361 lines
12 KiB
Markdown
361 lines
12 KiB
Markdown
# Image Approximation #
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_Note_
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1. 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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2. 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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3. I'm using [OPENCV](http://opencv.willowgarage.com/wiki/) 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.
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[Sample Code](http://code.google.com/p/wavelet1d/source/browse/trunk/wavelet2d/demo/imagedemo2.cpp)
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```
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#include <iostream>
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#include <fstream>
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#include <vector>
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#include <string>
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#include <complex>
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#include <cmath>
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#include <algorithm>
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#include "wavelet2s.h"
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#include "cv.h"
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#include "highgui.h"
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#include "cxcore.h"
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using namespace std;
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using namespace cv;
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void findthresh(vector<double> &vector1, int N, double& t){
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sort(vector1.begin(), vector1.end(), greater<double>());
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t = vector1.at(N-1);
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}
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void* maxval(vector<vector<double> > &arr, double &max){
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max = 0;
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for (unsigned int i =0; i < arr.size(); i++) {
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for (unsigned int j =0; j < arr[0].size(); j++) {
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if (max <= arr[i][j]){
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max = arr[i][j];
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}
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}
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}
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return 0;
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}
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void* maxval1(vector<double> &arr, double &max){
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max = 0;
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for (unsigned int i =0; i < arr.size(); i++) {
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if (max <= arr[i]){
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max = arr[i];
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}
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}
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return 0;
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}
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int main() {
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IplImage* img = cvLoadImage("lena512.bmp");
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if (!img){
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cout << " Can't read Image. Try Different Format." << endl;
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exit(1);
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}
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int height, width;
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height = img->height;
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width = img->width;
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int nc = img->nChannels;
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// uchar* ptr2 =(uchar*) img->imageData;
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int pix_depth = img->depth;
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CvSize size;
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size.width =width;
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size.height=height;
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cout << "depth" << pix_depth << "Channels" << nc << endl;
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cvNamedWindow("Original Image", CV_WINDOW_AUTOSIZE);
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cvShowImage("Original Image", img);
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cvWaitKey();
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cvDestroyWindow("Original Image");
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cvSaveImage("orig.bmp",img);
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int rows =(int) height;
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int cols =(int) width;
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Mat matimg(img);
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vector<vector<double> > vec1(rows, vector<double>(cols));
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int k =1;
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for (int i=0; i < rows; i++) {
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for (int j =0; j < cols; j++){
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unsigned char temp;
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temp = ((uchar*) matimg.data + i * matimg.step)[j * matimg.elemSize() + k ];
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vec1[i][j] = (double) temp;
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}
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}
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string nm = "db2";
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vector<double> l1,h1,l2,h2;
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filtcoef(nm,l1,h1,l2,h2);
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// unsigned int lf=l1.size();
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// int rows_n =(int) (rows+ J*(lf-1));
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// int cols_n =(int) (cols + J * ( lf -1));
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// Finding 2D DWT Transform of the image using symetric extension algorithm
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// Extension is set to 0 (eg., int e = 0)
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vector<int> length;
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vector<double> output,flag;
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int J =6;
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dwt_2d(vec1,J,nm,output,flag,length);
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double max;
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vector<int> length2;
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// This algorithm computes DWT of image of any given size. Together with convolution and
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// subsampling operations it is clear that subsampled images are of different length than
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// dyadic length images. In order to compute the "effective" size of DWT we do additional
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// calculations.
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dwt_output_dim_sym(length,length2,J);
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// length2 is gives the integer vector that contains the size of subimages that will
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// combine to form the displayed output image. The last two entries of length2 gives the
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// size of DWT ( rows_n by cols_n)
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int siz = length2.size();
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int rows_n=length2[siz-2];
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int cols_n = length2[siz-1];
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vector<vector< double> > dwtdisp(rows_n, vector<double>(cols_n));
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dispDWT(output,dwtdisp, length ,length2, J);
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// dispDWT returns the 2D object dwtdisp which will be displayed using OPENCV's image
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// handling functions
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vector<vector<double> > dwt_output= dwtdisp;
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// Storing the DWT coefficients in two different vectors that will be used to approximate
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// Image with two different sets of chosen coefficients.
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vector<double> dwt_coef1;
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vector<double> dwt_coef2;
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dwt_coef1 = output;
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dwt_coef2 = output;
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maxval(dwt_output,max);// max value is needed to take care of overflow which happens because
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// of convolution operations performed on unsigned 8 bit images
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//Displaying Scaled Image
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// Creating Image in OPENCV
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IplImage *cvImg; // image used for output
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CvSize imgSize; // size of output image
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imgSize.width = cols_n;
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imgSize.height = rows_n;
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cvImg = cvCreateImage( imgSize, 8, 1 );
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// dwt_hold is created to hold the dwt output as further operations need to be
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// carried out on dwt_output in order to display scaled images.
