OpenCV使用陷波滤波器减少摩尔波纹 C++

陷波滤波器是更有用的选择性滤波器。陷波滤波器拒绝事先定义的关于矩形中心的一个邻域的频率。

零相移滤波器必须是关于原点对称的，因此一个中心位于(u0,v0)的陷波在位置(-u0,-v0)必须有一个对应的陷波。

陷波带阻滤波器可以用中心已被平移到陷波滤波器中心的高通滤波器的乘积来构造。一般形式为：

$H_{NR}(u,v) = \prod_{k=1}^{Q}H_{k}(u,v)H_{-k}(u,v)$

其中， $H_{k}(u,v)H_{-k}(u,v)$ 是高通滤波器，他们的中心分别位于(u_k, v_k)和(-u_k, -v_k);这些中心是根据频率矩形的中心(M/2,N/2)确定的。对于每个滤波器，距离计算由下式执行：

$D_{k}(u,v) = \left [ (u-M/2-u_{k})^{2} + (v-N/2-v_{k})^{2} \right ]^{1/2}$

$D_{-k}(u,v) = \left [ (u-M/2+u_{k})^{2} + (v-N/2+v_{k})^{2} \right ]^{1/2}$

例如下面是一个n阶布特沃斯陷波带阻滤波器，它包含三个陷波对；

$H_{NR}(u,v) = \prod_{k=1}^{3}\left [ \frac{1}{1+\left [ D_{0k}/D_{k}(u,v) \right ]^{2n}} \right ]\left [ \frac{1}{1+\left [ D_{0k}/D_{-k}(u,v) \right ]^{2n}} \right ]$

$D_{k}$ 和 $D_{-k}$ 由上式计算得出；常数 $D_{0k}$ 对每一个陷波对都是相同的。对于不同陷波对可以不同。其他陷波带阻滤波器可用相同方法构建。

前面说过，1-带阻滤波就是带通，因此陷波带通滤波器：

$H_{NP}(u,v)=1-H_{NR}(u,v)$

陷波滤波是选择性的修改DFT的局部区域。典型处理是交互式完成，它直接对DFT处理，

下面使用陷波滤波减少图像的摩尔波纹。

使用布特沃斯 n=4,D0=30处理

原图像 ---------------------- 处理后图像

原图像频谱图 --------------------------------------- 处理后图像频谱图

陷波滤波器

通过鼠标选择矩形区域，找出最大值点，当做(u,v)；

代码实现：

#include "opencv2/opencv.hpp"

typedef cv::Mat Mat;

Mat image_add_border( Mat &src )
{
int w=2*src.cols;
int h=2*src.rows;
std::cout << "src: " << src.cols << "*" << src.rows << std::endl;

cv::Mat padded;
copyMakeBorder( src, padded, 0, h-src.rows, 0, w-src.cols,
cv::BORDER_CONSTANT, cv::Scalar::all(0));
padded.convertTo(padded,CV_32FC1);
std::cout << "opt: " << padded.cols << "*" << padded.rows << std::endl;
return padded;
}

//transform to center 中心化
void center_transform( cv::Mat &src )
{
for(int i=0; i<src.rows; i++){
float *p = src.ptr<float>(i);
for(int j=0; j<src.cols; j++){
p[j] = p[j] * pow(-1, i+j);
}
}
}

//对角线交换内容
void zero_to_center(cv::Mat &freq_plane)
{
// freq_plane = freq_plane(Rect(0, 0, freq_plane.cols & -2, freq_plane.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=freq_plane.cols/2;int cy=freq_plane.rows/2;//以下的操作是移动图像 (零频移到中心)
cv::Mat part1_r(freq_plane, cv::Rect(0,0,cx,cy)); //元素坐标表示为(cx,cy)
cv::Mat part2_r(freq_plane, cv::Rect(cx,0,cx,cy));
cv::Mat part3_r(freq_plane, cv::Rect(0,cy,cx,cy));
cv::Mat part4_r(freq_plane, cv::Rect(cx,cy,cx,cy));

cv::Mat tmp;
part1_r.copyTo(tmp); //左上与右下交换位置(实部)
part4_r.copyTo(part1_r);
tmp.copyTo(part4_r);

part2_r.copyTo(tmp); //右上与左下交换位置(实部)
part3_r.copyTo(part2_r);
tmp.copyTo(part3_r);
}

void show_spectrum( cv::Mat &complexI )
{
cv::Mat temp[] = {cv::Mat::zeros(complexI.size(),CV_32FC1),
cv::Mat::zeros(complexI.size(),CV_32FC1)};
//显示频谱图
cv::split(complexI, temp);
cv::Mat aa;
cv::magnitude(temp[0], temp[1], aa);
// zero_to_center(aa);
cv::divide(aa, aa.cols*aa.rows, aa);
double min, max;
cv::Point min_loc, max_loc;
cv::minMaxLoc(aa, &min, &max, &min_loc, &max_loc );
std::cout << "min: " << min << " max: " << max << std::endl;
std::cout << "min_loc: " << min_loc << " max_loc: " << max_loc << std::endl;
cv::circle( aa, min_loc, 20, cv::Scalar::all(1), 3);
cv::circle( aa, max_loc, 20, cv::Scalar::all(1), 3);

