# 数字图像处理之均值滤波，高斯滤波，中值滤波，双边滤波

2017-10-29 11:18:57来源:CSDN作者:qq_30356613人点击

## C++代码实现：

`static void exchange(int& a, int& b){		int t = 0;	t = a;	a = b;	b = t;}static void bubble_sort(int* K, int lenth){	for (int i = 0; i < lenth; i++)		for (int j = i + 1; j < lenth; j++)		{			if (K[i]>K[j])				exchange(K[i], K[j]);		}}///产生二维的高斯内核static cv::Mat generate_gassian_kernel(double u, double sigma, cv::Size size){	int width = size.width;	int height = size.height;	cv::Mat gassian_kernel(cv::Size(width, height), CV_64FC1);	double sum = 0;	double sum_sum = 0;	for (int i = 0; i < width; i++)		for (int j = 0; j < height; j++)		{			sum = 1.0 / 2.0 / CV_PI / sigma / sigma * exp(-1.0 * ((i - width / 2)*(i - width / 2) + (j - width / 2)*(j - width / 2)) / 2.0 / sigma / sigma);			sum_sum += sum;			gassian_kernel.ptr<double>(i)[j] = sum;		}	for (int i = 0; i < width; i++)		for (int j = 0; j < height; j++)		{			gassian_kernel.ptr<double>(i)[j] /= sum_sum;		}	return gassian_kernel;}///均值滤波void lmt_main_blur(cv::Mat& img_in, cv::Mat& img_out, int kernel_size){	img_out = img_in.clone();	cv::Mat mat1;	cv::copyMakeBorder(img_in, mat1, kernel_size, kernel_size, kernel_size, kernel_size, cv::BORDER_REPLICATE);	int cols = mat1.cols;	int rows = mat1.rows;	int channels = img_out.channels();	const uchar* const pt = mat1.ptr<uchar>(0);	uchar* pt_out = img_out.ptr<uchar>(0);	for (int i = kernel_size; i < rows - kernel_size; i++)	{		for (int j = kernel_size; j < cols - kernel_size; j++)		{			if (channels == 1)			{				long long int sum_pixel = 0;				for (int m = -1 * kernel_size; m < kernel_size; m++)					for (int n = -1 * kernel_size; n < kernel_size; n++)					{						sum_pixel += pt[(i + m)*cols + (j + n)];					}				img_out.ptr<uchar>(i - kernel_size)[j - kernel_size] = (double)sum_pixel / (kernel_size*kernel_size * 4);			}			else if (channels == 3)			{				long long int sum_pixel = 0;				long long int sum_pixel1 = 0;				long long int sum_pixel2 = 0;				for (int m = -1 * kernel_size; m < kernel_size; m++)					for (int n = -1 * kernel_size; n < kernel_size; n++)					{						sum_pixel += pt[((i + m)*cols + (j + n))*channels + 0];						sum_pixel1 += pt[((i + m)*cols + (j + n))*channels + 1];						sum_pixel2 += pt[((i + m)*cols + (j + n))*channels + 2];					}				img_out.ptr<uchar>(i - kernel_size)[(j - kernel_size)*channels + 0] = (double)sum_pixel / (double)(kernel_size*kernel_size * 4);				img_out.ptr<uchar>(i - kernel_size)[(j - kernel_size)*channels + 1] = (double)sum_pixel1 / (double)(kernel_size*kernel_size * 4);				img_out.ptr<uchar>(i - kernel_size)[(j - kernel_size)*channels + 2] = (double)sum_pixel2 / (double)(kernel_size*kernel_size * 4);			}		}	}}///中值滤波void lmt_median_blur(cv::Mat& img_in, cv::Mat& img_out, int kernel_size){	img_out = img_in.clone();	cv::Mat mat1;	cv::copyMakeBorder(img_in, mat1, kernel_size, kernel_size, kernel_size, kernel_size, cv::BORDER_REPLICATE);	int cols = mat1.cols;	int rows = mat1.rows;	int channels = img_out.channels();	cv::Mat mat[3];	cv::Mat mat_out[3];	cv::split(mat1, mat);	cv::split(img_out, mat_out);	for (int k = 0; k < 3; k++)	{		const uchar* const pt = mat[k].ptr<uchar>(0);		uchar* pt_out = mat_out[k].ptr<uchar>(0);		for (int i = kernel_size; i < rows - kernel_size; i++)		{			for (int j = kernel_size; j < cols - kernel_size; j++)			{				long long int sum_pixel = 0;				int* K = new int[kernel_size*kernel_size * 4];				int ker_num = 0;				for (int m = -1 * kernel_size; m < kernel_size; m++)					for (int n = -1 * kernel_size; n < kernel_size; n++)					{						K[ker_num] = pt[(i + m)*cols + (j + n)];						ker_num++;					}				bubble_sort(K, ker_num);				mat_out[k].ptr<uchar>(i - kernel_size)[j - kernel_size] = K[ker_num / 2];			}		}	}	cv::merge(mat_out, 3, img_out);}///高斯滤波void lmt_gaussian_blur(cv::Mat& img_src, cv::Mat& img_dst, cv::Size kernel_size){	img_dst = cv::Mat(cv::Size(img_src.cols, img_src.rows), img_src.type());	int cols = img_src.cols;	int rows = img_src.rows;	int channels = img_src.channels();	cv::Mat gassian_kernel = generate_gassian_kernel(0, 1, kernel_size);	int width = kernel_size.width / 2;	int height = kernel_size.height / 2;	for (int i = height; i < rows - height; i++)	{		for (int j = width; j < cols - width; j++)		{			for (int k = 0; k < channels; k++)			{				double sum = 0.0;				for (int m = -height; m <= height; m++)				{					for (int n = -width; n <= width; n++)					{						sum += (double)(img_src.ptr<uchar>(i + m)[(j + n)*channels + k]) * gassian_kernel.ptr<double>(height + m)[width + n];					}				}				if (sum > 255.0)					sum = 255;				if (sum < 0.0)					sum = 0;				img_dst.ptr<uchar>(i)[j*channels + k] = (uchar)sum;			}		}	}	}///双边滤波void lmt_bilateral_filter(cv::Mat& img_in, cv::Mat& img_out, const int r, double sigma_d, double sigma_r){	int i, j, m, n, k;	int nx = img_in.cols, ny = img_in.rows, m_nChannels = img_in.channels();	const int w_filter = 2 * r + 1; // 滤波器边长  	double gaussian_d_coeff = -0.5 / (sigma_d * sigma_d);	double gaussian_r_coeff = -0.5 / (sigma_r * sigma_r);	double  **d_metrix = new double *[w_filter];	for (int i = 0; i < w_filter; ++i)		d_metrix[i] = new double[w_filter];		double r_metrix[256];  // similarity weight  	img_out = cv::Mat(img_in.size(),img_in.type());	uchar* m_imgData = img_in.ptr<uchar>(0);	uchar* m_img_outData = img_out.ptr<uchar>(0);	// copy the original image  	double* img_tmp = new double[m_nChannels * nx * ny];	for (i = 0; i < ny; i++)		for (j = 0; j < nx; j++)			for (k = 0; k < m_nChannels; k++)			{				img_tmp[i * m_nChannels * nx + m_nChannels * j + k] = m_imgData[i * m_nChannels * nx + m_nChannels * j + k];			}	// compute spatial weight  	for (i = -r; i <= r; i++)		for (j = -r; j <= r; j++)		{			int x = j + r;			int y = i + r;			d_metrix[y][x] = exp((i * i + j * j) * gaussian_d_coeff);		}	// compute similarity weight  	for (i = 0; i < 256; i++)	{		r_metrix[i] = exp(i * i * gaussian_r_coeff);	}	// bilateral filter  	for (i = 0; i < ny; i++)		for (j = 0; j < nx; j++)		{			for (k = 0; k < m_nChannels; k++)			{				double weight_sum, pixcel_sum;				weight_sum = pixcel_sum = 0.0;				for (m = -r; m <= r; m++)					for (n = -r; n <= r; n++)					{						if (m*m + n*n > r*r) continue;						int x_tmp = j + n;						int y_tmp = i + m;						x_tmp = x_tmp < 0 ? 0 : x_tmp;						x_tmp = x_tmp > nx - 1 ? nx - 1 : x_tmp;   // 边界处理，replicate  						y_tmp = y_tmp < 0 ? 0 : y_tmp;						y_tmp = y_tmp > ny - 1 ? ny - 1 : y_tmp;						int pixcel_dif = (int)abs(img_tmp[y_tmp * m_nChannels * nx + m_nChannels * x_tmp + k] - img_tmp[i * m_nChannels * nx + m_nChannels * j + k]);						double weight_tmp = d_metrix[m + r][n + r] * r_metrix[pixcel_dif];  // 复合权重  						pixcel_sum += img_tmp[y_tmp * m_nChannels * nx + m_nChannels * x_tmp + k] * weight_tmp;						weight_sum += weight_tmp;					}				pixcel_sum = pixcel_sum / weight_sum;				m_img_outData[i * m_nChannels * nx + m_nChannels * j + k] = (uchar)pixcel_sum;			} // 一个通道  		} // END ALL LOOP  	for (i = 0; i < w_filter; i++)		delete[] d_metrix[i];	delete[] d_metrix;}`

