高斯滤波器的原理及其实现过程（附模板代码）
时间：2020-05-25 09:35:05
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[导读]本文主要介绍了高斯滤波器的原理及其实现过程 高斯滤波器是一种线性滤波器，能够有效的抑制噪声，平滑图像。其作用原理和均值滤波器类似，都是取滤波器窗口内的像素的均值作为输出。其窗口模板的系数和均值滤波器不同，均值滤波器的模板系数都是相同的为1;而
小数形式的模板，就是直接计算得到的值，没有经过任何的处理;
整数形式的，则需要进行归一化处理，将模板左上角的值归一化为1，下面会具体介绍。使用整数的模板时，需要在模板的前面加一个系数，系数为
也就是模板系数和的倒数。
高斯模板的生成
知道模板生成的原理，实现起来也就不困难了
void generateGaussianTemplate(double window[][11], int ksize, double sigma){static const double pi = 3.1415926;int center = ksize / 2; // 模板的中心位置，也就是坐标的原点double x2, y2;for (int i = 0; i < ksize; i++){x2 = pow(i - center, 2);for (int j = 0; j < ksize; j++){y2 = pow(j - center, 2);double g = exp(-(x2 + y2) / (2 * sigma * sigma));g /= 2 * pi * sigma;window[i][j] = g;}}double k = 1 / window[0][0]; // 将左上角的系数归一化为1for (int i = 0; i < ksize; i++){for (int j = 0; j < ksize; j++){window[i][j] *= k;}}}
void generateGaussianTemplate(double window[][11], int ksize, double sigma){static const double pi = 3.1415926;int center = ksize / 2; // 模板的中心位置，也就是坐标的原点double x2, y2;double sum = 0;for (int i = 0; i < ksize; i++){x2 = pow(i - center, 2);for (int j = 0; j < ksize; j++){y2 = pow(j - center, 2);double g = exp(-(x2 + y2) / (2 * sigma * sigma));g /= 2 * pi * sigma;sum += g;window[i][j] = g;}}//double k = 1 / window[0][0]; // 将左上角的系数归一化为1for (int i = 0; i < ksize; i++){for (int j = 0; j < ksize; j++){window[i][j] /= sum;}}}
3×3,σ=0.8的小数型模板。
void GaussianFilter(const Mat &src, Mat &dst, int ksize, double sigma){CV_Assert(src.channels() || src.channels() == 3); // 只处理单通道或者三通道图像const static double pi = 3.1415926;// 根据窗口大小和sigma生成高斯滤波器模板// 申请一个二维数组，存放生成的高斯模板矩阵double **templateMatrix = new double*[ksize];for (int i = 0; i < ksize; i++)templateMatrix[i] = new double[ksize];int origin = ksize / 2; // 以模板的中心为原点double x2, y2;double sum = 0;for (int i = 0; i < ksize; i++){x2 = pow(i - origin, 2);for (int j = 0; j < ksize; j++){y2 = pow(j - origin, 2);// 高斯函数前的常数可以不用计算，会在归一化的过程中给消去double g = exp(-(x2 + y2) / (2 * sigma * sigma));sum += g;templateMatrix[i][j] = g;}}for (int i = 0; i < ksize; i++){for (int j = 0; j < ksize; j++){templateMatrix[i][j] /= sum;cout << templateMatrix[i][j] << " ";}cout << endl;}// 将模板应用到图像中int border = ksize / 2;copyMakeBorder(src, dst, border, border, border, border, BorderTypes::BORDER_REFLECT);int channels = dst.channels();int rows = dst.rows - border;int cols = dst.cols - border;for (int i = border; i < rows; i++){for (int j = border; j < cols; j++){double sum[3] = { 0 };for (int a = -border; a <= border; a++){for (int b = -border; b <= border; b++){if (channels == 1){sum[0] += templateMatrix[border + a][border + b] * dst.at<uchar>(i + a, j + b);}else if (channels == 3){Vec3b rgb = dst.at<Vec3b>(i + a, j + b);auto k = templateMatrix[border + a][border + b];sum[0] += k * rgb[0];sum[1] += k * rgb[1];sum[2] += k * rgb[2];}}}for (int k = 0; k < channels; k++){if (sum[k] < 0)sum[k] = 0;else if (sum[k] > 255)sum[k] = 255;}if (channels == 1)dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]);else if (channels == 3){Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) };dst.at<Vec3b>(i, j) = rgb;}}}// 释放模板数组for (int i = 0; i < ksize; i++)delete[] templateMatrix[i];delete[] templateMatrix;}
// 分离的计算void separateGaussianFilter(const Mat &src, Mat &dst, int ksize, double sigma){CV_Assert(src.channels()==1 || src.channels() == 3); // 只处理单通道或者三通道图像// 生成一维的高斯滤波模板double *matrix = new double[ksize];double sum = 0;int origin = ksize / 2;for (int i = 0; i < ksize; i++){// 高斯函数前的常数可以不用计算，会在归一化的过程中给消去double g = exp(-(i - origin) * (i - origin) / (2 * sigma * sigma));sum += g;matrix[i] = g;}// 归一化for (int i = 0; i < ksize; i++)matrix[i] /= sum;// 将模板应用到图像中int border = ksize / 2;copyMakeBorder(src, dst, border, border, border, border, BorderTypes::BORDER_REFLECT);int channels = dst.channels();int rows = dst.rows - border;int cols = dst.cols - border;// 水平方向for (int i = border; i < rows; i++){for (int j = border; j < cols; j++){double sum[3] = { 0 };for (int k = -border; k <= border; k++){if (channels == 1){sum[0] += matrix[border + k] * dst.at<uchar>(i, j + k); // 行不变，列变化；先做水平方向的卷积}else if (channels == 3){Vec3b rgb = dst.at<Vec3b>(i, j + k);sum[0] += matrix[border + k] * rgb[0];sum[1] += matrix[border + k] * rgb[1];sum[2] += matrix[border + k] * rgb[2];}}for (int k = 0; k < channels; k++){if (sum[k] < 0)sum[k] = 0;else if (sum[k] > 255)sum[k] = 255;}if (channels == 1)dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]);else if (channels == 3){Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) };dst.at<Vec3b>(i, j) = rgb;}}}// 竖直方向for (int i = border; i < rows; i++){for (int j = border; j < cols; j++){double sum[3] = { 0 };for (int k = -border; k <= border; k++){if (channels == 1){sum[0] += matrix[border + k] * dst.at<uchar>(i + k, j); // 列不变，行变化；竖直方向的卷积}else if (channels == 3){Vec3b rgb = dst.at<Vec3b>(i + k, j);sum[0] += matrix[border + k] * rgb[0];sum[1] += matrix[border + k] * rgb[1];sum[2] += matrix[border + k] * rgb[2];}}for (int k = 0; k < channels; k++){if (sum[k] < 0)sum[k] = 0;else if (sum[k] > 255)sum[k] = 255;}if (channels == 1)dst.at<uchar>(i, j) = static_cast<uchar>(sum[0]);else if (channels == 3){Vec3b rgb = { static_cast<uchar>(sum[0]), static_cast<uchar>(sum[1]), static_cast<uchar>(sum[2]) };dst.at<Vec3b>(i, j) = rgb;}}}delete[] matrix;}
CV_EXPORTS_W void GaussianBlur( InputArray src, OutputArray dst, Size ksize,double sigmaX, double sigmaY = 0,int borderType = BORDER_DEFAULT );
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