imtransform had shift my center

Hi, I had 3 images which size 200*200. I would want to aggregate those image with same center after they have been imtransform. Those 3 images are eye scanning. so let's say there is a optic disc, assume it is a circle and I had it's center coordinate. So for example the first image center is 100,100 (this is perfect),2nd is 101,101(so I had to shift -1,-1 to aggregate the 2nd image with the 1st), the last one is 130,130. However, I had calculate that even the optic disc(the circle) had it own center, the image is not scan properly. Therefore I had to rotate my images. I had a Tform and tried to use imtransform. It look okay after the images transform, and I know the image will have difference size, since the I don't want any information lose. Then I change the image size to 300,300. Since I need to aggregate those 3 images to center 150,150 which is the middle of the images. I had try to use imtranslate, which should be fine. However, everytime I try to aggregate the image, the shifting/center is not correct. Below is the code which I had tried.

for n=1:no_of_pics        
          temp_recover=cell2mat(T(n,1));
          %if it is left eye, it need to be fliped
          if analyzingEye=='OS'
              temp_recover=flipdim(temp_thickness,2);
          end           

          temp_recover(isnan(temp_recover))=0;
          %peaks is the center detected by hough method
          temp_xcenter=ceil(peaks(1,n)*200/668);
          temp_ycenter=ceil(peaks(2,n)*200/668);
          % matrix below is trying to rotate the image about the certain center not the origin
          temp_tocenter=[1 0 0;0 1 0;-(150-temp_xcenter) -(150-temp_ycenter) 1];
          temp_back=[1 0 0;0 1 0;150-temp_xcenter 150-temp_ycenter 1];
          temp_recover=imtransform(temp_recover,maketform('affine',temp_tocenter*cell2mat(TTFORM(n,1))*temp_back),'XData',[1 301],'YData',[1 301]);
end

However by using this method, the center is shifted to somewhere I don't know. Therefore, I had use another code;

for n=1:no_of_pics        
          temp_recover=cell2mat(T(n,1));
          if analyzingEye=='OS'
              temp_recover=flipdim(temp_thickness,2);
          end
          temp_recover(isnan(temp_recover))=0;
          temp_xcenter=ceil(peaks(1,n)*200/668);
          temp_ycenter=ceil(peaks(2,n)*200/668); 
          temp_recover=imtransform(temp_recover,maketform('affine',cell2mat(TTFORM(n,1))));
          %I am trying to expand the matrix to 300*300 so that I can aggregate the center and no information lost
          temp_recover(300,300)=0;       
          temp_recover=imtranslate(temp_recover,[151-temp_xcenter,151-temp_ycenter],'fillvalue',0);
end

It did better, but still the circle is not perfectly match. I am very frustrated on this. Can someone point out where I had done wrong? Thank you very much

Answer 1

[Marco Yu]

Right for anyone have same problem with me. Here is the better solution. Firstly, you create a translation matrix i.e.

 %dx dy are the length that you need to translate
 shift=[1 0 0;0 1 0;dx dy 1]

then you need a matrix to transform to origin

 %so if you want to rotate at point(150,150)
 to_center=[1 0 0;0 1 0;-150 -150 1]

then you need your rotation matrix which is

 %theta is the angle
 rotation=[cosd(theta) -sind(theta) 0;sind(theta) cosd(theta) 0;0 0 1]

then you need to transform back

 back=[1 0 0;0 1 0;150 150 1]

therefore, the overall matrix will be

 final=shift*to_center*rotation*back

hope this can help you :)

Answer 2

[Marco Yu]

I have an low rank solutions: firstly, I had use pure translation to aggregate the center and expand the image to size 300*300

 if analyzingEye=='OD'
                temp_recover=imtransform(temp_recover,maketform('affine',[1 0 0;0 1 0;151-peaks(1,n)*200/668 151-peaks(2,n)*200/668 1]),'XData',[1 300],'YData',[1 300]);
            else
                temp_recover=imtransform(temp_recover,maketform('affine',[1 0 0;0 1 0;151-(200)+peaks(1,n)*200/668 151-peaks(2,n)*200/668 1]),'XData',[1 300],'YData',[1 300]);
 end

then I do the rotation with imtransform, however since imtransform will rotate the image from origin, therefore I had to do some matrix multiplication.

 temp_tocenter=[1 0 0;0 1 0;-151 -151 1];
 temp_back=[1 0 0;0 1 0;151 151 1];
 temp_recover=imtransform(temp_recover,maketform('affine',temp_tocenter*cell2mat(TTFORM(n,1))*temp_back),'XData',[1 300],'YData',[1 300]);

The reason I call this low rank is because this will do the interpolation twice. I suppose this will reduce the accuracy and quality of the image.I did try to merge the code above to see the result. However, it is not good. I am not sure whether it is because of the function(imtransform) problems nor I am lack of mathematical knowledge. If anyone can give a help, I would be very appreciated.