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vector<vector<double> > dwt_hold(rows_n, vector<double>( cols_n));
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dwt_hold = dwt_output;
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// Setting coefficients of created image to the scaled DWT output values
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for (int i = 0; i < imgSize.height; i++ ) {
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for (int j = 0; j < imgSize.width; j++ ){
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if ( dwt_output[i][j] <= 0.0){
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dwt_output[i][j] = 0.0;
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}
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if ( i <= (length2[0]) && j <= (length2[1]) ) {
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((uchar*)(cvImg->imageData + cvImg->widthStep*i))[j] =
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(char) ( (dwt_output[i][j] / max) * 255.0);
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} else {
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((uchar*)(cvImg->imageData + cvImg->widthStep*i))[j] =
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(char) (dwt_output[i][j]) ;
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}
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}
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}
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cvNamedWindow( "DWT Image", 1 ); // creation of a visualisation window
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cvShowImage( "DWT Image", cvImg ); // image visualisation
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cvWaitKey();
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cvDestroyWindow("DWT Image");
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cvSaveImage("dwt.bmp",cvImg);
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// Case 1 : Only 10% of the largest coefficients are considered
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// Output is the 1D DWT vector
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int n_coef1= int (output.size()/ 10);
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cout << n_coef1 << endl;
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// Finding Threshold Value corresponding to n_coef1
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vector<double> temp1;
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cout << "size: " << (int) temp1.size() << "\n";
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cout << "capacity: " << (int) temp1.capacity() << "\n";
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cout << "max_size: " << (int) temp1.max_size() << "\n";
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for (unsigned int i =0; i < dwt_coef1.size(); i++) {
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double tempval = abs(dwt_coef1[i]);
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temp1.push_back(tempval);
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}
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double thresh1= 0.0;
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findthresh(temp1,n_coef1,thresh1);
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cout << "thresh" << thresh1 << endl;
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ofstream temp("temp.txt");
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for (unsigned int i =0; i < temp1.size(); i++){
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temp << temp1[i] << " " ;
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}
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// Reset coeffficients value depending on threshold value
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for (unsigned int i =0; i < dwt_coef1.size(); i++) {
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double temp = abs(dwt_coef1[i]);
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if (temp < thresh1){
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dwt_coef1.at(i)= 0.0;
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}
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}
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// Finding IDWT
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vector<vector<double> > idwt_output(rows, vector<double>(cols));
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idwt_2d( dwt_coef1,flag, nm, idwt_output,length);
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double max1;
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maxval(idwt_output,max1);
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//Displaying Reconstructed Image
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IplImage *dvImg;
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CvSize dvSize; // size of output image
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dvSize.width = idwt_output[0].size();
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dvSize.height = idwt_output.size();
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cout << idwt_output.size() << idwt_output[0].size() << endl;
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dvImg = cvCreateImage( dvSize, 8, 1 );
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for (int i = 0; i < dvSize.height; i++ ){
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for (int j = 0; j < dvSize.width; j++ ){
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if ( idwt_output[i][j] <= 0.0){
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idwt_output[i][j] = 0.0;
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}
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((uchar*)(dvImg->imageData + dvImg->widthStep*i))[j] =
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(char) ((idwt_output[i][j] / max1) * 255 ) ;
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}
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}
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cvNamedWindow( "10% Coeff Reconstructed Image", 1 ); // creation of a visualisation window
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cvShowImage( "10% Coeff Reconstructed Image", dvImg ); // image visualisation
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cvWaitKey();
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cvDestroyWindow("10% Coeff Reconstructed Image");
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cvSaveImage("recon.bmp",dvImg);
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// Case 2 : Only 2% of the largest coefficients are considered
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// Output is the 1D DWT vector
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int n_coef2= int (output.size()/ 50);
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cout << n_coef2 << endl;
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// Finding Threshold Value corresponding to n_coef1
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vector<double> temp2;
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for (unsigned int i =0; i < dwt_coef2.size(); i++) {
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double tempval = abs(dwt_coef2[i]);
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temp2.push_back(tempval);
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}
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double thresh2= 0.0;
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findthresh(temp2,n_coef2,thresh2);
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cout << "thresh" << thresh2 << endl;
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// Reset coeffficients value depending on threshold value
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for (unsigned int i =0; i < dwt_coef2.size(); i++) {
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double temp = abs(dwt_coef2[i]);
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if (temp < thresh2){
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dwt_coef2.at(i)= 0.0;
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}
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}
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// Finding IDWT
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vector<vector<double> > idwt_output2(rows, vector<double>(cols));
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idwt_2d( dwt_coef2,flag, nm, idwt_output2,length);
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double max2;
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maxval(idwt_output2,max2);
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//Displaying Reconstructed Image
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IplImage *dvImg2;
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CvSize dvSize2; // size of output image
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dvSize2.width = idwt_output2[0].size();
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dvSize2.height = idwt_output2.size();
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cout << idwt_output2.size() << idwt_output2[0].size() << endl;
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dvImg2 = cvCreateImage( dvSize2, 8, 1 );
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for (int i = 0; i < dvSize2.height; i++ ) {
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for (int j = 0; j < dvSize2.width; j++ ) {
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if ( idwt_output2[i][j] <= 0.0){
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idwt_output2[i][j] = 0.0;
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}
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((uchar*)(dvImg2->imageData + dvImg2->widthStep*i))[j] =
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(char) ((idwt_output2[i][j]/ max2) * 255 ) ;
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}
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}
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cvNamedWindow( "2% Coeff Reconstructed Image", 1 ); // creation of a visualisation window
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cvShowImage( "2% Coeff Reconstructed Image", dvImg2 ); // image visualisation
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cvWaitKey();
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cvDestroyWindow("2% Coeff Reconstructed Image");
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cvSaveImage("recon2.bmp",dvImg2);
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return 0;
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}
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```
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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.
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Input Image
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DWT of Input Image
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Image Approximation using only 10% coefficients
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Image Approximation using only 2% coefficients.
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