12 KiB
12 KiB
Image Approximation
Note
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dwt_2d and dwt_2d_sym functions are interchangeable in the following code as they take the same arguments. You may have to make some trivial modifications due to different sized output coeffficients.
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Please make sure that right header file is included. Following sample program links to wavelet2s.h which is the header for static libraries. wavelet2d.h must be included for shared libraries.
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I'm using OPENCV to handle images as i already use OPENCV for other image processing work. You may want to use some simpler image libraries as OPENCV is a full image processing suite and is very bulky or you can just use 2D matrices/build your own image classes. Regardless, DWT/IDWT operations are more important than the choice of libraries.
#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <complex>
#include <cmath>
#include <algorithm>
#include "wavelet2s.h"
#include "cv.h"
#include "highgui.h"
#include "cxcore.h"
using namespace std;
using namespace cv;
void findthresh(vector<double> &vector1, int N, double& t){
sort(vector1.begin(), vector1.end(), greater<double>());
t = vector1.at(N-1);
}
void* maxval(vector<vector<double> > &arr, double &max){
max = 0;
for (unsigned int i =0; i < arr.size(); i++) {
for (unsigned int j =0; j < arr[0].size(); j++) {
if (max <= arr[i][j]){
max = arr[i][j];
}
}
}
return 0;
}
void* maxval1(vector<double> &arr, double &max){
max = 0;
for (unsigned int i =0; i < arr.size(); i++) {
if (max <= arr[i]){
max = arr[i];
}
}
return 0;
}
int main() {
IplImage* img = cvLoadImage("lena512.bmp");
if (!img){
cout << " Can't read Image. Try Different Format." << endl;
exit(1);
}
int height, width;
height = img->height;
width = img->width;
int nc = img->nChannels;
// uchar* ptr2 =(uchar*) img->imageData;
int pix_depth = img->depth;
CvSize size;
size.width =width;
size.height=height;
cout << "depth" << pix_depth << "Channels" << nc << endl;
cvNamedWindow("Original Image", CV_WINDOW_AUTOSIZE);
cvShowImage("Original Image", img);
cvWaitKey();
cvDestroyWindow("Original Image");
cvSaveImage("orig.bmp",img);
int rows =(int) height;
int cols =(int) width;
Mat matimg(img);
vector<vector<double> > vec1(rows, vector<double>(cols));
int k =1;
for (int i=0; i < rows; i++) {
for (int j =0; j < cols; j++){
unsigned char temp;
temp = ((uchar*) matimg.data + i * matimg.step)[j * matimg.elemSize() + k ];
vec1[i][j] = (double) temp;
}
}
string nm = "db2";
vector<double> l1,h1,l2,h2;
filtcoef(nm,l1,h1,l2,h2);
// unsigned int lf=l1.size();
// int rows_n =(int) (rows+ J*(lf-1));
// int cols_n =(int) (cols + J * ( lf -1));
// Finding 2D DWT Transform of the image using symetric extension algorithm
// Extension is set to 0 (eg., int e = 0)
vector<int> length;
vector<double> output,flag;
int J =6;
dwt_2d(vec1,J,nm,output,flag,length);
double max;
vector<int> length2;
// This algorithm computes DWT of image of any given size. Together with convolution and
// subsampling operations it is clear that subsampled images are of different length than
// dyadic length images. In order to compute the "effective" size of DWT we do additional
// calculations.
dwt_output_dim_sym(length,length2,J);
// length2 is gives the integer vector that contains the size of subimages that will
// combine to form the displayed output image. The last two entries of length2 gives the
// size of DWT ( rows_n by cols_n)
int siz = length2.size();
int rows_n=length2[siz-2];
int cols_n = length2[siz-1];
vector<vector< double> > dwtdisp(rows_n, vector<double>(cols_n));
dispDWT(output,dwtdisp, length ,length2, J);
// dispDWT returns the 2D object dwtdisp which will be displayed using OPENCV's image
// handling functions
vector<vector<double> > dwt_output= dwtdisp;
// Storing the DWT coefficients in two different vectors that will be used to approximate
// Image with two different sets of chosen coefficients.
vector<double> dwt_coef1;
vector<double> dwt_coef2;
dwt_coef1 = output;
dwt_coef2 = output;
maxval(dwt_output,max);// max value is needed to take care of overflow which happens because
// of convolution operations performed on unsigned 8 bit images
//Displaying Scaled Image
// Creating Image in OPENCV
IplImage *cvImg; // image used for output
CvSize imgSize; // size of output image
imgSize.width = cols_n;
imgSize.height = rows_n;
cvImg = cvCreateImage( imgSize, 8, 1 );
// dwt_hold is created to hold the dwt output as further operations need to be
// carried out on dwt_output in order to display scaled images.
