How to properly convert image between Cartesian and polar coordinate systems using `cv2.warpPolar`?

Question

How to convert images from Cartesian coordinate system to polar coordinate system and back, using cv2.warpPolar method, without cropping the view therefore losing details?

I observed that for images that are not perfect squares, in the resultant polar system, lines that are parallel to x-axis will become circles instead of ellipses, so a fair chunk of the image will be out of view, therefore information is lost.

I want the circles to become ellipses of the same aspect ratio as the original image so that all of the converted image is squeezed into the view and no information is lost.

For example, this produces a test image:

import numpy as np
import cv2

img = np.zeros(shape=(1080, 1920, 3), dtype=np.uint8)
img[:, :, 0] = np.linspace(0, 255, 1920, dtype=np.uint8)[np.newaxis, :]
img[:, :, 2] = np.linspace(0, 255, 1080, dtype=np.uint8)[:, np.newaxis]
img[0:180, 0:320, 1] = 255
img[900:1080, 0:320, 1] = 255
img[900:1080, 1600:1920, 1] = 255
img[0:180, 1600:1920, 1] = 255
cv2.imshow('test image', img); cv2.waitKey(0)
cv2.imwrite('D:/test_image.jpg', img)

This warps the test image to polar coordinates:

r = (1920*1920+1080*1080)**.5/2
polar = cv2.warpPolar(img, dsize=(1920, 1080), center=(960, 540), maxRadius=r, flags=cv2.WARP_INVERSE_MAP)
cv2.imshow('polar image', polar); cv2.waitKey(0)
cv2.imwrite('D:/polar_test_image.jpg', polar)

And this warps it back to Cartesian:

linear = cv2.warpPolar(polar, dsize=(1920, 1080), center=(960, 540), maxRadius=r, flags=cv2.WARP_POLAR_LINEAR)
cv2.imshow('cartesian image', linear); cv2.waitKey(0)
cv2.imwrite('D:/cartesian_test_image.jpg', linear)

But what I want is this:

The above image is converted using PhotoShop CS6.

And warped back by PhotoShop CS6:

How do I generate the same results as PhotoShop?

---

I thought I was clear enough but you didn't get it.

I want the warped image to not be a perfect square, it should have exactly the same resolution and aspect ratio as the input image instead.

And there should be no extra black portions. Just like the effect in PhotoShop.

Answer 1

The picture you "want" is easily achieved by rotating the input by 90 degrees. You want the green and cyan squares in the center? Then rotate counterclockwise by 90 degrees, so they're on the left side, before warping. Then they'll be in the center.

You have to make sure a circle of the given radius fits in the dimensions you specify in dsize .

Use dsize=(2*r,2*r) and center accordingly.

Either that or you have to use a different radius value.