Thin-plate spline

import matplotlib.pyplot as plt
import seaborn as sns

from ktch.landmark import GeneralizedProcrustesAnalysis
from ktch.plot import tps_grid_2d_plot
from ktch.datasets import load_landmark_mosquito_wings

Load mosquito wing landmark dataset

from Rohlf and Slice 1990 Syst. Zool.

data_landmark_mosquito_wings = load_landmark_mosquito_wings(as_frame=True)
data_landmark_mosquito_wings.coords

		x	y
specimen_id	coord_id
1	0	-0.4933	0.0130
	1	-0.0777	0.0832
	2	0.2231	0.0861
	3	0.2641	0.0462
	4	0.2645	0.0261
...	...	...	...
127	13	-0.2028	0.0371
	14	0.0490	0.0347
	15	-0.0422	0.0204
	16	0.1004	-0.0180
	17	-0.1473	-0.0057

2286 rows × 2 columns

GPA

see also :ref:generalized_Procrustes_analysis

X = data_landmark_mosquito_wings.coords.to_numpy().reshape(-1, 18 * 2)

gpa = GeneralizedProcrustesAnalysis(tol=10**-5)

X_aligned = gpa.fit_transform(X)

Mean shape and an aligned shape

X_reference = gpa.mu_  # mean shape
X_target = X_aligned.reshape(-1, 18, 2)[0]  # the 0-th aligned shape

fig = plt.figure()
ax = fig.add_subplot(111)

sns.scatterplot(x=X_reference[:, 0], y=X_reference[:, 1], ax=ax)
sns.scatterplot(x=X_target[:, 0], y=X_target[:, 1], ax=ax)

ax.set_aspect("equal")

Transformation grids of thin-plate splines

tps_grid_2d_plot(X_reference, X_target, outer=0.2, grid_size=0.03)

<Axes: >