vector<vector<double> > dwt_hold(rows_n, vector<double>( cols_n));
dwt_hold = dwt_output;
// Setting coefficients of created image to the scaled DWT output values
for (int i = 0; i < imgSize.height; i++ ) {
for (int j = 0; j < imgSize.width; j++ ){
if ( dwt_output[i][j] <= 0.0){
dwt_output[i][j] = 0.0;
}
if ( i <= (length2[0]) && j <= (length2[1]) ) {
((uchar*)(cvImg->imageData + cvImg->widthStep*i))[j] =
(char) ( (dwt_output[i][j] / max) * 255.0);
} else {
((uchar*)(cvImg->imageData + cvImg->widthStep*i))[j] =
(char) (dwt_output[i][j]) ;
}
}
}
cvNamedWindow( "DWT Image", 1 ); // creation of a visualisation window
cvShowImage( "DWT Image", cvImg ); // image visualisation
cvWaitKey();
cvDestroyWindow("DWT Image");
cvSaveImage("dwt.bmp",cvImg);
// Case 1 : Only 10% of the largest coefficients are considered
// Output is the 1D DWT vector
int n_coef1= int (output.size()/ 10);
cout << n_coef1 << endl;
// Finding Threshold Value corresponding to n_coef1
vector<double> temp1;
cout << "size: " << (int) temp1.size() << "\n";
cout << "capacity: " << (int) temp1.capacity() << "\n";
cout << "max_size: " << (int) temp1.max_size() << "\n";
for (unsigned int i =0; i < dwt_coef1.size(); i++) {
double tempval = abs(dwt_coef1[i]);
temp1.push_back(tempval);
}
double thresh1= 0.0;
findthresh(temp1,n_coef1,thresh1);
cout << "thresh" << thresh1 << endl;
ofstream temp("temp.txt");
for (unsigned int i =0; i < temp1.size(); i++){
temp << temp1[i] << " " ;
}
// Reset coeffficients value depending on threshold value
for (unsigned int i =0; i < dwt_coef1.size(); i++) {
double temp = abs(dwt_coef1[i]);
if (temp < thresh1){
dwt_coef1.at(i)= 0.0;
}
}
// Finding IDWT
vector<vector<double> > idwt_output(rows, vector<double>(cols));
idwt_2d( dwt_coef1,flag, nm, idwt_output,length);
double max1;
maxval(idwt_output,max1);
//Displaying Reconstructed Image
IplImage *dvImg;
CvSize dvSize; // size of output image
dvSize.width = idwt_output[0].size();
dvSize.height = idwt_output.size();
cout << idwt_output.size() << idwt_output[0].size() << endl;
dvImg = cvCreateImage( dvSize, 8, 1 );
for (int i = 0; i < dvSize.height; i++ ){
for (int j = 0; j < dvSize.width; j++ ){
if ( idwt_output[i][j] <= 0.0){
idwt_output[i][j] = 0.0;
}
((uchar*)(dvImg->imageData + dvImg->widthStep*i))[j] =
(char) ((idwt_output[i][j] / max1) * 255 ) ;
}
}
cvNamedWindow( "10% Coeff Reconstructed Image", 1 ); // creation of a visualisation window
cvShowImage( "10% Coeff Reconstructed Image", dvImg ); // image visualisation
cvWaitKey();
cvDestroyWindow("10% Coeff Reconstructed Image");
cvSaveImage("recon.bmp",dvImg);
// Case 2 : Only 2% of the largest coefficients are considered
// Output is the 1D DWT vector
int n_coef2= int (output.size()/ 50);
cout << n_coef2 << endl;
// Finding Threshold Value corresponding to n_coef1
vector<double> temp2;
for (unsigned int i =0; i < dwt_coef2.size(); i++) {
double tempval = abs(dwt_coef2[i]);
temp2.push_back(tempval);
}
double thresh2= 0.0;
findthresh(temp2,n_coef2,thresh2);
cout << "thresh" << thresh2 << endl;
// Reset coeffficients value depending on threshold value
for (unsigned int i =0; i < dwt_coef2.size(); i++) {
double temp = abs(dwt_coef2[i]);
if (temp < thresh2){
dwt_coef2.at(i)= 0.0;
}
}
// Finding IDWT
vector<vector<double> > idwt_output2(rows, vector<double>(cols));
idwt_2d( dwt_coef2,flag, nm, idwt_output2,length);
double max2;
maxval(idwt_output2,max2);
//Displaying Reconstructed Image
IplImage *dvImg2;
CvSize dvSize2; // size of output image
dvSize2.width = idwt_output2[0].size();
dvSize2.height = idwt_output2.size();
cout << idwt_output2.size() << idwt_output2[0].size() << endl;
dvImg2 = cvCreateImage( dvSize2, 8, 1 );
for (int i = 0; i < dvSize2.height; i++ ) {
for (int j = 0; j < dvSize2.width; j++ ) {
if ( idwt_output2[i][j] <= 0.0){
idwt_output2[i][j] = 0.0;
}
((uchar*)(dvImg2->imageData + dvImg2->widthStep*i))[j] =
(char) ((idwt_output2[i][j]/ max2) * 255 ) ;
}
}
cvNamedWindow( "2% Coeff Reconstructed Image", 1 ); // creation of a visualisation window
cvShowImage( "2% Coeff Reconstructed Image", dvImg2 ); // image visualisation
cvWaitKey();
cvDestroyWindow("2% Coeff Reconstructed Image");
cvSaveImage("recon2.bmp",dvImg2);
return 0;
}
This code decomposes a 512X512 grayscale image to 6 levels using db2 wavelets and uses a) only 10% coefficients and b) only 2% coefficients to reconstruct the image.
Input Image
DWT of Input Image
Image Approximation using only 10% coefficients
Image Approximation using only 2% coefficients.
