Fun with remap

Maps a rectangular image into a circle using cv.remap

To build the mapping we do the following simple geometry calculation:

shift the origin (0,0) coordinate to the center of the image
convert the cartesian x-y coordinates to polar r-theta form
determine the length of the line with the same theta that touches the border of the rectangle
retain the theta, but scale the r value based on how much the line has to shrink to fit into the circle.
convert the modified r-theta values back into x-y coordinates

Sources:

source image

fname = which('coins.png');
if isempty(fname)
    fname = fullfile(mexopencv.root(), 'test', 'apple.jpg');
end
src = imread(fname);

coordinates space, shifted so that origin is at the center of the image

[h,w,~] = size(src);
c = [w,h] / 2;
[X,Y] = meshgrid(single(1:w)-c(1), single(1:h)-c(2));

convert cartesian coordinates to polar form (r,theta)

R = hypot(Y,X);
T = atan(Y./X);  % NOTE: atan not atan2

% handle NaN case when atan(0/0) in the center
T(isnan(T)) = 0;

scale R

radius = min(h,w) / 2;
D = min(abs(c(1)./cos(T)), abs(c(2)./sin(T)));
R = R ./ (radius ./ D);

remap points

map_X = c(1) + sign(X) .* R .* cos(abs(T));
map_Y = c(2) + sign(Y) .* R .* sin(abs(T));

destination image

dst = cv.remap(src, map_X, map_Y);

show result

subplot(121), imshow(src), title('image')
subplot(122), imshow(dst), title('remapped')