compute_ssim_index.m

image denoising toolbox in matlab

function [mssim, ssim_map] = compute_ssim_index(img1, img2, K, window, L)

%========================================================================
%SSIM Index, Version 1.0
%Copyright(c) 2003 Zhou Wang
%All Rights Reserved.
%
%The author is with Howard Hughes Medical Institute, and Laboratory
%for Computational Vision at Center for Neural Science and Courant
%Institute of Mathematical Sciences, New York University.
%
%----------------------------------------------------------------------
%Permission to use, copy, or modify this software and its documentation
%for educational and research purposes only and without fee is hereby
%granted, provided that this copyright notice and the original authors'
%names appear on all copies and supporting documentation. This program
%shall not be used, rewritten, or adapted as the basis of a commercial
%software or hardware product without first obtaining permission of the
%authors. The authors make no representations about the suitability of
%this software for any purpose. It is provided "as is" without express
%or implied warranty.
%----------------------------------------------------------------------
%
%This is an implementation of the algorithm for calculating the
%Structural SIMilarity (SSIM) index between two images. Please refer
%to the following paper:
%
%Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image
%quality assessment: From error visibility to structural similarity"
%IEEE Transactios on Image Processing, vol. 13, no. 4, pp.600-612,
%Apr. 2004.
%
%Kindly report any suggestions or corrections to [e-mail]
%
%----------------------------------------------------------------------
%
%Input : (1) img1: the first image being compared
%        (2) img2: the second image being compared
%        (3) K: constants in the SSIM index formula (see the above
%            reference). defualt value: K = [0.01 0.03]
%        (4) window: local window for statistics (see the above
%            reference). default widnow is Gaussian given by
%            window = fspecial('gaussian', 11, 1.5);
%        (5) L: dynamic range of the images. default: L = 255
%
%Output: (1) mssim: the mean SSIM index value between 2 images.
%            If one of the images being compared is regarded as 
%            perfect quality, then mssim can be considered as the
%            quality measure of the other image.
%            If img1 = img2, then mssim = 1.
%        (2) ssim_map: the SSIM index map of the test image. The map
%            has a smaller size than the input images. The actual size:
%            size(img1) - size(window) + 1.
%
%Default Usage:
%   Given 2 test images img1 and img2, whose dynamic range is 0-255
%
%   [mssim ssim_map] = ssim_index(img1, img2);
%
%Advanced Usage:
%   User defined parameters. For example
%
%   K = [0.05 0.05];
%   window = ones(8);
%   L = 100;
%   [mssim ssim_map] = ssim_index(img1, img2, K, window, L);
%
%See the results:
%
%   mssim                        %Gives the mssim value
%   imshow(max(0, ssim_map).^4)  %Shows the SSIM index map
%
%========================================================================

Lmax = 1;

if (nargin < 2 | nargin > 5)
   ssim_index = -Inf;
   ssim_map = -Inf;
   return;
end

if (size(img1) ~= size(img2))
   ssim_index = -Inf;
   ssim_map = -Inf;
   return;
end

[M N] = size(img1);

if (nargin == 2)
   if ((M < 11) | (N < 11))
	   ssim_index = -Inf;
	   ssim_map = -Inf;
      return
   end
   window = fspecial('gaussian', 11, 1.5);	%
   K(1) = 0.01;								      % default settings
   K(2) = 0.03;								      %
   L = Lmax;                                  %
end

if (nargin == 3)
   if ((M < 11) | (N < 11))
	   ssim_index = -Inf;
	   ssim_map = -Inf;
      return
   end
   window = fspecial('gaussian', 11, 1.5);
   L = Lmax;
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
		   ssim_index = -Inf;
   		ssim_map = -Inf;
	   	return;
      end
   else
	   ssim_index = -Inf;
   	ssim_map = -Inf;
	   return;
   end
end

if (nargin == 4)
   [H W] = size(window);
   if ((H*W) < 4 | (H > M) | (W > N))
	   ssim_index = -Inf;
	   ssim_map = -Inf;
      return
   end
   L = Lmax;
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
		   ssim_index = -Inf;
   		ssim_map = -Inf;
	   	return;
      end
   else
	   ssim_index = -Inf;
   	ssim_map = -Inf;
	   return;
   end
end

if (nargin == 5)
   [H W] = size(window);
   if ((H*W) < 4 | (H > M) | (W > N))
	   ssim_index = -Inf;
	   ssim_map = -Inf;
      return
   end
   if (length(K) == 2)
      if (K(1) < 0 | K(2) < 0)
		   ssim_index = -Inf;
   		ssim_map = -Inf;
	   	return;
      end
   else
	   ssim_index = -Inf;
   	ssim_map = -Inf;
	   return;
   end
end

