Improving the efficiency of the function PolarToIm

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JoaquinB
JoaquinB 2020-3-9
Hello, I am working with a 3D polar binary image of dimensions 280x3072x4000 , which I would like to convert to a cartesian image with center on x=2143, y=2091
I found the function PolarToIm but since my image is really large, the loops takes around 7 hours, which is impractical for me.
I think there should be a way of optimising this code to improve its efficiency and making it faster. The interpolation part (using the function interpolate given by Matlab) , pol2cart or vectorization might be the key but I'm not good enough to implement it. Any ideas?
I attach the PolarToIm code and my image
function imR = PolarToIm (imP, rMin, rMax, Mr, Nr)
% POLARTOIM converts polar image to rectangular image.
%
% V0.1 16 Dec, 2007 (Created) Prakash Manandhar, pmanandhar@umassd.edu
%
% 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
Thanks

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