I am trying to horizontally stretch an image in a very specific way. Each x prime coordinate should follow a tangent path with respect to the original x coordinate. I believe there are two ways to do this:

1. Inverse the tangent function and map it normally
2. Map the tangent function and then inverse the mapping

Using

Method 2: Attempt Image

The results show that the attempt (normal tan function with inverted map) has less stretching near the edges of the image than expected. Almost everywhere else on the images are identical except the edges. I did not post the original picture to save space.

CodePudding user response：

I've played around with that invert_map procedure. It seems slightly susceptible to oscillation.

use this instead:

def invert_map(F):
    (h, w) = F.shape[:2] # (h, w, 2), "xymap"
    I = np.zeros_like(F)
    I[:,:,1], I[:,:,0] = np.indices((h,w)) # identity map
    P = np.copy(I)
    for i in range(10):
        correction = I - cv2.remap(F, P, None, interpolation=cv2.INTER_LINEAR)
        P  = correction * 0.5
    return P

I simply damped the correction by 0.5, which makes the fixed point iteration tamer, converging a lot faster too.

In my experiments with your tan map, I've found that 5-10 iterations are good enough already, and there's no further progress in further iterations.

Entire notebook of my explorations: https://gist.github.com/crackwitz/67f76f8a9eff21476b080c06d20660d0

Feature request: https://github.com/opencv/opencv/issues/22120