i need a matlab code for arnold cat map scrambling

i need a matlab code for arnold cat map scrambling

[amreena najeeb]

how arnold's cat map work?? on which principle????

[Walter Roberson]

https://en.wikipedia.org/wiki/Arnold%27s_cat_map

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/?term=tag%3A%22cat+map%22

[mamoona]

hey! do you have the matlab code for image scrambling and unscrambling using arnold cat map? i am working on colored images.

Answer 1

[Image Analyst]

See attached demo.

[lena kappa]

Awesome demo!!!

How can u save every iteration in a file?

[Image Analyst]

You can use imwrite(). It should already be in the code.

	% Save the image, if desired.
	filename = sprintf('Arnold Cat Iteration %d.png', iteration);
% 	imwrite(currentScrambledImage, filename);
	fprintf('Saved image file %s to disk.\n', filename);

Just uncomment the immwrite() line. In case it's not in there, I'm attaching my latest m-file.

[lena kappa]

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 20;
myFolder = 'C:\Users\algo\Desktop';

%===============================================================================
% Get the name of the demo image the user wants to use.
% Let's let the user select from a list of all the demo images that ship with the Image Processing Toolbox.
folder = fileparts(which('a1.jpg')); % Determine where demo folder is (works with all versions).
% Demo images have extensions of TIF, PNG, and JPG.  Get a list of all of them.
imageFiles = [dir(fullfile(folder,'*.TIF')); dir(fullfile(folder,'*.PNG')); dir(fullfile(folder,'*.jpg'))];
for k = 1 : length(imageFiles)
% 	fprintf('%d: %s\n', k, files(k).name);
	[~, baseFileName, extension] = fileparts(imageFiles(k).name);
	ca{k} = [baseFileName, extension];
end
% Sort the base file names alphabetically.
[ca, sortOrder] = sort(ca);
imageFiles = imageFiles(sortOrder);
button = menu('Use which gray scale demo image?', ca); % Display all image file names in a popup menu.
% Get the base filename.
baseFileName = imageFiles(button).name; % Assign the one on the button that they clicked on.
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);

% Read in an image.
grayImage = imread(fullFileName);

% Get the dimensions of the image.  
% numberOfColorChannels should be = 1 for a gray scale image, and 3 for an RGB color image.
[rows, columns, numberOfColorChannels] = size(grayImage);

% Set a max size so the demo doesn't take too long.
maxAllowableSize = 401;
% Note: the number of iterations needed to return to the original image
% is very sensitive to the size of the image.  For example if 
% maxAllowableSize = 201 it takes 68 iterations, but if
% maxAllowableSize = 200 it takes 150 iterations.

% Make sure the image is square.
if rows ~= columns
	% It's not yet square.  Make it square and resize if needed.
	N = max([rows, columns]);
	if N > maxAllowableSize
		N = maxAllowableSize;
	end
	grayImage = imresize(grayImage, [N, N]);
end
[rows, columns, numberOfColorChannels] = size(grayImage);

if rows > maxAllowableSize
	% Make it smaller to speed up demo.
	N = maxAllowableSize;
	grayImage = imresize(grayImage, [N, N]);
end
% Update values.
[rows, columns, numberOfColorChannels] = size(grayImage);

% Display starting image.
%subplot(1, 2, 1);
imshow(grayImage);
axis on;
caption = sprintf('Original Image, %s', baseFileName);
title(caption, 'FontSize', fontSize);

% Set up figure properties:
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);
% Get rid of tool bar and pulldown menus that are along top of figure.
% set(gcf, 'Toolbar', 'none', 'Menu', 'none');
% Give a name to the title bar.
set(gcf, 'Name', 'Arnolds Cat Map ', 'NumberTitle', 'Off') 

startingTime = tic;
iteration = 1;
% Initialize image.
oldScrambledImage = grayImage;
% The number of iterations needed to restore the image can be shown never to exceed 3N.
N = rows;
while iteration <= 3 * N
	% Scramble the image based on the old image.
	for row = 1 : rows % y
		for col = 1 : columns % x
			c = mod((2 * col) + row, N) + 1; % x coordinate
			r = mod(col + row, N) + 1; % y coordinate
			% Move the pixel.  Note indexes are (row, column) = (y, x) NOT (x, y)!
			currentScrambledImage(row, col, :) = oldScrambledImage(r, c, :);
		end
	end
	
