(只剩下常数没有x,y是因为在相减的过程中把x，y抵消掉了)

：

<img src="https://pic2.zhimg.com/v2-b39cae58ca1a5f39c46ac5ba918787f5_b.png" data-rawwidth="349" data-rawheight="147" class="content_image" width="349">

(这里取sigma为1.0)

归一化就得到高！斯！掩！膜！了：

<img src="https://pic1.zhimg.com/v2-0d1b6a4c714641309b05a89343425cac_b.png" data-rawwidth="305" data-rawheight="146" class="content_image" width="305">

所以你看，高斯掩膜的求解与位置(x,y)无关，因为在计算过程中x,y被抵消掉了，

因！此！——

高斯掩膜只要求解一次就够了！ 当得到了这个模板，对图像的所有像素用这同一套模板去卷积就OK了！

# coding:utf8
import cv2
from filter import *
from  scipy.signal.signaltools import convolve2dclass MyGaussianBlur():# 初始化def __init__(self, kernel=3, sigema=1.5):self.kernel = kernel if kernel>=3 else 3self.radius = (kernel-1)/2self.sigema = sigema# 高斯的计算公式def calc(self, x, y):res1 = 1 / (2 * math.pi * self.sigema * self.sigema)res2 = math.exp(-(x * x + y * y) / (2 * self.sigema * self.sigema))return res1 * res2# 得到滤波模版def template(self):sideLength = self.kernelresult = np.zeros((sideLength, sideLength))for i in range(sideLength):for j in range(sideLength):result[i, j] = self.calc(i - self.radius, j - self.radius)all = result.sum()return result / all# 卷积滤波函数def filter_conv(self, image):template = self.template()arr = np.array(image)channel = arr.shape[2]newData = arr.copy()for k in range(channel):newData[:, :, k] = convolve2d(arr[:, :, k], template, mode='same')return newData# 滤波函数def filter(self, image):template = self.template()arr = np.array(image)height = arr.shape[0]width = arr.shape[1]channel = arr.shape[2]newData = arr.copy()for k in range(channel):for i in range(self.radius, height - self.radius):for j in range(self.radius, width - self.radius):t = arr[i - self.radius:i + self.radius + 1, j - self.radius:j + self.radius + 1, k]a = np.multiply(t, template)newData[i, j, k] = int(a.sum())return newDataif __name__ == '__main__':img = cv2.imread('test_data/0010.jpg')sigma=1.0kernel=3cv2.imshow('img0', img)img1 = cv2.GaussianBlur(img, (kernel, kernel), sigma)cv2.imshow('img1', img1)img2 = MyGaussianBlur(kernel=kernel, sigema=sigma).filter(img)cv2.imshow('img2', img2)img3 = MyGaussianBlur(kernel=kernel, sigema=sigma).filter_conv(img)cv2.imshow('img3', img3)cv2.waitKey(0)print MyGaussianBlur(kernel=kernel, sigema=sigma).template()"""[[ 0.07511361  0.1238414   0.07511361][ 0.1238414   0.20417996  0.1238414 ][ 0.07511361  0.1238414   0.07511361]]"""