Thin Plate Splines (TPS) Transforms



In [1]:

    
import numpy as np
from menpo.transform import ThinPlateSplines
from menpo.shape import PointCloud

Let's create the landmarks used in Principal Warps paper (http://user.engineering.uiowa.edu/~aip/papers/bookstein-89.pdf)



In [2]:

    
# landmarks used in Principal Warps paper
# http://user.engineering.uiowa.edu/~aip/papers/bookstein-89.pdf
src_landmarks = np.array([[3.6929, 10.3819],
                          [6.5827,  8.8386],
                          [6.7756, 12.0866],
                          [4.8189, 11.2047],
                          [5.6969, 10.0748]])

tgt_landmarks = np.array([[3.9724, 6.5354],
                          [6.6969, 4.1181],
                          [6.5394, 7.2362],
                          [5.4016, 6.4528],
                          [5.7756, 5.1142]])

src = PointCloud(src_landmarks)
tgt = PointCloud(tgt_landmarks)
tps = ThinPlateSplines(src, tgt)

Let's visualize the TPS



In [3]:

    
%matplotlib inline
tps.view();

This proves that the result is correct



In [4]:

    
np.allclose(tps.apply(src_landmarks), tgt_landmarks)









    Out[4]:





True

Here is another example with a deformed diamond.



In [5]:

    
# deformed diamond
src_landmarks = np.array([[ 0, 1.0],
                          [-1, 0.0],
                          [ 0,-1.0],
                          [ 1, 0.0]])

tgt_landmarks = np.array([[ 0, 0.75],
                          [-1, 0.25],
                          [ 0,-1.25],
                          [ 1, 0.25]])

src = PointCloud(src_landmarks)
tgt = PointCloud(tgt_landmarks)
tps = ThinPlateSplines(src, tgt)



In [6]:

    
%matplotlib inline
tps.view();



In [7]:

    
np.allclose(tps.apply(src_landmarks), tgt_landmarks)









    Out[7]:





True