2D DWT/IDWT Demo

Notes

dwt_2d and dwt_2d_sym functions are interchangeable in the following code as they take the same arguments.
Please make sure that right header file is included. Following sample program links to wavelet2d.h which is the header for shared libraries. wavelet2s.h must be included for static libraries.
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.

Sample Code


#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <complex>
#include <cmath>
#include <algorithm>
#include "wavelet2d.h"
#include "cv.h"
#include "highgui.h"
#include "cxcore.h"

using namespace std;
using namespace cv;

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("snow.jpg");
    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 = "db3";
    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 3 (eg., int e = 3)

    vector<int> length;
    vector<double> output,flag;
    int J =3;
    dwt_2d_sym(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;

    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);

    // Finding IDWT

    vector<vector<double> > idwt_output(rows, vector<double>(cols));

    idwt_2d_sym(output,flag, nm, idwt_output,length);



    //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++ )
            ((uchar*)(dvImg->imageData + dvImg->widthStep*i))[j] =
                    (char) (idwt_output[i][j])  ;

    cvNamedWindow( "Reconstructed Image", 1 ); // creation of a visualisation window
    cvShowImage( "Reconstructed Image", dvImg ); // image visualisation
    cvWaitKey();
    cvDestroyWindow("Reconstructed Image");
    cvSaveImage("recon.bmp",dvImg);

    return 0;
}

Input Image is a low resolution 250X189 grayscale snow.jpg image.

Input 250X189 Image

3-Level Decomposition using db3 wavelet

Perfectly Reconstructed Image

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2D DWT/IDWT Demo

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