Transformation matrix to rotate image

I'm trying to find a matrix such that its multiplication with another matrix rotates the latter :

Let be my image/matrix and the vectorized image/matrix.

I'm looking for a "rotation" matrix F such as where is the vectorized rotated image.

Here's what I tried :

by identification

Any idea on how construct such matrix with matlab ?

Answer 1

[Matt J]

See the section Image Transformations with Localized Responses (localfunc2mat) under the Examples tab of this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/44669-convert-linear-functions-to-matrix-form?s_tid=srchtitle

[Nawel]

I'll check it. Thank you !

[Matt J]

You're very welcome, but if it does what you need please Accept-click the answer.

[Nawel]

I have checked it and I'm not sure the code returns a rotation matrix for an image. I might be wrong but how would you obain a rotation matrix that rotates an image as the one below using the code ?

[Matt J]

Did you read the demo under the Examples tab that I referenced? You should have found a direct demonstration there. Here it is again:

xsiz=[256,256];
X1=imresize( double(im2gray(imread('cameraman.tif')))  ,xsiz);
X2=imresize( double(im2gray(imread('peppers.png')))  ,xsiz);

tic;
[A,ysiz]=localfunc2mat(@(x) imrotate(x,-30,'crop') ,...
                        xsiz,2); %convert to matrix form
toc

Elapsed time is 0.955735 seconds.

Y1=reshape( A*X1(:) , ysiz); %rotate images with matrix multiplication
Y2=reshape( A*X2(:) , ysiz);

montage({X1,Y1,X2,Y2},'DisplayRange',[0,256],'Size',[2,2])

[Nawel]

Hi again,

Thank you for your answer !