OpenCV C++实现频域滤波器汇总 理想低通、理想高通、巴特沃思低通、巴特沃思高通、高斯低通、高斯高通
根据各个滤波公式及前几章内容，可实现理想低通、理想高通、巴特沃思低通、巴特沃思高通、高斯低通、高斯高通滤波器；
效果图：
高斯低通 D0=30
巴特沃思低通 D0=30,n=2
理想低通D0=30：
高斯高通D0=80：
巴特沃思高通 D0=80,n=2
理想高通D0=80：
代码实现：
#include
#include
using namespace std;
using namespace cv;
cv::Mat image_make_border(cv::Mat &src )
{
int w=getOptimalDFTSize(src.cols);
int h=getOptimalDFTSize(src.rows);
Mat padded;
copyMakeBorder(src,padded,0,h-src.rows,0,w-src.cols,BORDER_CONSTANT,Scalar::all(0));
padded.convertTo(padded,CV_32FC1);
return padded;
}
//频率域滤波
Mat frequency_filter(Mat &scr,Mat &blur)
{
//***********************DFT*******************
Mat plane[]={scr, Mat::zeros(scr.size() , CV_32FC1)}; //创建通道，存储dft后的实部与虚部（CV_32F，必须为单通道数）
Mat complexIm;
merge(plane,2,complexIm);//合并通道 （把两个矩阵合并为一个2通道的Mat类容器）
dft(complexIm,complexIm);//进行傅立叶变换，结果保存在自身
//***************中心化********************
split(complexIm,plane);//分离通道（数组分离）
// plane[0] = plane[0](Rect(0, 0, plane[0].cols & -2, plane[0].rows & -2));//这里为什么&上-2具体查看opencv文档
// //其实是为了把行和列变成偶数 -2的二进制是11111111.......10 最后一位是0
int cx=plane[0].cols/2;int cy=plane[0].rows/2;//以下的操作是移动图像 (零频移到中心)
Mat part1_r(plane[0],Rect(0,0,cx,cy)); //元素坐标表示为(cx,cy)
Mat part2_r(plane[0],Rect(cx,0,cx,cy));
Mat part3_r(plane[0],Rect(0,cy,cx,cy));
Mat part4_r(plane[0],Rect(cx,cy,cx,cy));
Mat temp;
part1_r.copyTo(temp); //左上与右下交换位置(实部)
part4_r.copyTo(part1_r);
temp.copyTo(part4_r);
part2_r.copyTo(temp); //右上与左下交换位置(实部)
part3_r.copyTo(part2_r);
temp.copyTo(part3_r);
Mat part1_i(plane[1],Rect(0,0,cx,cy)); //元素坐标(cx,cy)
Mat part2_i(plane[1],Rect(cx,0,cx,cy));
Mat part3_i(plane[1],Rect(0,cy,cx,cy));
Mat part4_i(plane[1],Rect(cx,cy,cx,cy));
part1_i.copyTo(temp); //左上与右下交换位置(虚部)
part4_i.copyTo(part1_i);
temp.copyTo(part4_i);
part2_i.copyTo(temp); //右上与左下交换位置(虚部)
part3_i.copyTo(part2_i);
temp.copyTo(part3_i);
//*****************滤波器函数与DFT结果的乘积****************
Mat blur_r,blur_i,BLUR;
multiply(plane[0], blur, blur_r); //滤波（实部与滤波器模板对应元素相乘）
multiply(plane[1], blur,blur_i);//滤波（虚部与滤波器模板对应元素相乘）
Mat plane1[]={blur_r, blur_i};
merge(plane1,2,BLUR);//实部与虚部合并
//*********************得到原图频谱图***********************************
magnitude(plane[0],plane[1],plane[0]);//获取幅度图像，0通道为实部通道，1为虚部，因为二维傅立叶变换结果是复数
plane[0]+=Scalar::all(1); //傅立叶变换后的图片不好分析，进行对数处理，结果比较好看
log(plane[0],plane[0]); // float型的灰度空间为[0，1])
normalize(plane[0],plane[0],1,0,CV_MINMAX); //归一化便于显示
idft( BLUR, BLUR); //idft结果也为复数
split(BLUR,plane);//分离通道，主要获取通道
magnitude(plane[0],plane[1],plane[0]); //求幅值(模)
normalize(plane[0],plane[0],1,0,CV_MINMAX); //归一化便于显示
return plane[0];//返回参数
}
//*****************理想低通滤波器***********************
Mat ideal_low_kernel(Mat &scr,float sigma)
{
Mat ideal_low_pass(scr.size(),CV_32FC1); //，CV_32FC1
float d0=sigma;//半径D0越小，模糊越大；半径D0越大，模糊越小
for(int i=0;i
if (d <= d0){
ideal_low_pass.at
}else{
ideal_low_pass.at
}
}
}
string name = "理想低通滤波器d0=" + std::to_string(sigma);
imshow(name, ideal_low_pass);
return ideal_low_pass;
}
//理想低通滤波器
cv::Mat ideal_low_pass_filter(Mat &src, float sigma)
{
Mat padded = image_make_border(src);
Mat ideal_kernel=ideal_low_kernel(padded,sigma);
Mat result = frequency_filter(padded,ideal_kernel);
return result;
}
Mat butterworth_low_kernel(Mat &scr,float sigma, int n)
{
Mat butterworth_low_pass(scr.size(),CV_32FC1); //，CV_32FC1
double D0 = sigma;//半径D0越小，模糊越大；半径D0越大，模糊越小
for(int i=0;i
butterworth_low_pass.at
}
}
string name = "巴特沃斯低通滤波器d0=" + std::to_string(sigma) + "n=" + std::to_string(n);
imshow(name, butterworth_low_pass);
return butterworth_low_pass;
}
//巴特沃斯低通滤波器
Mat butterworth_low_paass_filter(Mat &src, float d0, int n)
{
//H = 1 / (1+(D/D0)^2n) n表示巴特沃斯滤波器的次数
//阶数n=1 无振铃和负值 阶数n=2 轻微振铃和负值 阶数n=5 明显振铃和负值 阶数n=20 与ILPF相似
