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ACmF.m

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+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Citation:
+% S. Enginoğlu, U. Erkan, and S. Memiş, 2020. Adaptive Cesáro Mean Filter  
+% for Salt-and-Pepper Noise Removal, El-Cezeri Journal of Science and 
+% Engineering, 7(1), 304-314.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Abbreviation of Journal Title: El-Cezeri J. Sci. Eng.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% https://doi.org/10.31202/ecjse.646359
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% https://www.researchgate.net/profile/Serdar_Enginoglu2
+% https://www.researchgate.net/profile/Ugur_Erkan
+% https://www.researchgate.net/profile/Samet_Memis2
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% % Demo: 
+% clc;
+% clear all;
+% io=imread("lena.tif");
+% Noise_Image=imnoise(io,'salt & pepper',0.8);
+% Denoised_Image=ACmF(Noise_Image);
+% psnr_results=psnr(io,Denoised_Image);
+% ssim_results=ssim(io,Denoised_Image);
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+function X=ACmF(A)
+A=double(A);
+ for p=5:-1:1  
+  pA=padarray(A,[p p],'symmetric');
+  pB=(pA~=0 & pA~=255);
+  [m,n]=size(pB);
+  for i=1+p:m-p
+    for j=1+p:n-p       
+       if (pB(i,j)==0)          
+            for k=1:p
+                if (isequal(pB(i-k:i+k,j-k:j+k),zeros(2*k+1,2*k+1))~=1)             
+                     R1=pA(i-k:i+k,j-k:j+k);
+                     R2=R1(R1>0 & R1<255);
+                     A(i-p,j-p)=mean(R2);
+                     break;
+                end
+            end
+       end
+    end 
+  end   
+ end
+  X=uint8(A);
+end
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

demo.m

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+clc;
+clear all;
+io=imread("lena.tif");
+Noise_Image=imnoise(io,'salt & pepper',0.8);
+Denoised_Image=ACmF(Noise_Image);
+psnr_results=psnr(io,Denoised_Image);
+ssim_results=ssim(io,Denoised_Image);

ssim.m

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+function [mssim, ssim_map] = ssim(img1, img2, K, window, L)
+
+%========================================================================
+%SSIM Index, Version 1.0
+%Copyright(c) 2003 Zhou Wang
+%All Rights Reserved.
+%
+%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 [email protected]
+%
+%----------------------------------------------------------------------
+%
+%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
+%
+%========================================================================
+
+
+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))   % 图像大小过小，则没有意义。
+           ssim_index = -Inf;
+           ssim_map = -Inf;
+      return
+   end
+   window = fspecial('gaussian', 11, 1.5);        % 参数一个标准偏差1.5，11*11的高斯低通滤波。
+   K(1) = 0.01;                                                                      % default settings
+   K(2) = 0.03;                                                                      %
+   L = 255;                                  %
+end
+
+if (nargin == 3)
+   if ((M < 11) | (N < 11))
+           ssim_index = -Inf;
+           ssim_map = -Inf;
+      return
+   end
+   window = fspecial('gaussian', 11, 1.5);
+   L = 255;
+   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 = 255;
+   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;    % 计算C1参数，给亮度L（x，y）用。
+C2 = (K(2)*L)^2;    % 计算C2参数，给对比度C（x，y）用。
+window = window/sum(sum(window)); %滤波器归一化操作。
+img1 = double(img1); 
+img2 = double(img2);
+
+mu1   = filter2(window, img1, 'valid');  % 对图像进行滤波因子加权
+mu2   = filter2(window, img2, 'valid');  % 对图像进行滤波因子加权
+
+mu1_sq = mu1.*mu1;     % 计算出Ux平方值。
+mu2_sq = mu2.*mu2;     % 计算出Uy平方值。
+mu1_mu2 = mu1.*mu2;    % 计算Ux*Uy值。
+
+sigma1_sq = filter2(window, img1.*img1, 'valid') - mu1_sq;  % 计算sigmax （标准差）
+sigma2_sq = filter2(window, img2.*img2, 'valid') - mu2_sq;  % 计算sigmay （标准差）
+sigma12 = filter2(window, img1.*img2, 'valid') - mu1_mu2;   % 计算sigmaxy（标准差）
+
+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 = mean2(ssim_map);
+
+return