	% Display the current image.
	caption = sprintf('Arnolds Cat Map, Iteration #%d', iteration);
    File = sprintf('arn%0.1f.png',iteration);
    exportgraphics(figure,fullfile(myFolder,File));
	fprintf('%s\n', caption);
	%subplot(1, 2, 2);
	imshow(currentScrambledImage);
	axis on;
	title(caption, 'FontSize', fontSize);
	drawnow;
    
	
	% Insert a delay if desired.
% 	pause(0.1);
	
	% Save the image, if desired.
	filename = sprintf('Arnold Cat Iteration %d.png', iteration);
% 	imwrite(currentScrambledImage, filename);
	fprintf('Saved image file %s to disk.\n', filename);
	
	if immse(currentScrambledImage, grayImage) == 0
		caption = sprintf('Back to Original after %d Iterations.', iteration);
		fprintf('%s\n', caption);
		title(caption, 'FontSize', fontSize);
		break;
	end
	
	% Make the current image the prior/old one so we'll operate on that the next iteration.
	oldScrambledImage = currentScrambledImage;
	% Update the iteration counter.
	iteration = iteration+1;
end
elapsedTime = toc(startingTime);
fprintf('Elapsed time = %.1f seconds.\n', elapsedTime);
% Note: an interesting experiment might be to put the above loop in a loop where you're
% changing N and see how iteration (the number of iterations to return to the original)
% changes depending on N.

yes what you are saying is corect but i want to save each iteration not only the last , i tried to modify your code this way but the pictures it saves for each iteration are empty for some reason.

[Image Analyst]

But why did you not uncomment the imwrite() line of code???

[lena kappa]

i did but i got an error saying :

Error using imwrite (line 541)

Unable to open file "Arnold Cat Iteration 1.png" for writing. You might not have write permission.

Error in arnolds_cat_map (line 113)

imwrite(currentScrambledImage, filename);

thats why i tried the other way

[Image Analyst]

What is the current folder name?

[lena kappa]

if you mean the folder where i have the code its C:\Users\alexk\Desktop\mas\cat

[Image Analyst]

Try saving something simple there, like

moon = imread('moon.tif');
imwrite(moon, 'C:\Users\alexk\Desktop\mas\cat\moon.tif');

If that doesn't work then try just copying any file with File Explorer to your desktop and see if that works. It seems like it's an operating system permissions issue, not a MATLAB problem.

[lena kappa]

no, i can save something there without an error

[lena kappa]

i tried your code and it did save the pic moon.tif in the corect file

[Image Analyst]

Then there is no reason that it should not work for the cat map images. In fact, I just uncommented the lines of code and ran it, and it saved them just fine.

[lena kappa]

HI image analyst! Do you know how can i save the path that one pixel is following while the iterations are done?

[Image Analyst]

No, I'd have to figure it out just like you would. Good luck.

[Walter Roberson]

Construct an array that is

A = reshape(1:(rows*columns), rows, columns)

Apply your catmap algorithm to this array, producing new array C.

If you created a correct catmap algorithm, then C has all of the entries in A, just in a different order, and no other entries.

C is now a mapping matrix, and for any given intermediate matrix, you can apply the cat-map transform as

I = your_image;
for K = 1 : steps
    I = I(C);
end

You can then modify this slightly to follow a particular pixel:

idx = sub2ind(size(your_image), row_of_interest, col_of_interest));
idxhistory = zeros(1, steps+1);
idxhistory(1) = idx;
I = your_image;
IA = A;

for K = 1 : steps
    I = I(C);
    IA = IA(C);
    idxhistory(K+1) = find(IA == idx);
end

and if you want to see it in terms of rows and columns:

[rowhistory, colhistory] = ind2sub(size(your_image), idxhistory);
plot3(0:steps, rowhistory, colhistory)
xlabel('step #'); ylabel('row'); zlabel('column')

[lena kappa]

thank you so much for your answer and your help!!!

