Find Homography

homography.py

def find_homography(X, X_dash):
    '''
    Given a set of N correspondences of the form [x,y] and [x',y'], fit homography.
    '''
    equations = []
    num_points = X.shape[0]
    for i in range(num_points):
        x, y = X[i, 0], X[i, 1] # Original points
        x_dash, y_dash = X_dash[i, 0], X_dash[i, 1] # Transformed points

        # First row for the equation
        equations.append([x, y, 1, 0, 0, 0, -x_dash * x, -x_dash * y, -x_dash])
        
        # Second row for the equation
        equations.append([0, 0, 0, x, y, 1, -y_dash * x, -y_dash * y, -y_dash])
        
    A = np.vstack(equations)
    U,S,V_t = np.linalg.svd(A)
    H = V_t[-1,:].reshape(3,3)
    
    # Normalize to make H[2, 2] = 1
    H = H/H[2,2]

    return H

def homogenous_transform(X, H):
  '''
  Apply the Homography matrix on given set of points and calculate the projected points
  '''
  num_points = X.shape[0]
  homogeneous_points = np.hstack([X, np.ones((num_points, 1))])  # Convert to homogeneous
  warped_points = np.dot(homogeneous_points, H.T)  # Apply homography
    
  return warped_points[:, :2] / warped_points[:, 2] # Normalize back to cartesian