est_homography.py

import numpy as np

def est_homography(X, Y):
    """ 
    Calculates the homography H of two planes such that Y ~ H*X
    If you want to use this function for hw5, you need to figure out 
    what X and Y should be. 

    Input:
        X: 4x2 matrix of (x,y) coordinates 
        Y: 4x2 matrix of (x,y) coordinates
    Returns:
        H: 3x3 homogeneours transformation matrix s.t. Y ~ H*X
        
    """
    
    X_ = np.hstack([X, np.ones([X.shape[0],1])])
    
    A = np.zeros([8,9])
    A[0::2, 0:3] = X_
    A[1::2, 3:6] = X_
    A[0::2, 6:9] = X_ * -Y[:,[0]]
    A[1::2, 6:9] = X_ * -Y[:,[1]]
    
    _, _, V = np.linalg.svd(A)
    H = V[-1,:] / V[-1, -1]
    H = np.reshape(H, [3,3])
    
    
    return H