Question
Question A is more important than question B. Thank You.
Given the following vectors
x = [1, 3, 5, 7, 6, 8, 5, 2],
y = [7, 11, 9, 6, 4, 3, 1, 3],
z = [3, 5, 7, 9, 8, 7, 6, 5]
Calculate the following.
a) Haar wavelet transforms of x, y, z.
b) Fourier transforms of x, y, z.
Explanation / Answer
#include "opencv2/opencv.hpp" #include #include #include using namespace cv; using namespace std; // Filter type #define NONE 0 // no filter #define HARD 1 // hard shrinkage #define SOFT 2 // soft shrinkage #define GARROT 3 // garrot filter //-------------------------------- // signum //-------------------------------- float sgn(float x) { float res=0; if(x==0) { res=0; } if(x>0) { res=1; } if(xT) { res=sgn(d)*(fabs(d)-T); } else { res=0; } return res; } //-------------------------------- // Hard shrinkage //-------------------------------- float hard_shrink(float d,float T) { float res; if(fabs(d)>T) { res=d; } else { res=0; } return res; } //-------------------------------- // Garrot shrinkage //-------------------------------- float Garrot_shrink(float d,float T) { float res; if(fabs(d)>T) { res=d-((T*T)/d); } else { res=0; } return res; } //-------------------------------- // Wavelet transform //-------------------------------- static void cvHaarWavelet(Mat &src,Mat &dst,int NIter) { float c,dh,dv,dd; assert( src.type() == CV_32FC1 ); assert( dst.type() == CV_32FC1 ); int width = src.cols; int height = src.rows; for (int k=0;k(k+1));y++) { for (int x=0; x>(k+1));x++) { c=(src.at(2*y,2*x)+src.at(2*y,2*x+1)+src.at(2*y+1,2*x)+src.at(2*y+1,2*x+1))*0.5; dst.at(y,x)=c; dh=(src.at(2*y,2*x)+src.at(2*y+1,2*x)-src.at(2*y,2*x+1)-src.at(2*y+1,2*x+1))*0.5; dst.at(y,x+(width>>(k+1)))=dh; dv=(src.at(2*y,2*x)+src.at(2*y,2*x+1)-src.at(2*y+1,2*x)-src.at(2*y+1,2*x+1))*0.5; dst.at(y+(height>>(k+1)),x)=dv; dd=(src.at(2*y,2*x)-src.at(2*y,2*x+1)-src.at(2*y+1,2*x)+src.at(2*y+1,2*x+1))*0.5; dst.at(y+(height>>(k+1)),x+(width>>(k+1)))=dd; } } dst.copyTo(src); } } //-------------------------------- //Inverse wavelet transform //-------------------------------- static void cvInvHaarWavelet(Mat &src,Mat &dst,int NIter, int SHRINKAGE_TYPE=0, float SHRINKAGE_T=50) { float c,dh,dv,dd; assert( src.type() == CV_32FC1 ); assert( dst.type() == CV_32FC1 ); int width = src.cols; int height = src.rows; //-------------------------------- // NIter - number of iterations //-------------------------------- for (int k=NIter;k>0;k--) { for (int y=0;y>k);y++) { for (int x=0; x>k);x++) { c=src.at(y,x); dh=src.at(y,x+(width>>k)); dv=src.at(y+(height>>k),x); dd=src.at(y+(height>>k),x+(width>>k)); // (shrinkage) switch(SHRINKAGE_TYPE) { case HARD: dh=hard_shrink(dh,SHRINKAGE_T); dv=hard_shrink(dv,SHRINKAGE_T); dd=hard_shrink(dd,SHRINKAGE_T); break; case SOFT: dh=soft_shrink(dh,SHRINKAGE_T); dv=soft_shrink(dv,SHRINKAGE_T); dd=soft_shrink(dd,SHRINKAGE_T); break; case GARROT: dh=Garrot_shrink(dh,SHRINKAGE_T); dv=Garrot_shrink(dv,SHRINKAGE_T); dd=Garrot_shrink(dd,SHRINKAGE_T); break; } //------------------- dst.at(y*2,x*2)=0.5*(c+dh+dv+dd); dst.at(y*2,x*2+1)=0.5*(c-dh+dv-dd); dst.at(y*2+1,x*2)=0.5*(c+dh-dv-dd); dst.at(y*2+1,x*2+1)=0.5*(c-dh-dv+dd); } } Mat C=src(Rect(0,0,width>>(k-1),height>>(k-1))); Mat D=dst(Rect(0,0,width>>(k-1),height>>(k-1))); D.copyTo(C); } } //-------------------------------- // //-------------------------------- int process(VideoCapture& capture) { int n = 0; const int NIter=4; char filename[200]; string window_name = "video | q or esc to quit"; cout > frame; if (frame.empty()) continue; cvtColor(frame, GrayFrame, CV_BGR2GRAY); GrayFrame.convertTo(Src,CV_32FC1); cvHaarWavelet(Src,Dst,NIter); Dst.copyTo(Temp); cvInvHaarWavelet(Temp,Filtered,NIter,GARROT,30); imshow(window_name, frame); double M=0,m=0; //---------------------------------------------------- // Normalization to 0-1 range (for visualization) //---------------------------------------------------- minMaxLoc(Dst,&m,&M); if((M-m)>0) {Dst=Dst*(1.0/(M-m))-m/(M-m);} imshow("Coeff", Dst); minMaxLoc(Filtered,&m,&M); if((M-m)>0) {Filtered=Filtered*(1.0/(M-m))-m/(M-m);} imshow("Filtered", Filtered); char key = (char)waitKey(5); switch (key) { case 'q': case 'Q': case 27: //escape key return 0; case ' ': //Save an image sprintf(filename,"filename%.3d.jpg",n++); imwrite(filename,frame); cout