Basic 3D TPS warp

tps3d.py

def coord_mapping(fixed_coords, c, matches_stationary, smoothing):
    """Apply 3D thin-plate spline mapping to fixed_coords.

    The RBF keypoints are given in matches_stationary. Smoothing is a
    surface energy regularization parameter.

    Parameters
    ----------
    fixed_coords : ndarray
        (N, 3) array of points to warp
    c : ndarray
        (M, 3) array of spline coefficients for z, y, and x axes
    matches_stationary : ndarray
        (M, 3) array of keypoint coordinates
    smoothing : float
        surface energy regularization parameter


    Returns
    -------
    moving_coords : ndarray
        (N, 3) array of warped points

    """
    nb_pts = fixed_coords.shape[0]
    dist = scipy.spatial.distance.cdist(fixed_coords, matches_stationary)
    nb_matches = matches_stationary.shape[0]
    T = np.zeros((nb_pts, 4+nb_matches))
    T[:, :4] = np.hstack([np.ones((nb_pts,1)), fixed_coords])
    T[:, 4:] = dist + nb_matches*smoothing
    moving_coords = T.dot(c)
    return moving_coords