%% Haar Transform 2D
% David Ruch and Patrick J. Van Fleet
% Minicourse #4, January 2008 Joint Mathematics Meetings
% San Diego, CA

%% Objective
% In this m-file, we will explore the two-dimensional discrete Haar
% wavelet transform.

%% Conventions
% This m-file uses the DiscreteWavelets Toolbox.  Help is available on all
% functions in the toolbox by accessing the Help menu and clicking on the
% DiscreteWavelets Toolbox.  
%
% Demos are also available.  Click the Demos tab under Help to access all
% demos.

%% Available Images
% The DiscreteWavelets packages comes with 18 grayscale images.  You can
% see information about these images (name, size, etc.) by issuing the 
% command ImageList.

ImageList('ImageType','GrayScale');

%% 
% You can also get a look at these images by using the command
% ShowThumbnails.  

ShowThumbnails('ImageType','GrayScale');

%% 
% No matter where you installed the DiscreteWavelets package on your
% computer, you can retrieve the absolute path and file name for each 
% included image.  The command ImageNames produces a list of file names.

gray = ImageNames('ImageType','GrayScale');
disp(gray{1});

%% Loading and Plotting Images
% Once you have the list of file names, it is very easy to load and plot
% images.  Let's load the first image in the list.

A = ImageRead(gray{1});
close;
ImagePlot(A);

%% Using HWT2D
% In the cell below, we compute and plot the two-dimensional HWT of image
% A.  We compute the transform of N[A] to speed up the computation.

B = HWT2D(A,1);
close;
WaveletDensityPlot(B,1,'DivideLinesThickness',2);

%% Using IHWT2D
% In the cell below, we compute the inverse transform of the image.

B = HWT2D(A,1);
WaveletDensityPlot(B,1,'DivideLinesThickness',2)

origA = IHWT2D(B,1);
figure;
ImagePlot(origA);

%% Iterating the Process
% Just as with the one-dimensional HWT, we can iterate the two-dimensional
% HWT.  In this case, the HWT2D is applied the approximation (blur) 
% portion of the transform.
% 
% Warning:  Make sure to know the maximum amount of iterations you can 
% compute before proceeding!!  You can use ImageList to display the 
% maximum number of iterations that can be performed on each of the 
% included images.

ImageList('ImageType','GrayScale');

%%
% Here we compute four iterations of the Haar wavelet transformation.

its = 4;
B = HWT2D(A, its);
close;
WaveletDensityPlot(B,its,'DivideLinesThickness',[2 2 2 2]);

%%
% You can plot various portions of the transform.  Here is the vertical
% portion of the third iteration.

WaveletDensityPlot(B,its,'Iteration',3,'Region','Vertical');

%%
% Here is the horizontal portion of the first iteration.

close;
WaveletDensityPlot(B,its,'Iteration',1,'Region','Horizontal');

%%
% Here is the blur.

close;
WaveletDensityPlot(B,its,'Region','Blur');

%%
% We can "blow up" the blur.

close;
WaveletDensityPlot(B,its,'Region','Blur','Magnification',8)

%%
close all;
displayEndOfDemoMessage(mfilename)