bwt_onelevel.m

function decomp = bwt_onelevel(im)
% function decomp = bwt_onelevel(im)
%
% BWT decomposition -- one level only
% Version 1.2
%
% Arguments:
%  im: A square image; side length must be a multiple of 3
%
% Result:
%  decomp: The decomposition is laid out as (per Figure 3 of Willmore 
%  et al 2008):
%
%  [ 90-odd  135-odd  45-even ]
%  [ 90-even 135-even 45-odd  ]
%  [ DC      0-even   0 -odd  ]
%
% Citation:
%  Willmore B, Prenger RJ, Wu MC and Gallant JL (2008). The Berkeley 
%  Wavelet Transform: A biologically-inspired orthogonal wavelet transform.
%  Neural Computation 20:6, 1537-1564 
%
% The article is available at:
%  <http://dx.doi.org/10.1162/neco.2007.05-07-513>
%
% Copyright (c) 2008 Ben Willmore
%
% Permission is hereby granted, free of charge, to any person
% obtaining a copy of this software and associated documentation
% files (the "Software"), to deal in the Software without
% restriction, including without limitation the rights to use,
% copy, modify, merge, publish, distribute, sublicense, and/or sell
% copies of the Software, and to permit persons to whom the
% Software is furnished to do so, subject to the following
% conditions:
% 
% The above copyright notice and this permission notice shall be
% included in all copies or substantial portions of the Software.
% 
% THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
% EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
% OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
% NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
% HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
% WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
% FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
% OTHER DEALINGS IN THE SOFTWARE.

sz = size(im);

if (length(sz) ~= 2) || (sz(1) ~= sz(2))
  disp('Input must be square');
  decomp = nan;
  return;
end

sz = sz(1);
ssz = sz/3;

if ( (ssz-floor(ssz)) > abs(ssz)*eps )
  fprintf('Side length must be a multiple of 3');
  decomp = nan;
  return;
end

params = [90 0; 135 0; 45 90; 90 90; 135 90; 45 0; -1 -1; 0 90; 0 0];

decomp = zeros(sz)+nan;

for ii = 1:size(params,1)
   y = floor((ii-1)/3);
   x = mod(ii-1,3);
   bw = makebw(params(ii,1),params(ii,2));
   
   decomp(y*ssz+1:y*ssz+ssz,x*ssz+1:x*ssz+ssz) = bwtfilter(im,bw);
end