_kernel, img)

plt.imshow(fl_py)