nmdemo.m

matlab程序

function nmdemo(Num)
%NMDEMO  Nonlinear multiresolution demos.
%
%  Type "nmdemo" and press enter to run.
%

% Pascal Getreuer 2005-2006

global G_DEMO

if nargin == 0
   if ~isempty(G_DEMO)
      figure(G_DEMO(1));
      return;
   end
   
   % Create main demo window
   G_DEMO(1) = figure('Name','WaveDemo','Numbertitle','off','Menubar','none',...
      'Resize','off','CloseRequestFcn',['global G_DEMO,if ishandle(G_DEMO(5)),',...
         'close(G_DEMO(5));end,clear global G_DEMO;closereq;'],'NextPlot','new');
   set(G_DEMO(1),'Position',[40,95,210,185]);
   G_DEMO(2) = uicontrol('Style','list','Position',[10,40,190,140],'String',{'1   S-Transform',...
         '2   Morphological Haar Wavelet','3   Linear Binary Wavelet',...
         '4   Morphological Binary Wavelet','5   Max-Lifting Wavelet',...
         '6   Denoising with Max-Lifting','7   ENO Interpolation',...
         '8   ENO Multiresolution','9   ENO Approximation','     References'});
   G_DEMO(3) = uicontrol('Style','pushbutton','String','Select','Position',[35,8,65,25],...
      'Callback',['global G_DEMO;',mfilename,'(get(G_DEMO(2),''Value''));']);
   G_DEMO(4) = uicontrol('Style','pushbutton','String','Close','Position',[114,8,65,25],...
      'Callback','close;');
   set(G_DEMO(3:4),'BackgroundColor',get(G_DEMO(1),'Color'));
   G_DEMO(5) = nan;
elseif ~isempty(G_DEMO)
   if ~ishandle(G_DEMO(5))
      G_DEMO(5) = figure('Name','','Numbertitle','off');   % Create a figure window
   else
      figure(G_DEMO(5));  % Reuse same figure window if possible
      clf;
   end