I wrote it like this:

clc;
clear all;

img = imread('1.png');
[rows, columns, numberOfColorChannels] = size(img);
A = reshape(1:(rows*columns), rows, columns)


iteration = 1;
% Initialize image.
oldScrambledImage = img;
% The number of iterations needed to restore the image can be shown never to exceed 3N.
N = rows;
%while iteration <= 3 * N
while iteration <= 5
	% Scramble the image based on the old image.
	for row = 1 : rows % y
		for col = 1 : columns % x
			c = mod((2 * col) + row, N) + 1; % x coordinate
			r = mod(col + row, N) + 1; % y coordinate
			% Move the pixel.  Note indexes are (row, column) = (y, x) NOT (x, y)!
			currentScrambledImage(row, col, :) = oldScrambledImage(r, c, :);
		end
    end
	
	% Make the current image the prior/old one so we'll operate on that the next iteration.
	oldScrambledImage = currentScrambledImage;
	% Update the iteration counter.
	iteration = iteration+1;
end


%follow a particular pixel:
idx = sub2ind((size(img), row_of_interest, col_of_interest));
idxhistory = zeros(1, steps+1);
idxhistory(1) = idx;
I = img;
IA = A;
for K = 1 : steps
    I = I(C);
    IA = IA(C);
    idxhistory(K+1) = find(IA == idx);
end

%[rowhistory, colhistory] = ind2sub(size(your_image), idxhistory);
%plot(0:steps, rowhistory, colhistory)
%xlabel('step #'); ylabel('row'); zlabel('column')

and i get this error :

Error: File: followpixelcatmap.m Line: 34 Column: 23
Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for
mismatched delimiters.

for this line of code:

idx = sub2ind((size(img), row_of_interest, col_of_interest));

do you know why??

[Image Analyst]

You're passing sub2ind() one argument - a 4 element row vector. You need to pass it three

idx = sub2ind(size(img), row_of_interest, col_of_interest);

You had too many parentheses in there that groups all your arguments together into one array.

[Walter Roberson]

Looks like I had an extra ) when I posted that line of code.

[lena kappa]

thank you so much for your time guys but i got a bit confused

idx = sub2ind(size(img), row_of_interest, col_of_interest);
idxhistory = zeros(1, steps+1);
idxhistory(1) = idx;
I = img;
IA = A;
for K = 1 : steps
    I = I(C);
    IA = IA(C);
    idxhistory(K+1) = find(IA == idx);
end

is row_of_interest=rows of my image and col_of_interest=colums of myy image?

and is steps= iterations of the cat map?

and what is C equal to? from this code?

clc;
clear all;

img = imread('1.png');
[rows, columns, numberOfColorChannels] = size(img);
A = reshape(1:(rows*columns), rows, columns)


iteration = 1;
% Initialize image.
oldScrambledImage = img;
% The number of iterations needed to restore the image can be shown never to exceed 3N.
N = rows;
%while iteration <= 3 * N
while iteration <= 5
	% Scramble the image based on the old image.
	for row = 1 : rows % y
		for col = 1 : columns % x
			c = mod((2 * col) + row, N) + 1; % x coordinate
			r = mod(col + row, N) + 1; % y coordinate
			% Move the pixel.  Note indexes are (row, column) = (y, x) NOT (x, y)!
			currentScrambledImage(row, col, :) = oldScrambledImage(r, c, :);
		end
    end
	
	% Make the current image the prior/old one so we'll operate on that the next iteration.
	oldScrambledImage = currentScrambledImage;
	% Update the iteration counter.
	iteration = iteration+1;
end

[Walter Roberson]

I wrote,

Construct an array that is

A = reshape(1:(rows*columns), rows, columns)

Apply your catmap algorithm to this array, producing new array C.

For example,

img = imread('1.png');
if size(img,3) > 1; img = rgb2gray(img); end
[rows, columns] = size(img);

A = reshape(1:(rows*columns), rows, columns);

C = arnold_catmap_step(A);

Now, you had written

Do you know how can i save the path that one pixel is following while the iterations are done?

so you need to pick a particular pixel to follow the path for.

row_of_interest = randi(rows)
col_of_interest = randi(columns)

idx = sub2ind(size(img), row_of_interest, col_of_interest);

N = rows;
maxsteps = 3*N;
idxhistory = zeros(1, steps+1);
idxhistory(1) = idx;

I = img;
IC = A;
for iteration = 1 : maxsteps
    I = I(C);
    IA = IA(C);
    idxhistory(iteration+1) = find(IA == idx);
end

Here, function arnod_catmap_step would be a function that you would write that would take an input image and apply a single scrambling iteration to it. Mostly you would extract your code

	% Scramble the image based on the old image.

and put it into a function.

