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??????????????????????????????????????????????????????2D???????????????????????????

?????????3D???????????????????????????????????????????????????????????????????????????

????????????????3D???????2D????????????3D????3x4????????????2D???

?????3x4???????3D???????x?y?z????2D??????????u?v??????????2D???????3D??????????????z=0??

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import cv2
import numpy as np
def get_inverse_perspective(perspective_matrix: np.array) -> np.array:
    """ This method calculates the inverse of perspective matrix by homography. """
    # Take 5 homogeneous points on the floor plane (Unit is in Meters)
    pts_dst = np.array([[0, 0, 0, 1],
                        [0, 1, 0, 1],
                        [1, 0, 0, 1],
                        [1, 1, 0, 1],
                        [0, 0, 0, 1]])
    
    # Obtain respective homogeneous points on the image plane
    pts_src = (perspective_matrix @ pts_dst.T).T
    # Convert homogeneous coordinates to Cartesian coordinates
    pts_src_cart = np.array([[x/w, y/w] for x, y, w in pts_src])
    pts_dst_cart = np.array([[x/w, y/w] for x, y, z, w in pts_dst])
    
    # Find the 3x3 Homography Matrix for transforming image plane to floorplane
    H, status = cv2.findHomography(pts_src_cart, pts_dst_cart)
    return H
def project_to_floor(image_coordinates: List[int], H: np.array) -> List[int]:
    """ This method takes the Homography matrix and the 2D image Cartesian coordinates. 
    It returns the (x, y) Cartesian coordinates in 3D world coordinates on floorplane (z=0). """
    # Adding 1 for homogeneous coordinate system
    x, y, w = H @ np.array([[*image_coordinates, 1]]).T
    return [x/w, y/w]
# Example usage
p = np.random.rand(3, 4)
H = get_inverse_perspective(p)
src_point = (5, 10)
dst_point = project_to_floor(src_point, H)

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