cv::imshow("src_img_spectrum",aa);
}

//频率域滤波
cv::Mat frequency_filter(cv::Mat &padded,cv::Mat &blur)
{
cv::Mat plane[]={padded, cv::Mat::zeros(padded.size(), CV_32FC1)};
cv::Mat complexIm;

cv::merge(plane,2,complexIm);
cv::dft(complexIm,complexIm);//fourior transform
show_spectrum(complexIm);

cv::multiply(complexIm, blur, complexIm);
cv::idft(complexIm, complexIm, CV_DXT_INVERSE); //idft
cv::Mat dst_plane[2];
cv::split(complexIm, dst_plane);
center_transform(dst_plane[0]);
// center_transform(dst_plane[1]);

cv::magnitude(dst_plane[0],dst_plane[1],dst_plane[0]); //求幅值(模)
// center_transform(dst_plane[0]); //center transform

return dst_plane[0];
}

//陷波滤波器
cv::Mat notch_kernel( cv::Mat &scr, std::vector<cv::Point> &notch_pot, float D0 )
{
cv::Mat notch_pass(scr.size(),CV_32FC2);
int row_num = scr.rows;
int col_num = scr.cols;
int n = 4;
for(int i=0; i<row_num; i++ ){
float *p = notch_pass.ptr<float>(i);
for(int j=0; j<col_num; j++ ){
float h_nr = 1.0;
for( unsigned int k = 0; k < notch_pot.size(); k++ ){
int u_k = notch_pot.at(k).y;
int v_k = notch_pot.at(k).x;
float dk = sqrt( pow((i-u_k),2) +
pow((j-v_k),2) );
float d_k = sqrt( pow((i+u_k),2) +
pow((j+v_k),2) );
float dst_dk = 1.0/(1.0 + pow(D0/dk, 2*n));
float dst_d_k = 1.0/(1.0 + pow(D0/d_k, 2*n));
h_nr = dst_dk * dst_d_k * h_nr;
// std::cout << "notch_pot: " << notch_pot.at(k) << std::endl;
}
p[2*j] = h_nr;
p[2*j+1] = h_nr;

}
}

cv::Mat temp[] = { cv::Mat::zeros(scr.size(), CV_32FC1),
cv::Mat::zeros(scr.size(), CV_32FC1) };
cv::split(notch_pass, temp);

std::string name = "notch滤波器d0=" + std::to_string(D0);
cv::Mat show;
cv::normalize(temp[0], show, 1, 0, CV_MINMAX);
cv::imshow(name, show);
return notch_pass;
}

std::string name_win("Notch_filter");
cv::Rect g_rectangle;
bool g_bDrawingBox = false;//是否进行绘制
cv::RNG g_rng(12345);

std::vector<cv::Point> notch_point;

void on_MouseHandle(int event, int x, int y, int flags, void*param);
void DrawRectangle(cv::Mat& img, cv::Rect box);

int main(int argc, char * argv[])
{
if( argc != 2){
std::cerr << "Usage: " << argv[0] << " <img_name> " << std::endl;
return -1;
}

Mat srcImage = cv::imread(argv[1], cv::IMREAD_GRAYSCALE);
if( srcImage.empty() )
return -1;
imshow( "src_img", srcImage );
Mat padded = image_add_border(srcImage);
center_transform( padded );
Mat plane[]={padded, cv::Mat::zeros(padded.size(), CV_32FC1)};
Mat complexIm;

merge(plane,2,complexIm);
cv::dft(complexIm,complexIm);//fourior transform
Mat temp[] = {cv::Mat::zeros(complexIm.size(),CV_32FC1),
cv::Mat::zeros(complexIm.size(),CV_32FC1)};
//显示频谱图
split(complexIm, temp);
Mat aa;
magnitude(temp[0], temp[1], aa);
divide(aa, aa.cols*aa.rows, aa);

cv::namedWindow(name_win);
cv::imshow(name_win,aa);

cv::setMouseCallback(name_win, on_MouseHandle, (void*)&aa);
Mat tempImage = aa.clone();
int key_value = -1;
while (1){
key_value = cv::waitKey(10);
if( key_value == 27 ){ //esc key,break
break;
}

}
if( !notch_point.empty() ){
for( unsigned int i = 0; i < notch_point.size(); i++ ){
cv::circle( tempImage, notch_point.at(i), 3, cv::Scalar(1), 2);
std::cout << notch_point.at(i) << std::endl;
}
}
cv::imshow(name_win, tempImage);

