Pixel Shuffling and inverse shuffling

I have tried to shuffle the image using tinkerbell map and Henon Map and obtained the output.But I cant do the inverse shuffling processes.The code is given below

clear all
clc
g=imread('cameraman.tif');
% g=double(g)/255;
subplot(231)
imshow(g)
original=g;
[m,n]=size(g);
mo=m;
num = 12;
K=10.^10;
% K=19;

%....................Shuffling.......................
 disp('........................Started Shuffling.....................')

%Tinkerbell shuffling
a=0.3;b=0.6000;c=2.0;d=0.27;

for k= 1:num
for i=1:m
    for j=1:n
      r = mod([round(abs((i^2)-(j^2)+(a*i)+(b*j))),round(abs((2*i*j)+(c*i)+(d*j)))], [m,n]);
%     r = mod([(i+j),(j+K*sin(((i+1)*n)/2*pi))],mo);
%     r = [((i-1)+(K*sin(j-1))),((j-1)+i)];
%     r = uint8(r);
      ggg(i,j)=g(r(1)+1,r(2)+1);
%       ggg(i,j)=g(r(1),r(2));

      end
  end
    g=ggg;
  end

   subplot(232)
   x=ggg;
   imshow(ggg,[]);
   title('Tinkerbell shuffled')

   %henon Shuffling
  [m,n]=size(x);
   a = 1.4;b=0.3;
  % num_iter=input('Enter the round for Arnold shuffling');
  num_iter = 5;
  %     a=1.4;
  %     b=0.3;
   for k=1:num_iter
  for i=1:m
      for j=1:m
          r = mod([round(abs(1-(a*(i^2))+j)),round(abs(b*i))],[m n]);
           xxx(i,j)=x(r(1)+1,r(2)+1);

       end
   end
    x=xxx;
   end
   subplot(233)
   imshow(xxx);
   title('henon Shuffled Image')
   save xxx x

   disp('........................Shuffling process completed succesfully.....................')

   %...................Inverse Shufling.............................

   disp('........................Started Inverse Shuffling.....................')
   %Henon Inverse Shuffling
   for k=1:num_iter
  for i=1:m
      for j=1:n
  r = mod([round(abs(1-(a*(i^2))+j)),round(abs(b*i))],[m n]);
  x1(r(1)+1,r(2)+1)=xxx(i,j);

       end
   end
    xxx=x1;
   end
   subplot(234)
   imshow(x1);
   title('henon Inverse Shuffled')

%Tinkerbell inverse shuffling
 a=0.3;b=0.6000;c=2.0;d=0.27;
for k=1:num
for i=1:m
    for j=1:n
         r = mod([round(abs((i^2)-(j^2)+(a*i)+(b*j))),round(abs((2*i*j)+(c*i)+(d*j)))], [m,n]);

          g1(r(1)+1,r(2)+1)=x1(i,j); 

       end
   end
    xxx=g1;
  end
   subplot(224)
   imshow(g1)
   title('Tinkerbell_inverse_shuffled')
    disp('........................Inverse Shuffling process completed succesfully.....................')

   psnr = psnr(g1,original)
   ssim=ssim(g1,original)

[marie lasz]

May I know that why you shuffled the image two times , I mean with two methods?

Answer 1

[Walter Roberson]

Suppose your shuffled image is S. Then

temp = reshape(1:numel(S), size(S));

temp will be an array of linear indices -- temp(k) will be k.

Now apply your forward shuffling routine to temp, generating temp_mapped . Each value in temp_mapped will appear only once, and the location temp_mapped == k is the place that the shuffle maps pixel #k to. So you can undo it:

unshuffled = zeros(size(S), class(S));
unshuffled(temp_map) = S;

and you can cross-check by shuffling this and checking that you get out S.

By the way, once you have temp_mapped, you can use it to do all future shuffling,

S1 = unsuffled(temp_map);
S2 = S1(temp_map);
S3 = S2(temp_map);

and S3 would be unsuffled shuffled 3 times, without having to do any further computation of indices.

[Renjith V Ravi]

Sorry, I am get confused regarding your reply.Please clarify

[Walter Roberson]

Replace

g=imread('cameraman.tif');

with

G = imread('cameraman.tif');
g = reshape( 1:numel(G), size(G) );

Then go through your shuffle code, producing ggg and xxx, but ignoring what is displayed.

After that,

GGG = G(ggg);
XXX = G(xxx);

are your two shuffled images, and you can imshow() those.

