How to rotate a 2D array (2D image) in 3D space around the x-axis?

Hi everyone,

I have a 2D image ( a 2D array ) and i want to rotate this image in 3D space around the x-axis using an angle

and i want to store the resulted rotated 2D image in a new 2D array.

For example, if i want to rotate this 2D image around the z-axis i can do it using:

A = imread('img.tif');

A_RotZ = imrotate(A,angle,'nearest','loose');

but i can't find how to do the same around x-axis.

A_RotX = ???

Any ideas?

[Matt J]

i want to store the resulted rotated 2D image in a new 2D array.

Surely you mean you want to store it in a 3D array. If the image is rotated about the x-axis it will no longer occupy the xy plane, so how would you be able to express it in 2D form?

[IOANNIS]

Thank you for the quick response.

If you keep a real 2D image in your hands and rotate it vertical, it will not become a 3D image. It is a rotated 2D image in a 3D space (check image attached). There are several similar question in matlabcentral/answers but, they explain how to make the visualization of this process, not how to get the image in a 2D-array.

for example: https://www.mathworks.com/matlabcentral/answers/1446034-how-to-rotate-a-surface-or-a-2d-plane-in-3d-cartesian-coordinate?s_tid=srchtitle

he has 2D points in a star form, and he rotates the 2D star in 3D space. The star is again 2D, but with other origin.

In my case i have an image, and i want to get back this rotated image as a 2D array (which will look like the 2D rotated star in the example)

Answer 1

[IOANNIS]

Finally!!

tform = projective2d([ cosd(TH) 0 0 ; 0 1 0 ; 0 0 cosd(TH) ]);

A_rotX = imwarp(A, tform);

imshowpair(A, A_rotX, 'montage');

I dont know why, but it worked!

Answer 2

[Matt J]

A=rand(5)

A = 5×5

0.9780 0.1184 0.2270 0.7351 0.5083 0.1574 0.6862 0.4062 0.9613 0.1056 0.8993 0.0520 0.0274 0.8168 0.0247 0.0745 0.2219 0.3940 0.5630 0.1267 0.5624 0.1992 0.1596 0.5698 0.8510

theta=90;
R=eye(3);
R(2:3,2:3) = [ cosd(theta) -sind(theta); ...
               sind(theta)  cosd(theta)];

A=cat(3,0*A,A,0*A);

A_RotX  = imwarp(A, rigid3d(R,[0;0;0]'))

A_RotX = 
A_RotX(:,:,1) =

         0         0         0         0         0
    0.5624    0.1992    0.1596    0.5698    0.8510
         0         0         0         0         0


A_RotX(:,:,2) =

         0         0         0         0         0
    0.0745    0.2219    0.3940    0.5630    0.1267
         0         0         0         0         0


A_RotX(:,:,3) =

         0         0         0         0         0
    0.8993    0.0520    0.0274    0.8168    0.0247
         0         0         0         0         0


A_RotX(:,:,4) =

         0         0         0         0         0
    0.1574    0.6862    0.4062    0.9613    0.1056
         0         0         0         0         0


A_RotX(:,:,5) =

         0         0         0         0         0
    0.9780    0.1184    0.2270    0.7351    0.5083
         0         0         0         0         0

[IOANNIS]

No, I dont want the positions of the rotated points, which are (x,y,z). I want the 2D plane (image) which is formed from these rotated points.

Lets better say, I want to project this image in an other plane, which has an angle around x-axis with the original plane

[IOANNIS]

You gave me a 3D image :( I need the plane of this rotation, which is 2D

[Matt J]

That is what I have given you.

[IOANNIS]

This works

tform = projective2d([1 -0.1 0.001; 0 1 0; 0 0 1]);

A_rotX = imwarp(A, tform);

imshowpair(A, A_rotX, 'montage');

but i dont know how to put the angle in it.

I tried to use in projective2d:

R=eye(3);

R(2:3,2:3) = [ cosd(theta) -sind(theta); ...

sind(theta) cosd(theta)];

but no success