How to rotate an image using interpolation?

I am using the code below to rotate an image . but I don’t know how to write interpolation function by myself and don't use the provided functions . I think for interpolation I have to use 4 equation and find 4 variable but I don’t know how to implement it.

Trotation=[cos(pi/4) sin(pi/4) 0 -sin(pi/4) cos(pi/4) 0 0 0 1];

Tpic=imread('D:\projects\University\Image proccessing\Rotation\1.jpg');

tform=maketform('affine' , Trotation);

g=imtransform(Tpic , tform);

imshow(g);

[Image Analyst]

Why don't you "use the provided functions" such as imrotate?

Answer 1

[sepideh tork]

     im1 = imread('lena.jpg');imshow(im1);  
[m,n,p]=size(im1);
thet = rand(1);
mm = m*sqrt(2);
nn = n*sqrt(2);
for t=1:mm
   for s=1:nn
      i = uint16((t-mm/2)*cos(thet)+(s-nn/2)*sin(thet)+m/2);
      j = uint16(-(t-mm/2)*sin(thet)+(s-nn/2)*cos(thet)+n/2);
      if i>0 && j>0 && i<=m && j<=n           
         im2(t,s,:)=im1(i,j,:);
      end
   end
end
figure;
imshow(im2);code
  end

Answer 2

[Aaditya Kalsi]

The idea is to find out the mapping of each pixel in the rotated image w.r.t the original image. Instead of saying (1, 1) in the original image is now at (3.4, 6.1), do the opposite. (1, 1) in the new image is (.4, 1.4) in the original one. You can now use Bilinear Interpolation to figure out the value. You can google Bilinear Interpolation for more details. Go through each (i, j) in the new image and bilinearly interpolate.

[sepideh tork]

i think its a good way to rotate image without using provide function, but how can writte the code? i mean finding the spatial of each pixel and make new oriention?

Answer 3

[Alex Taylor]

If you want to apply pure rotation to an image, there is a specific Image Processing Toolbox function imrotate that will do this without the need to construct a transform matrix.

I = fitsread('solarspectra.fts');
I = mat2gray(I);
J = imrotate(I,-1,'bilinear','crop');
figure, imshow(I)
figure, imshow(J)

Imrotate provides three interpolation options: bicubic, bilinear, and nearest neighbor. I'm not clear from your question whether you need to implement some sort of custom interpolation routine to use in the resampling step. If you are happy with these interpolation options, imrotate is the way to go.