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import numpy as np
from scipy.spatial.distance import pdist, cdist, squareform
from sklearn.metrics import pairwise_distances
class ThinPlateSplines:
def __init__(self, ctrl_pts: np.ndarray, target_pts: np.ndarray, reg=0.0):
"""
:param ctrl_pts: [N, d] tensor of control d-dimensional points
:param target_pts: [N, d] tensor of target d-dimensional points
:param reg: regularization coefficient
"""
self.__ctrl_pts = ctrl_pts
self.__target_pts = target_pts
self.__reg = reg
self.__num_ctrl_pts = ctrl_pts.shape[0]
self.__dim = ctrl_pts.shape[1]
self.__K = None
self.__compute_coeffs()
self.__aff_params = self.__coeffs[self.__num_ctrl_pts:, ...] # Affine parameters of the TPS
self.__non_aff_paramms = self.__coeffs[:self.__num_ctrl_pts, ...] # Non-affine parameters of he TPS
def __compute_coeffs(self):
target_pts_aug = np.vstack([self.__target_pts,
np.zeros([self.__dim + 1, self.__dim])]).astype(self.__target_pts.dtype)
T_i = np.linalg.inv(self.__make_T()).astype(self.__target_pts.dtype)
self.__coeffs = np.matmul(T_i, target_pts_aug).astype(self.__target_pts.dtype)
def __make_T(self):
# cp: [K x 2] control points
# T: [(K+3) x (K+3)]
P = np.hstack([np.ones([self.__num_ctrl_pts, 1], dtype=np.float), self.__ctrl_pts])
zeros = np.zeros([self.__dim + 1, self.__dim + 1], dtype=np.float)
self.__K = self.__U_dist(self.__ctrl_pts)
alfa = np.mean(self.__K)
self.__K = self.__K + np.ones_like(self.__K) * np.power(alfa, 2) * self.__reg
top = np.hstack([P, self.__K])
bottom = np.hstack([P.transpose(), zeros])
return np.vstack([top, bottom])
def __U_dist(self, ctrl_pts, int_pts=None):
dist = pairwise_distances(ctrl_pts, int_pts)
if ctrl_pts.shape[-1] == 2:
u_dist = np.square(dist) * np.log(dist + 1e-6)
else:
u_dist = np.sqrt(dist)
return u_dist
def __lift_pts(self, int_pts: np.ndarray, num_pts):
# int_pts: [N x 2], input points
# cp: [K x 2], control points
# pLift: [N x (3+K)], lifted input points
int_pts_lift = np.hstack([self.__U_dist(self.__ctrl_pts, int_pts),
np.ones([num_pts, 1], dtype=np.float),
int_pts])
return int_pts_lift
def _get_coefficients(self):
return self.__coeffs
def interpolate(self, int_points):
"""
:param int_points: [K, d] flattened d-points of a mesh
:return:
"""
num_pts = int_points.shape[0]
int_points_lift = self.__lift_pts(int_points, num_pts)
return np.dot(int_points_lift, self.__coeffs)
@property
def bending_energy(self):
aux = tf.matmul(self.__non_aff_paramms, self.__K, transpose_a=True)
return tf.matmul(aux, self.__non_aff_paramms)
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