wavefast.m ( File view )

  • By yueqiaohuayuan 2014-11-17
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			function [c, s] = wavefast(x, n, varargin)
%WAVEFAST Perform multi-level 2-dimensional fast wavelet transform.
%   [C, L] = WAVEFAST(X, N, LP, HP) performs a 2D N-level FWT of
%   image (or matrix) X with respect to decomposition filters LP and
%   HP.
%
%   [C, L] = WAVEFAST(X, N, WNAME) performs the same operation but
%   fetches filters LP and HP for wavelet WNAME using WAVEFILTER.
%
%   Scale parameter N must be less than or equal to log2 of the
%   maximum image dimension.  Filters LP and HP must be even. To
%   reduce border distortion, X is symmetrically extended. That is,
%   if X = [c1 c2 c3 ... cn] (in 1D), then its symmetric extension
%   would be [... c3 c2 c1 c1 c2 c3 ... cn cn cn-1 cn-2 ...].
%
%   OUTPUTS:
%     Matrix C is a coefficient decomposition vector:
%
%      C = [ a(n) h(n) v(n) d(n) h(n-1) ... v(1) d(1) ]
%
%     where a, h, v, and d are columnwise vectors containing
%     approximation, horizontal, vertical, and diagonal coefficient
%     matrices, respectively.  C has 3n + 1 sections where n is the
%     number of wavelet decompositions. 
%
%     Matrix S is an (n+2) x 2 bookkeeping matrix:
%
%      S = [ sa(n, :); sd(n, :); sd(n-1, :); ... ; sd(1, :); sx ]
%
%     where sa and sd are approximation and detail size entries.
%
%   See also WAVEBACK and WAVEFILTER.

%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins
%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004
%   $Revision: 1.5 $  $Date: 2003/10/13 01:14:17 $

% Check the input arguments for reasonableness.
error(nargchk(3, 4, nargin));

if nargin == 3
   if ischar(varargin{
1
})   
      [lp, hp] = wavefilter(varargin{
1
}, 'd');
   else 
      error('Missing wavelet name.');   
   end
else
      lp = varargin{
1
};     hp = varargin{
2
};   
end

fl = length(lp);      sx = size(x);

if (ndims(x) ~= 2) | (min(sx) < 2) | ~isreal(x) | ~isnumeric(x)
   error('X must be a real, numeric matrix.');     
end
  
if (ndims(lp) ~= 2) | ~isreal(lp) | ~isnumeric(lp) ...
       | (ndims(hp) ~= 2) | ~isreal(hp) | ~isnumeric(hp) ...
       | (fl ~= length(hp)) | rem(fl, 2) ~= 0
   error(['LP and HP must be even and equal length real, ' ...
          'numeric filter vectors.']); 
end
  
if ~isreal(n) | ~isnumeric(n) | (n < 1) | (n > log2(max(sx)))
   error(['N must be a real scalar between 1 and ' ...
          'log2(max(size((X))).']);    
end
  
% Init the starting output data structures and initial approximation.
c = [];       s = sx;     app = double(x);

% For each decomposition ...
for i = 1:n
   % Extend the approximation symmetrically.
   [app, keep] = symextend(app, fl);
   
   % Convolve rows with HP and downsample. Then convolve columns
   % with HP and LP to get the diagonal and vertical coefficient
...
...
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