C1 = (K(1)*L)^2;
C2 = (K(2)*L)^2;
window = window/sum(sum(window));
img1 = double(img1);
img2 = double(img2);

mu1   = filter2(window, img1, 'valid');
mu2   = filter2(window, img2, 'valid');
mu1_sq = mu1.*mu1;
mu2_sq = mu2.*mu2;
mu1_mu2 = mu1.*mu2;
sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;
sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;
sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;

if (C1 > 0 & C2 > 0)
   ssim_map = ((2*mu1_mu2 + C1).*(2*sigma12 + C2))./((mu1_sq + mu2_sq + C1).*(sigma1_sq + sigma2_sq + C2));
else
   numerator1 = 2*mu1_mu2 + C1;
   numerator2 = 2*sigma12 + C2;
	denominator1 = mu1_sq + mu2_sq + C1;
   denominator2 = sigma1_sq + sigma2_sq + C2;
   ssim_map = ones(size(mu1));
   index = (denominator1.*denominator2 > 0);
   ssim_map(index) = (numerator1(index).*numerator2(index))./(denominator1(index).*denominator2(index));
   index = (denominator1 ~= 0) & (denominator2 == 0);
   ssim_map(index) = numerator1(index)./denominator1(index);
end

mssim = mean(ssim_map(:));

return



function h = fspecial(varargin)
%FSPECIAL Create 2-D special filters.
%   H = FSPECIAL(TYPE) creates a two-dimensional filter H of the
%   specified type. Possible values for TYPE are:
%
%     'average'   averaging filter
%     'disk'      circular averaging filter
%     'gaussian'  Gaussian lowpass filter
%     'laplacian' filter approximating the 2-D Laplacian operator
%     'log'       Laplacian of Gaussian filter
%     'motion'    motion filter
%     'prewitt'   Prewitt horizontal edge-emphasizing filter
%     'sobel'     Sobel horizontal edge-emphasizing filter
%     'unsharp'   unsharp contrast enhancement filter
%
%   Depending on TYPE, FSPECIAL may take additional parameters
%   which you can supply.  These parameters all have default
%   values. 
%
%   H = FSPECIAL('average',HSIZE) returns an averaging filter H of size
%   HSIZE. HSIZE can be a vector specifying the number of rows and columns in
%   H or a scalar, in which case H is a square matrix.
%   The default HSIZE is [3 3].
%
%   H = FSPECIAL('disk',RADIUS) returns a circular averaging filter
%   (pillbox) within the square matrix of side 2*RADIUS+1.
%   The default RADIUS is 5.
%
%   H = FSPECIAL('gaussian',HSIZE,SIGMA) returns a rotationally
%   symmetric Gaussian lowpass filter  of size HSIZE with standard
%   deviation SIGMA (positive). HSIZE can be a vector specifying the
%   number of rows and columns in H or a scalar, in which case H is a
%   square matrix.
%   The default HSIZE is [3 3], the default SIGMA is 0.5.
%
%   H = FSPECIAL('laplacian',ALPHA) returns a 3-by-3 filter
%   approximating the shape of the two-dimensional Laplacian
%   operator. The parameter ALPHA controls the shape of the
%   Laplacian and must be in the range 0.0 to 1.0.
%   The default ALPHA is 0.2.
%
%   H = FSPECIAL('log',HSIZE,SIGMA) returns a rotationally symmetric
%   Laplacian of Gaussian filter of size HSIZE with standard deviation
%   SIGMA (positive). HSIZE can be a vector specifying the number of rows
%   and columns in H or a scalar, in which case H is a square matrix.
%   The default HSIZE is [5 5], the default SIGMA is 0.5.
%
%   H = FSPECIAL('motion',LEN,THETA) returns a filter to approximate, once
%   convolved with an image, the linear motion of a camera by LEN pixels,
%   with an angle of THETA degrees in a counter-clockwise direction. The
%   filter becomes a vector for horizontal and vertical motions.  The
%   default LEN is 9, the default THETA is 0, which corresponds to a
%   horizontal motion of 9 pixels.
%
%   H = FSPECIAL('prewitt') returns 3-by-3 filter that emphasizes
%   horizontal edges by approximating a vertical gradient. If you need to
%   emphasize vertical edges, transpose the filter H: H'.
%
%       [1 1 1;0 0 0;-1 -1 -1].
%
%   H = FSPECIAL('sobel') returns 3-by-3 filter that emphasizes
%   horizontal edges utilizing the smoothing effect by approximating a
%   vertical gradient. If you need to emphasize vertical edges, transpose
%   the filter H: H'.
%
%       [1 2 1;0 0 0;-1 -2 -1].
%
%   H = FSPECIAL('unsharp',ALPHA) returns a 3-by-3 unsharp contrast
%   enhancement filter. FSPECIAL creates the unsharp filter from the
%   negative of the Laplacian filter with parameter ALPHA. ALPHA controls
%   the shape of the Laplacian and must be in the range 0.0 to 1.0.
%   The default ALPHA is 0.2.
%
%   Class Support
%   -------------
%   H is of class double.
%
%   Example