Expressing every point of my image in polar coordinates, where the origin is a point that was chosen from the image

Hi guys. I have an image with a circle at the centre of it. Now, I want to express every point in my image in terms of polar coordinates ( I am more interested in evaluating the angles ) the origin being the centre of the circle. So far I've done this:

if true
I = imread ( Image ); 
I1 = size ( I ); 
R = ( I1 ( 1 ) ) ; 
C = ( I1 ( 2 ) ) ; 
[ Rv , Cv ] = ndgrid ( 1:R , 1:C ) ;

% I've already calculated the location of the circle using imfindcircles

Rv_transla = Rv - centres ( 2 ); 
Cv_transla = Cv - centres ( 1 );

% and then this horrible loop to account for all the cases

 for c = 1:C ;
for r = 1:R ;
if Cv_transla ( r , c ) > 0;
angle ( r , c ) = atand ( Rv_transla ( r , c ) / Cv_transla ( r , c ));
else if ( Cv_transla ( r , c ) < 0 & Rv_transla ( r , c ) < 0 ); 
angle ( r , c ) = atand ( (Rv_transla ( r , c ) / Cv_transla ( r , c )) - 180 ); 
else if ( Cv_transla ( r , c ) == 0 & Rv_transla > 0 );  
angle ( r , c ) = 90;  
else if ( Cv_transla ( r , c ) == 0 & Rv_transla < 0 );  
angle ( r , c ) = -90; 
else if ( Cv_transla ( r , c ) == 0 & Rv_transla == 0 );  
angle ( r , c ) = 'undefined'  
                             end  
                         end 
                       end 
                     end  
                    end 
                  end  
                end

% which does not give me the expected results. I know it's really messy, but any help would be much appreciated. I've attached the image just to give you a better idea.

Thanks.

Answer 1

[Pratik Anand]

You can use cart2pol command to achieve that. You can refer to its documentation here

Answer 2

[Image Analyst]

Why do you have all these cases? Simply scan the image pixel-by-pixel computing the radius and angle (using the atan2d function) of each pixel from the circle center.