Mat ker = notch_kernel( complexIm,notch_point, 30 );
cv::multiply(complexIm, ker, complexIm);

split(complexIm, temp);
magnitude(temp[0], temp[1], aa);
divide(aa, aa.cols*aa.rows, aa);
imshow( "aa", aa );
cv::idft(complexIm, complexIm, CV_DXT_INVERSE); //idft
cv::Mat dst_plane[2];
cv::split(complexIm, dst_plane);
center_transform(dst_plane[0]);
// center_transform(dst_plane[1]);

// cv::magnitude(dst_plane[0],dst_plane[1],dst_plane[0]); //求幅值(模)

cv::normalize(dst_plane[0], dst_plane[0], 1, 0, CV_MINMAX);
imshow( "dest", dst_plane[0] );
cv::waitKey(0);

return 1;
}

void on_MouseHandle(int event, int x, int y, int falgs, void* param)
{
Mat& image = *(cv::Mat*)param;

switch (event){ //鼠标移动消息
case cv::EVENT_MOUSEMOVE:{
if (g_bDrawingBox){ //标识符为真，则记录下长和宽到Rect型变量中

g_rectangle.width = x - g_rectangle.x;
g_rectangle.height = y - g_rectangle.y;
}
}
break;

case cv::EVENT_LBUTTONDOWN:{
g_bDrawingBox = true;
g_rectangle = cv::Rect(x, y, 0, 0);//记录起点
std::cout << "start point( " << g_rectangle.x << "," << g_rectangle.y << ")" << std::endl;
}
break;

case cv::EVENT_LBUTTONUP: {
g_bDrawingBox = false;
bool w_less_0 = false, h_less_0 = false;

if (g_rectangle.width < 0){ //对宽高小于0的处理
g_rectangle.x += g_rectangle.width;
g_rectangle.width *= -1;
w_less_0 = true;

}
if (g_rectangle.height < 0){
g_rectangle.y += g_rectangle.height;
g_rectangle.height *= -1;
h_less_0 = true;
}
std::cout << "end Rect[ " << g_rectangle.x << "," << g_rectangle.y << "," << g_rectangle.width<< ","
<< g_rectangle.height << "]" <<std::endl;

if( g_rectangle.height > 0 && g_rectangle.width > 0 ){
Mat imageROI = image(g_rectangle).clone();
double min, max;
cv::Point min_loc, max_loc;
cv::minMaxLoc( imageROI, &min, &max, &min_loc, &max_loc);
cv::circle(imageROI, max_loc, 10, 1);
max_loc.x += g_rectangle.x;
max_loc.y += g_rectangle.y;

notch_point.push_back(max_loc);

cv::circle(image, max_loc, 10, 1);
// cv::imshow( "ROI", imageROI );
cv::imshow( "src", image );
}

}
break;
}
}

cv::Mat notchFilter_BTW(int rows,int cols,std::vector<cv::Point> np,
float* D,int n=1,int cvtype=CV_32FC2)
{
cv::Mat filt(rows,cols,cvtype,cv::Scalar::all(0));
int cx=cols/2,cy=rows/2;
int numNotch=np.size();
float* D2=D;
for(int i=0;i<numNotch;i++)
{
D2[i]=D[i]*D[i];
}
int uk[numNotch],vk[numNotch];//在画面上的实际陷波坐标点
int u_k[numNotch],v_k[numNotch];//陷波共轭点
float Dk[numNotch],D_k[numNotch];//陷波半径r
float Hk[numNotch],H_k[numNotch];

for(int i=0;i<rows;i++)
{
for(int j=0;j<cols;j++)
{
int u=cx-j,v=cy-i;//中心坐标
for(int s=0;s<numNotch;s++)
{
uk[s]=u+np[s].x,vk[s]=v+np[s].y;
Dk[s]=uk[s]*uk[s]+vk[s]*vk[s];//距离中心半径的平方
Hk[s]=1-1/(1+pow(Dk[s]/D2[s],n));

u_k[s]=u-np[s].x,v_k[s]=v-np[s].y;
D_k[s]=u_k[s]*u_k[s]+v_k[s]*v_k[s];
H_k[s]=1-1/(1+pow(D_k[s]/D2[s],n));
}
//.data返回的是uchar*型指针，所以要强制转换成浮点数型
float* p=(float*)(filt.data+i*filt.step[0]+j*filt.step[1]);

for(int c=0;c<filt.channels();c++)
{
p[c]=Hk[0]*H_k[0];
for(int k=1;k<numNotch;k++)
{
p[c]*=Hk[k]*H_k[k];
}
}

}
}
return filt;
}

其中，M/2-u_k,N/2- v_k就是计算出来的坐标值，不需要用到M/2, N/2。

OpenCV使用陷波滤波器减少摩尔波纹 C++

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