import numpy as np
import cv2

def coordinate_inverse_mapping(image, inverse_mapping_func):
    height, width = image.shape[:2]

    # Create mapping arrays for x and y coordinates 
    # (x_old and y_old' keys i.e., number index are the new position, 
    #             their values are the old position)
    
    x_old = np.zeros((height, width), dtype=np.float32)
    y_old = np.zeros((height, width), dtype=np.float32)
    x_new = np.linspace(0, 1, width)
    y_new = np.linspace(0, 1, height)
    
    # Call the inverse mapping function to populate the new coordinate maps
    for i, y in enumerate(y_new):
        for j, x in enumerate(x_new):
            # inverse_mapping_func: x_old, y_old -> x_old, y_old
            x_old[i, j], y_old[i, j] = inverse_mapping_func(x, y)
            x_old[i, j] *= (width - 1)
            y_old[i, j] *= (height - 1)

    return x_old, y_old