## Opencv API函数实现：

opencv相关函数简介：

src待滤波图像

dst滤波后图像

d滤波器半径

sigmaColor滤波器值域的sigma

sigmaSpace滤波器空间域的sigma

borderType边缘填充方式 BORDER_REPLICATE BORDER_REFLECT BORDER_DEFAULT BORDER_REFLECT_101BORDER_TRANSPARENT BORDER_ISOLATED

src待滤波图像

dst滤波后图像

ksize 均值滤波器的大小

anchor均值滤波器的锚点也就是模板移动点

borderType边缘填充方式 BORDER_REPLICATE BORDER_REFLECT BORDER_DEFAULT BORDER_REFLECT_101BORDER_TRANSPARENT BORDER_ISOLATED

src待滤波图像

dst滤波后图像

ksize 高斯滤波器的大小

sigmaX 高斯滤波器的x方向的滤波器高斯sigma

sigmaY 高斯滤波器的y方向的滤波器高斯sigma

borderType边缘填充方式 BORDER_REPLICATE BORDER_REFLECT BORDER_DEFAULT BORDER_REFLECT_101BORDER_TRANSPARENT BORDER_ISOLATED

src待滤波图像

dst滤波后图像

ksize 中值滤波器的大小

`void bilateral_filter_show(void){	cv::Mat mat1 = cv::imread("F://CVlibrary//obama.jpg", CV_LOAD_IMAGE_GRAYSCALE); //灰度图加载进来，BGR->HSV 然后取H参数	if (mat1.empty())		return;	cv::imshow("原图像", mat1); 	cv::Mat src = cv::imread("F://CVlibrary//obama.jpg");	cv::imshow("原始彩色图像", src);	std::cout << "channel = " << mat1.channels() << std::endl;		cv::Mat mat3;	cv::bilateralFilter(src, mat3, 5, 50, 50,cv::BORDER_DEFAULT);	cv::imshow("opencv给出的双边滤波器", mat3);	cv::Mat mat4;	cv::blur(src, mat4, cv::Size(3, 3));	cv::imshow("均值滤波", mat4);	cv::Mat mat5;	cv::GaussianBlur(src, mat5, cv::Size(5, 5), 1,1);	cv::imshow("高斯滤波器", mat5);	cv::Mat mat6;	cv::medianBlur(src, mat6, 3);	cv::imshow("中值滤波", mat6); 	cv::Mat mat7;	lmt_gaussian_blur(src, mat7, cv::Size(5, 5));	cv::imshow("my gaussian image",mat7);	cv::waitKey(0);}`