[Python] How to undistort a fisheye image with self-defined intrinsic matrix and distortion...

I have an image with grayscale changing with cos(wx), and I simulate the fisheye effect on it using the following python code, where K and D are intrinsic matrix and distortion parameter respectively.

def fisheye_effect(original_img):
h, w = original_img.shape[:2]
K = np.array([[w, 0, w / 2],
[0, h , h / 2],
[0, 0, 1]])
D = np.array([2.0, 1.0, 0, 0])
map1, map2 = cv2.fisheye.initUndistortRectifyMap(K, D, None, new_K, (w, h), cv2.CV_16SC2)
fisheye_img = cv2.remap(original_img, map1, map2, interpolation=cv2.INTER_LINEAR, borderMode=cv2.BORDER_CONSTANT)
cv2.imwrite(fisheye_path, fisheye_img)


Here's the original image



And here's the distorted fisheye image



Now, my question is that how to undistort the fisheye image based on my self-defined K and D?

I attempted to do it using the following code and it can somehow undistort the image, but the black borders remain.

def undistort(fisheye_img):
h, w = fisheye_img.shape[:2]
new_D = np.array([0.3, -0.05, 0, 0])
new_K = cv2.fisheye.estimateNewCameraMatrixForUndistortRectify(K, new_D, (w, h), np.eye(3), balance=0.0)
map1, map2 = cv2.fisheye.initUndistortRectifyMap(K, new_D, None, new_K, (w, h), cv2.CV_32F)
undistorted_img = cv2.remap(fisheye_img, map1, map2, interpolation=cv2.INTER_LINEAR, borderMode=cv2.BORDER_CONSTANT)


Here's the undistortion result.
Anyone knows how can I undistort the fisheye image and let it look like the original one without cropping out the black border?



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