To unshuffle,

unshuffled_ggg = zeros(size(G), class(G));
unshuffled_ggg(ggg) = GGG;

unshuffled_xxx = zeros(size(G), class(G));
unshuffled_xxx(xxx) = XXX;

and now unshuffled_g and unshuffled_xxx are the result of undoing the shuffling of GGG and XXX

[Renjith V Ravi]

Anyway, I went for single shuffling,instead of double for easiness.But,I couldn't get the original image after unshuffling.The code is given below

clear all
close all
clc
num=1;
G = imread('cameraman.tif');
[m,n]=size(G);
g = reshape( 1:numel(G), size(G) );
a=0.3;b=0.6000;c=2.0;d=0.27;
%Tinkerbell shuffling
for k= 1:num
for i=1:m
  for j=1:n
    r = mod([round(abs((i^2)-(j^2)+(a*i)+(b*j))),round(abs((2*i*j)+(c*i)+(d*j)))], [m,n]);
    ggg(i,j)=g(r(1)+1,r(2)+1);
    end
end
  g=ggg;
end
GGG = G(ggg);

    disp('shuffling completed')

%inverse shuffling

% unshuffled_ggg = zeros(size(G), class(G));
% unshuffled_ggg(ggg) = GGG;

a=0.3;b=0.6000;c=2.0;d=0.27;
for k=1:num
for i=1:m
    for j=1:n
         r = mod([round(abs((i^2)-(j^2)+(a*i)+(b*j))),round(abs((2*i*j)+(c*i)+(d*j)))], [m,n]);

          g1(r(1)+1,r(2)+1)=GGG(i,j); 

       end
   end
    unshuffled_ggg=g1;
  end
   unshuffled_ggg = zeros(size(G), class(G));
   unshuffled_ggg(ggg) = GGG;

imshowpair(G,unshuffled_ggg, 'montage'); %better that subplot

[Walter Roberson]

You should remove

g=ggg;

but that will not affect the problem (the line just makes things harder later)

numel(unique(ggg)) is less than numel(ggg) which means that your code is mapping multiple locations to the same destination. The location (67,70) is reached in 8 different ways:

   191   107
    91   130
    35   153
   229   174
    35   204
     6   255
    17   255
   128   255

If you explore [6, 255] and [17, 255] then you can substitute in 255 for j in both cases, giving you

[ mod(round(abs(i^2 + (3*i)/10 - 64872)), 256), mod(round(abs(512*i + 1377/20)), 256)]

when you check round(abs(i^2 + (3*i)/10 - 64872) at i = 6 and i = 17 you will find that they are they generate two different values that are the same mod 256.

Because your mapping send multiple inputs to the same output location, there is no way to unshuffle it: you are losing information as you go. If you iterate enough times you would probably lose quite a lot.

[Walter Roberson]

Your henon map is even worse, giving only 19843 unique results of the mapping. It is so bad that with a 256 x 256 image, none of the values in column 79 and afterwards make it into the final image!

[Walter Roberson]

Let me put it another way:

Try starting with an all-white GGG and initialize g1 to all zero. Then apply your henon shuffling. If the shuffling works correctly, then every white input location will be moved to a unique corresponding location in g1, and the result in g1 would be all white as well. But try it and you will see that the result in g1 would be mostly black, indicating that nothing was moved into most locations.

[VINAY KUMAR SHARMA]

what can be done for unique henon map code, its values are repeating??

[RAVI KUMAR]

Are you able to get the correct inverse shuffling?

[juveria fatima]

am not getting the inverse

its showing error

Index exceeds matrix dimensions.

Error in rough (line 62)

x1(r(1)+1,r(2)+1)=xxx(i,j);

pleae help me to resolve

Answer 2

[Hyelda Kefas]

I was able to do the INVERSE SHUFFLE for the Henon map. I don't know whether it is perfectly correct or not. Let's rub minds and get the perfect solution for you. Thanks

clear all
clc
g=imread('cameraman.tif');
g = imresize(g, [256 256]);
g=g(:,:,1);
subplot(2,2,1)
imshow(g,[])
title('Original Image')

   %HENON SHUFFLING
    [m,n]=size(g);
     a = 3;
     b = 3;
    num_iter = 1;

     for k=1:num_iter
    for i=1:m
        for j=1:n
            r = mod([round(abs(1-(a*(i^2))+j)),round(abs(b*i))],[m n]);
             x(i,j)=g(r(1)+1,r(2)+1);
         end
     end
      g=x;
     end
     subplot(2,2,2)
     imshow(x,[]);
     title('Henon Shuffled Image')

     %HENON INVERSE SHUFFLING
     [m,n]=size(x);
     a = 3;
     b = 3;
    num_iter = 1;

     for k=1:num_iter
    for i=1:m
        for j=1:n
    r1 = mod([round(abs(1-(a*(i^2))+j)),round(abs(b*i))],[m n]);
    x1(r1(1)+1,r1(2)+1)=x(i,j);
    %x(i,j)=x1(r(1)+1,r(2)+1);
         end
     end
      x=x1;
     end
     subplot(2,2,3)
     imshow(x1,[]);
     title('Henon Inverse Shuffled')   
     set(gcf,'units','normalized','outerposition',[0 0 1 1]);