fast Cartesian to Polar to Cartesian in Python

Question

I want to transform in Python 2d arrays/images to polar, process then, and subsequently transform them back to cartesian. The following is the result from ImajeJ Polar Trans

Answer 1

the CV source code mentions a LinearPolar. it doesn't seem to be documented, but appears to be similar to LogPolar. have you tried that?

Answer 2

Latest versions of opencv supports a function cv2.linearPolar. This may be another solution that does not involve the use of opencv:

def polar2cart(r, theta, center):

    x = r  * np.cos(theta) + center[0]
    y = r  * np.sin(theta) + center[1]
    return x, y

def img2polar(img, center, final_radius, initial_radius = None, phase_width = 3000):

    if initial_radius is None:
        initial_radius = 0

    theta , R = np.meshgrid(np.linspace(0, 2*np.pi, phase_width), 
                            np.arange(initial_radius, final_radius))

    Xcart, Ycart = polar2cart(R, theta, center)

    Xcart = Xcart.astype(int)
    Ycart = Ycart.astype(int)

    if img.ndim ==3:
        polar_img = img[Ycart,Xcart,:]
        polar_img = np.reshape(polar_img,(final_radius-initial_radius,phase_width,3))
    else:
        polar_img = img[Ycart,Xcart]
        polar_img = np.reshape(polar_img,(final_radius-initial_radius,phase_width))

    return polar_img

Answer 3

Here's an example of the log-polar transform implemented using SciPy:

https://github.com/stefanv/supreme/blob/master/supreme/transform/transform.py#L51

Given that this is only a coordinate transformation, it should be easier to adapt to your problem than the OpenCV version.