Mat padded = image_make_border(src);
Mat butterworth_kernel=butterworth_low_kernel(padded,d0, n);
Mat result = frequency_filter(padded,butterworth_kernel);
return result;
}
Mat gaussian_low_pass_kernel(Mat scr,float sigma)
{
Mat gaussianBlur(scr.size(),CV_32FC1); //，CV_32FC1
float d0=2*sigma*sigma;//高斯函数参数，越小，频率高斯滤波器越窄，滤除高频成分越多，图像就越平滑
for(int i=0;i
gaussianBlur.at
}
}
// Mat show = gaussianBlur.clone();
// //归一化到[0,255]供显示
// normalize(show, show, 0, 255, NORM_MINMAX);
// //转化成CV_8U型
// show.convertTo(show, CV_8U);
// std::string pic_name = "gaussi" + std::to_string((int)sigma) + ".jpg";
// imwrite( pic_name, show);
imshow("高斯低通滤波器",gaussianBlur);
return gaussianBlur;
}
//高斯低通
Mat gaussian_low_pass_filter(Mat &src, float d0)
{
Mat padded = image_make_border(src);
Mat gaussian_kernel=gaussian_low_pass_kernel(padded,d0);//理想低通滤波器
Mat result = frequency_filter(padded,gaussian_kernel);
return result;
}
Mat ideal_high_kernel(Mat &scr,float sigma)
{
Mat ideal_high_pass(scr.size(),CV_32FC1); //，CV_32FC1
float d0=sigma;//半径D0越小，模糊越大；半径D0越大，模糊越小
for(int i=0;i
if (d <= d0){
ideal_high_pass.at
}
else{
ideal_high_pass.at
}
}
}
string name = "理想高通滤波器d0=" + std::to_string(sigma);
imshow(name, ideal_high_pass);
return ideal_high_pass;
}
//理想高通滤波器
cv::Mat ideal_high_pass_filter(Mat &src, float sigma)
{
Mat padded = image_make_border(src);
Mat ideal_kernel=ideal_high_kernel(padded,sigma);
Mat result = frequency_filter(padded,ideal_kernel);
return result;
}
Mat butterworth_high_kernel(Mat &scr,float sigma, int n)
{
Mat butterworth_low_pass(scr.size(),CV_32FC1); //，CV_32FC1
double D0 = sigma;//半径D0越小，模糊越大；半径D0越大，模糊越小
for(int i=0;i
butterworth_low_pass.at
}
}
string name = "巴特沃斯高通滤波器d0=" + std::to_string(sigma) + "n=" + std::to_string(n);
imshow(name, butterworth_low_pass);
return butterworth_low_pass;
}
//巴特沃斯高通滤波器
Mat butterworth_high_paass_filter(Mat &src, float d0, int n)
{
//H = 1 / (1+(D0/D)^2n) n表示巴特沃斯滤波器的次数
Mat padded = image_make_border(src);
Mat butterworth_kernel=butterworth_high_kernel(padded,d0, n);
Mat result = frequency_filter(padded,butterworth_kernel);
return result;
}
Mat gaussian_high_pass_kernel(Mat scr,float sigma)
{
Mat gaussianBlur(scr.size(),CV_32FC1); //，CV_32FC1
float d0=2*sigma*sigma;
for(int i=0;i
gaussianBlur.at
}
}
imshow("高斯高通滤波器",gaussianBlur);
return gaussianBlur;
}
//高斯高通
Mat gaussian_high_pass_filter(Mat &src, float d0)
{
Mat padded = image_make_border(src);
Mat gaussian_kernel=gaussian_high_pass_kernel(padded,d0);//理想低通滤波器
Mat result = frequency_filter(padded,gaussian_kernel);
return result;
}
int main( int argc, char *argv[])
{
const char* filename = argc >=2 ? argv[1] : "../data/lena.jpg";
Mat input = imread(filename, IMREAD_GRAYSCALE);
if( input.empty())
return -1;
imshow("input",input);//显示原图
cv::Mat ideal_low = ideal_low_pass_filter(input, 30);
ideal_low = ideal_low(cv::Rect(0,0, input.cols, input.rows));
imshow("理想低通", ideal_low);
cv::Mat bw_low = butterworth_low_paass_filter(input, 30, 2);
bw_low = bw_low(cv::Rect(0,0, input.cols, input.rows));
imshow("巴特沃斯低通", bw_low);
cv::Mat gaussion_low = gaussian_low_pass_filter(input, 30);
gaussion_low = gaussion_low(cv::Rect(0,0, input.cols, input.rows));
imshow("高斯低通", gaussion_low);
cv::Mat ideal_high = ideal_high_pass_filter(input, 80);
ideal_high = ideal_high(cv::Rect(0,0, input.cols, input.rows));
imshow("理想高通", ideal_high);
cv::Mat bw_high = butterworth_high_paass_filter(input, 80, 2);
bw_high = bw_high(cv::Rect(0,0, input.cols, input.rows));
imshow("巴特沃斯高通", bw_high);
cv::Mat gaussion_high = gaussian_high_pass_filter(input, 80);
gaussion_high = gaussion_high(cv::Rect(0,0, input.cols, input.rows));
imshow("高斯高通", gaussion_high);
waitKey();
return 0;
}