   switch Num
   case 1  %%% Demo 1: S-Transform %%%
      fprintf(['\n     S-Transform\n\n',...
            'The sequential transform or "S-transform" is a nonlinear modification to\n',...
            'the Haar wavelet such that an integer-valued signal has integer-value\n'...
            'transform coefficients.  The decomposition is\n\n',...
            '   s[n] = floor( (x[2n] + x[2n+1])/2 )\n   d[n] = x[2n+1] - x[2n]\n\n',...
            'and reconstruction is\n\n   x[2n]   = s[n] - floor(d[n]/2)\n',...
            '   x[2n+1] = s[n] + floor( (d[n] + 1)/2 )\n\n',...
            'The figure shows an example decomposition.  This transform is implemented\n',...
            'in SEQHAAR and SEQHAAR2.\n\n\n']);
      set(G_DEMO(5),'Name','S-Transform');      
      x = [1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,0,0,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,...
         0,0,3,3,3,3,3,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3];
      subplot(2,1,1);
      plot(0:63,x,'.-');
      xlim([0,63]);
      title('Original');
      subplot(2,1,2);
      y = seqhaar(x,2); % Apply the S-transform with two stages of decomposition
      plot(0:15,y(1:16),'b.-',16:63,y(17:64),'b.',...
         [15.5,15.5],[-4,4],'k',[31.5,31.5],[-4,4],'k');
      axis([0,63,-4,4]);
      title('Two levels of decomposition');
   case 2  %%% Demo 2: Morphological Haar Wavelet %%%
      fprintf(['\n     Morphological Haar Wavelet\n\n',...
            'Like the S-transform (see previous demo), the morphological Haar wavelet\n',...
            'is a nonlinear modification of the Haar wavelet such that applying the\n',...
            'transform to an integer-valued signal results in an integer-valued output.\n',...
            'The morphological Haar wavelet uses erosion instead of averaging for its\n',...
            'decimation operator.  Consequently, jumps are represented more crisply than\n',...
            'with the S-transform.  The morphological Haar wavelet decomposition is\n\n',...
            '   s[n] = min {x[2n], x[2n+1]}\n   d[n] = x[2n] - x[2n+1]\n\n',...
            'and reconstruction is\n\n   x[2n]   = s[n] + max {d[n], 0}\n',...
            '   x[2n+1] = s[n] - min {d[n], 0}\n\n',...
            'The figure shows an example decomposition.  This transform is implemented\n',...
            'in MHAAR.\n\n\n']);
      set(G_DEMO(5),'Name','Morphological Haar Wavelet');
      x = [1,1,1,1,1,1,1,1,1,1,1,1,4,4,4,4,4,4,4,0,0,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,...
         0,0,3,3,3,3,3,4,4,4,4,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,3,3];
      subplot(2,1,1);
      plot(0:63,x,'.-');
      xlim([0,63]);
      title('Original');
      subplot(2,1,2);
      y = mhaar(x,2);
      plot(0:15,y(1:16),'b.-',16:63,y(17:64),'b.',...
         [15.5,15.5],[-4,4],'k',[31.5,31.5],[-4,4],'k');
      axis([0,63,-4,4]);
      title('Two levels of decomposition');
   case 3  %%% Demo 3: Linear Binary Wavelet %%%
      fprintf(['\n     Linear Binary Wavelet\n\n',...
            'A binary wavelet transform converts a binary image to a multiresolution\n',...
            'representation where all transform coefficients are 0 or 1.  One such\n',...
            'transform is demonstrated here.  The decomposition is\n\n',...
            '   s[n]  = x[2n] + x[2n-1] + x[2n-2]\n',...
            '   d[n]  = x[2n] + x[2n-1]\n\n',...
            'and retain only the lowest bit in s[n] and d[n], (e.g. \n',...
            's[n] = mod(s[n],2) ).  Reconstruction is\n\n',...
            '   s2[2n] = s[n],  s2[2n+1] = 0\n',...
            '   d2[2n] = d[n],  d2[2n+1] = 0\n',...
            '   x[n]   = s2[n] + s2[n-1] + d2[n] + d2[n-1] + d2[n-2]\n\n',...
            'Again, retain only the lowest bit in x(n).  The figure shows an example\n',...
            'decomposition.  Note the "binary blurring" in the upper-left corner\n',...
            '(LLL subband).  This transform is implemented in LINBWT and LINBWT2.\n\n\n']);
      set(G_DEMO(5),'Name','Linear Binary Wavelet');
      [x,y] = meshgrid(1:128,1:128);
      x = ((abs(x-64).^.7+abs(y-64).^.7) < 17);
      subplot(1,2,1);
      imagesc(x);               % Display original image
      colormap([0,0,0;1,1,1]);
      axis image;
      title('Original');
      subplot(1,2,2);
      imagesc(linbwt2(x,2));    % Display decomposition
      line([64.5,64.5],[1,128]);
      line([1,128],[64.5,64.5]);
      line([32.5,32.5],[1,64.5]);
      line([1,64.5],[32.5,32.5]);
      colormap([0,0,0;1,1,1]);
      axis image;
      title('Two levels of decomposition');
   case 4  %%% Demo 4: Morphological Binary Wavelet %%%
      fprintf(['\n     Morphological Binary Wavelet\n\n',...
            'Another binary wavelet transform is the 2D median morphological wavelet.\n',...
            'The transform uses a 5-element median in the decimation operator.  Its\n',...
            'implementation is computationally cheap with only median operations and\n',...
            'XOR operations.  The decomposition is\n\n',...
            '   s[n,m]  = median {x[2n,2m], x[2n,2m], x[2n+1,2m], ...\n',...
            '                       x[2n,2m+1], x[2n+1,2m+1]}\n',...
            '   dv[n,m] = x[2n,2m] XOR x[2n,2m+1]\n   dh[n,m] = x[2n,2m] XOR x[2n+1,2m]\n',...
            '   dd[n,m] = x[2n,2m] XOR x[2n+1,2m+1]\n\n',...
            'and reconstruction is\n\n',...
            '   x[2n,2m]     = s[n,m] XOR min {dv[n,m], dh[n,m], dd[n,m]}\n',...
            '   x[2n+1,2m]   = x[2n,2m] XOR dh[n,m]\n   x[2n,2m+1]   = x[2n,2m] XOR dv[n,m]\n',...
            '   x[2n+1,2m+1] = x[2n,2m] XOR dd[n,m]\n\n',...
            'The figure shows an example decomposition.  This binary wavelet preserves\n',...
            'edges more crisply than the transform in the previous demo; it does not\n',...
            'have "binary blurring".  This transform is implemented in MORPHBWT2.\n\n\n']);
      set(G_DEMO(5),'Name','Morphological Binary Wavelet');
      [x,y] = meshgrid(1:128,1:128);
      x = ((abs(x-64).^.7+abs(y-64).^.7) < 17);
      subplot(1,2,1);
      imagesc(x);                  % Display original image
      colormap([0,0,0;1,1,1]);
      axis image;
      title('Original');
      subplot(1,2,2);
      imagesc(morphbwt2(x,2));     % Display Decomposition
      hold on;
      line([64.5,64.5],[1,128]);
      line([1,128],[64.5,64.5]);
      line([32.5,32.5],[1,64.5]);
      line([1,64.5],[32.5,32.5]);
      colormap([0,0,0;1,1,1]);
      axis image;