You might notice that I do not have you call arnold_catmap_step() inside the for iterations loop. You could do that. However, it turns out that once you have created the C array by applying one scrambling step to the index array, A, that each further scrambling step can be done as a single lookup without having to do looping.

[Walter Roberson]

For example,

img = uint8([255 1 255 1; 240 128 240 128; 64 63 62 61; 238 0 127 92])

img = 4×4

255 1 255 1 240 128 240 128 64 63 62 61 238 0 127 92

image(img)

[r,c] = size(img)

r = 4

c = 4

C = reshape(randperm(r*c),r,c)

C = 4×4

6 16 15 8 10 4 11 14 2 12 13 7 9 1 3 5

IA = reshape(1:(r*c), r, c)

IA = 4×4

1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16

 I = img

I = 4×4

255 1 255 1 240 128 240 128 64 63 62 61 238 0 127 92

 for K = 1 : 4
    I = I(C)
    IA = IA(C)
    figure(); image(I)
 end

I = 4×4

128 92 61 0 240 238 62 128 240 127 1 63 255 255 64 1

IA = 4×4

6 16 15 8 10 4 11 14 2 12 13 7 9 1 3 5

I = 4×4

238 1 63 255 62 255 1 128 240 64 0 127 61 128 240 92

IA = 4×4

4 5 7 1 11 9 13 14 10 3 8 12 15 6 2 16

I = 4×4

255 92 127 128 1 61 0 128 62 240 255 64 63 238 240 1

IA = 4×4

9 16 12 6 13 15 8 14 11 2 1 3 7 4 10 5

I = 4×4

61 1 64 238 0 63 255 128 1 240 128 240 127 255 62 92

IA = 4×4

15 5 3 4 8 7 1 14 13 10 6 2 12 9 11 16

Here, I is the progressively scrambled image, and IA is the scrambling indices. C is acting as a permutation matrix.

[lena kappa]

Thank you so much for your help Walter!

So this is my function:

function currentScrambledImage = arnold_catmap_step(img)


[rows, columns, numberOfColorChannels] = size(img);
oldScrambledImage = img;
% The number of iterations needed to restore the image can be shown never to exceed 3N.
N = rows;
% Scramble the image based on the old image.
	for row = 1 : rows % y
		for col = 1 : columns % x
			c = mod((2 * col) + row, N) + 1; % x coordinate
			r = mod(col + row, N) + 1; % y coordinate
			% Move the pixel.  Note indexes are (row, column) = (y, x) NOT (x, y)!
			currentScrambledImage(row, col, :) = oldScrambledImage(r, c, :);
		end
    end

end  

i think it does what you suggested.

But when i run this code:

clc;
clear all;

img = imread('1.png');
if size(img,3) > 1; img = rgb2gray(img); end
[rows, columns] = size(img);
A = reshape(1:(rows*columns), rows, columns);
C = arnold_catmap_step(A);

row_of_interest = randi(rows)
col_of_interest = randi(columns)
idx = sub2ind(size(img), row_of_interest, col_of_interest);
N = rows;
maxsteps = 3*N;
idxhistory = zeros(1, maxsteps+1);
idxhistory(1) = idx;
I = img;
IA = A;
for iteration = 1 : maxsteps
    I = I(C);
    IA = IA(C);
    idxhistory(iteration+1) = find(IA == idx);
end

[rowhistory, colhistory] = ind2sub(size(img), idxhistory);
plot(0:maxsteps, rowhistory, colhistory)
xlabel('step #'); ylabel('row'); zlabel('column')

i get this error:

Error using plot
Data must be a single input of y-values or one or more pairs of x- and y-values.

Error in followpixelcatmap (line 26)
plot(0:maxsteps, rowhistory, colhistory)

is my function correct and do you know why i get that error?

[Image Analyst]

Why do you need to know the path each pixel takes while being scrambled? Are you just curiosity, or is there a real use case?

[lena kappa]

no purely for optical reasons ,i dont think it can have any real practical scientific use, i was just curious, but if you think it has any i would be very intrested to hear your take on the matter

[lena kappa]

i think the error is because it wants plot3 not plot

[Walter Roberson]

Yes, plot3() not plot(), sorry.

[mamoona]

hey! do you have the matlab code for image scrambling and unscrambling using arnold cat map? i am working on colored images.

[Walter Roberson]

@mamoona

The code is posted above.

[mamoona]

thank u got it !!