wave2gray.m

function w = wave2gray(c, s, scale, border)
%WAVE2GRAY Display wavelet decomposition coefficients.
%   W = WAVE2GRAY(C, S, SCALE, BORDER) displays and returns a
%   wavelet coefficient image.
%
%   EXAMPLES:
%     wave2gray(c, s);                      Display w/defaults.
%     foo = wave2gray(c, s);                Display and return.
%     foo = wave2gray(c, s, 4);             Magnify the details.
%     foo = wave2gray(c, s, -4);            Magnify absolute values.
%     foo = wave2gray(c, s, 1, 'append');   Keep border values.
%
%   INPUTS/OUTPUTS:
%     [C, S] is a wavelet decomposition vector and bookkeeping
%     matrix.
%
%     SCALE       Detail coefficient scaling
%     ----------------------------------------------------------
%     0 or 1      Maximum range (default)
%     2,3...      Magnify default by the scale factor
%     -1, -2...   Magnify absolute values by abs(scale)
%     
%     BORDER      Border between wavelet decompositions
%     ----------------------------------------------------------
%     'absorb'    Border replaces image (default)
%     'append'    Border increases width of image
%     
%     Image W:   ------- ------ ------------ -------------------
%                |      |      |            |
%                | a(n) | h(n) |            |
%                |      |      |            |
%                ------- ------     h(n-1)  |
%                |      |      |            |
%                | v(n) | d(n) |            |        h(n-2)
%                |      |      |            |
%                ------- ------ ------------
%                |             |            |        
%                |    v(n-1)   |   d(n-1)   |
%                |             |            |
%                -------------- ------------ -------------------
%                |                          |
%                |          v(n-2)          |        d(n-2) 
%                |                          |
%     
%     Here, n denotes the decomposition step scale and a, h, v, d are
%     approximation, horizontal, vertical, and diagonal detail
%     coefficients, respectively.

%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins
%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004
%   $Revision: 1.6 $  $Date: 2003/11/21 15:01:44 $

% Check input arguments for reasonableness.
error(nargchk(2, 4, nargin));
 
if (ndims(c) ~= 2) | (size(c, 1) ~= 1)
  error('C must be a row vector.');   end
  
if (ndims(s) ~= 2) | ~isreal(s) | ~isnumeric(s) | (size(s,2) ~= 2)
  error('S must be a real, numeric two-column array.');   end
  
elements = prod(s, 2);
if (length(c) < elements(end)) | ...
      ~(elements(1) + 3 * sum(elements(2:end - 1)) >= elements(end))
   error(['[C S] must be a standard wavelet ' ...
          'decomposition structure.']); 
end

if (nargin > 2) & (~isreal(scale) | ~isnumeric(scale))
   error('SCALE must be a real, numeric scalar.'); 
end
 
if (nargin > 3) & (~ischar(border))
  error('BORDER must be character string.');  
end

if nargin == 2 
   scale = 1;  % Default scale. 
end          

if nargin < 4 
   border = 'absorb';  % Default border.
end   
  
% Scale coefficients and determine pad fill.
absflag = scale < 0;
scale = abs(scale);   
if scale == 0 
   scale = 1; 
end

[cd, w] = wavecut('a', c, s);   w = mat2gray(w);
cdx = max(abs(cd(:))) / scale;
if absflag 
   cd = mat2gray(abs(cd), [0, cdx]);   fill = 0;
else 
   cd = mat2gray(cd, [-cdx, cdx]);   fill = 0.5;   
end
  
% Build gray image one decomposition at a time.
for i = size(s, 1) - 2:-1:1
   ws = size(w);
   
   h = wavecopy('h', cd, s, i);
   pad = ws - size(h);     frontporch = round(pad / 2);
   h = padarray(h, frontporch, fill, 'pre');
   h = padarray(h, pad - frontporch, fill, 'post');
   
   v = wavecopy('v', cd, s, i);
   pad = ws - size(v);     frontporch = round(pad / 2);
   v = padarray(v, frontporch, fill, 'pre');
   v = padarray(v, pad - frontporch, fill, 'post');
   
   d = wavecopy('d', cd, s, i);
   pad = ws - size(d);     frontporch = round(pad / 2);
   d = padarray(d, frontporch, fill, 'pre');
   d = padarray(d, pad - frontporch, fill, 'post');
   
   % Add 1 pixel white border.
   switch lower(border)
   case 'append'
      w = padarray(w, [1 1], 1, 'post');    
      h = padarray(h, [1 0], 1, 'post');
      v = padarray(v, [0 1], 1, 'post');
   case 'absorb'
      w(:, end) = 1;   w(end, :) = 1;   
      h(end, :) = 1;   v(:, end) = 1;
   otherwise
      error('Unrecognized BORDER parameter.');
   end
   
   w = [w h; v d];                 % Concatenate coefs.
end

if nargout == 0 
   imshow(w);                      % Display result.
end