Converting a 3D polar binary image to a cartesian 3D binary image

Hello, i do have a grayscale binary image B, of dimensions 280x3072x4000.

I would like to convert it to a cartesian image, with the origin (centre) on x=2143, y=2091, in the cartesian space. ( I dont care about the grayscale values, i just want the pixels that were 1 on my polar image to keep being 1 on my cartesian image)

Im an trying to use the PolarToIm functiont avalible on File Exchange but I dont know anything about the size scale factor and how i should modify it to apply it to my image ( I think the creator had an image where the dimensions of his image were odd for example)

Edit: Function is working fine for my image but it takes too long for my image (around 7 hours). Does anyone know how to improve the efficiency of this code? Maybe introducing the interpolation or vectorising?

function imR = PolarToIm (imP, rMin, rMax, Mr, Nr)
% POLARTOIM converts polar image to rectangular image. 
%
% V0.1 16 Dec, 2007 (Created) Prakash Manandhar, [e-mail]
%
% This is the inverse of ImToPolar. imP is the polar image with M rows and
% N columns of data (double data between 0 and 1). M is the number of
% samples along the radius from rMin to rMax (which are between 0 and 1 and
% rMax > rMin). Mr and Nr are the number of pixels in the rectangular
% domain. The center of the image is assumed to be the origin for the polar
% co-ordinates, and half the width of the image corresponds to r = 1.
% Bilinear interpolation is performed for points not in the imP image and
% points not between rMin and rMax are rendered as zero. The output is a Mr
% x Nr grayscale image (with double values between 0.0 and 1.0).


imR = zeros(Mr, Nr);
Om =  2143;  %(Mr+1)/2; % co-ordinates of the center of the image
On =  2091;  %(Nr+1)/2;
sx = (Mr-1)/2; % scale factors
sy = (Nr-1)/2;

[M N] = size(imP);

delR = (rMax - rMin)/(M-1);
delT = 2*pi/N;

for xi = 1:Mr
for yi = 1:Nr
    x = (xi - Om)/sx;
    y = (yi - On)/sy;
    r = sqrt(x*x + y*y);
    if r >= rMin & r <= rMax
       t = atan2(y, x);
       if t < 0
           t = t + 2*pi;
       end
       imR (xi, yi) = interpolate (imP, r, t, rMin, rMax, M, N, delR, delT);
    end
end
end

function v = interpolate (imP, r, t, rMin, rMax, M, N, delR, delT)
    ri = 1 + (r - rMin)/delR;
    ti = 1 + t/delT;
    rf = floor(ri);
    rc = ceil(ri);
    tf = floor(ti);
    tc = ceil(ti);
    if tc > N
        tc = tf;
    end
    if rf == rc & tc == tf
        v = imP (rc, tc);
    elseif rf == rc
        v = imP (rf, tf) + (ti - tf)*(imP (rf, tc) - imP (rf, tf));
    elseif tf == tc
        v = imP (rf, tf) + (ri - rf)*(imP (rc, tf) - imP (rf, tf));
    else
       A = [ rf tf rf*tf 1
             rf tc rf*tc 1
             rc tf rc*tf 1
             rc tc rc*tc 1 ];
       z = [ imP(rf, tf)
             imP(rf, tc)
             imP(rc, tf)
             imP(rc, tc) ];
       a = A\double(z);
       w = [ri ti ri*ti 1];
       v = w*a;
    end

    

I guess I could use pol2cart function but i dont know how to apply it to an image.

Thanks

[Prabhan Purwar]

Could you please attach your image.

[JoaquinB]

There you go Prabhan,

Thanks

Answer 1

[Prabhan Purwar]

Hi,

Try making use of the code, illustrated in the following link:

https://in.mathworks.com/matlabcentral/answers/92062-how-do-i-transform-image-data-recorded-in-polar-coordinates-so-that-i-can-view-the-image-in-matlab-7 (Image transformation using pol2cart function)

Hope it helps!!

[JoaquinB]

Is it possible to select a certain centre of the cartesian image?

I mean, I do have the cartesian coordinates of the centre (X=2143, Y= 2091) that I would like my cartesian image to have so i can compare it with other images. How would you apply it into the code?

Giving xyz0 in ffgrid function the values?

Thanks Prabhan