function [x,y,v,rmax,tx,ty] = transform_to_unit_circle(img,center,radius,coef)

[n1, n2] = size(img);

tx = (n2+1)/2;
ty = (n1+1)/2;
m00 = sum(img(:));
if center == 2
    w = 1:n2;
    v = 1:n1;
    if m00 ~= 0
        tx = (sum(img*w'))/m00;
        ty = (sum(v*img))/m00;
    end
end

rmax = sqrt(max([(1-tx)^2+(1-ty)^2,(n2-tx)^2+(1-ty)^2,(n2-tx)^2+(n1-ty)^2,(1-tx)^2+(n1-ty)^2]));
[y,x,v] = find(img);

if isempty(v)
    return
end

x = x - tx; % moving the image to the center of image
y = y - ty;

if radius == 2
    rmax = max((x.^2+y.^2).^0.5); % maximum of pixel distances from the center
elseif radius == 3
    mc = max(img(:));
    rmax = sqrt(m00/mc)*sqrt(n2/n1+n1/n2)/sqrt(2);
end

rmax = rmax*coef;

x = x/rmax;
y = y/rmax;

end