Rotate image in Matlab about arbitrary points

Question

I am trying to rotate an image in Matlab about an arbitrary set of points.

So far, I have used imrotate, but it looks like imrotate only rotates about the center.

Is there a nice way of doing this without first padding the image and then using imrotate?

Thank you

[Rotating about an arbitrary point is the same as rotating and then translating](https://stackoverflow.com/questions/56728791/how-can-we-rotate-an-rgb-image-using-nearest-neighbor-interpolation-algorithm-ab/56730080#56730080). This question is a duplicate of [this other one](https://stackoverflow.com/questions/10026905/how-to-rotate-an-image-about-a-point-that-is-not-the-images-center-point-using) but the answer there is not very good IMO, so I won't close this question. — Cris Luengo, Nov 08 '19 at 01:31
[This other question](https://stackoverflow.com/questions/25458442/rotate-a-2d-image-around-specified-origin-in-python) has an answer with code, but it's Python. Maybe you'll be albe to translate that? — Cris Luengo, Nov 08 '19 at 01:32

Rotem · Accepted Answer · 2019-11-08T22:16:26.080

The "nice way" is using imwarp

Building the transformation matrix is a little tricky.
I figured out how to build it from a the following question: Matlab image rotation
The transformation supports rotation, translation and zoom.

Parameters:
(x0, y0) is the center point that you rotate around it.
phi is rotation angle.
sx, sy are horizontal and vertical zoom (set to value to 1).
W and H are width and height of input (and output) images.

Building 3x3 transformation matrix:

T = [sx*cos(phi), -sx*sin(phi), 0
     sy*sin(phi),  sy*cos(phi), 0
     (W+1)/2-((sx*x0*cos(phi))+(sy*y0*sin(phi))), (H+1)/2+((sx*x0*sin(phi))-(sy*y0*cos(phi))), 1];

Using imwarp:

tform = affine2d(T);
J = imwarp(I, tform, 'OutputView', imref2d([H, W]), 'Interp', 'cubic');

Here is a complete executable code sample:

I = imresize(imread('peppers.png'), 0.5); %I is the input image

[H, W, ~] = size(I);  %Height and Width of I

phi = 120*pi/180; %Rotate 120 degrees

%Zoom coefficients
sx = 1;
sy = 1;

%Center point (the point that the image is rotated around it).
x0 = (W+1)/2 + 50;
y0 = (H+1)/2 + 20;

%Draw white cross at the center of the point of the input image.
I(y0-0.5:y0+0.5, x0-19.5:x0+19.5, :) = 255;
I(y0-19.5:y0+19.5, x0-0.5:x0+0.5, :) = 255;

%Build transformation matrix.
T = [sx*cos(phi), -sx*sin(phi), 0
     sy*sin(phi),  sy*cos(phi), 0
     (W+1)/2-((sx*x0*cos(phi))+(sy*y0*sin(phi))), (H+1)/2+((sx*x0*sin(phi))-(sy*y0*cos(phi))), 1];

tform = affine2d(T);
J = imwarp(I, tform, 'OutputView', imref2d([H, W]), 'Interp', 'cubic');

%Draw black cross at the center of the output image:
J(end/2:end/2+1, end/2-15:end/2+15, :) = 0;
J(end/2-15:end/2+15, end/2:end/2+1, :) = 0;

%Shows that the center of the output image is the point that the image was rotated around it.
figure;imshow(J)

Input image:

Output image:

Note:
Important advantage over other methods (like imrotate after padding), is that the center coordinates don't have to be integer values.
You can rotate around (100.4, 80.7) for example.

Rotate image in Matlab about arbitrary points

1 Answers1