Alphamorph

alphamorph is a Python package for non-rigid transformations of point clouds.

Unlike the traditional usage of registration between a source and a target, alphamorph transforms a source point cloud into a target shape, in this case a circle.

This is done by finding alpha shapes, that will be used as anchors for thin-plate splines.

In layman terms, it is "making the bed" by 1) finding where are the bed corners and 2) pushing and pulling the sheets!

Features

• Point Cloud Transformation: Given a noisy point cloud, apply a non-rigid transformation so it fits a shape
• Visualization: Easily visualize the original, distorted, and transformed point clouds.

Installation

You can install alphamorph via pip:

pip install alphamorph

Minimal Working Example

import numpy as np
from alphamorph.apply import alphamorph_apply
points = np.random.rand(1000, 2)
new_points = alphamorph_apply(points, alpha=2.5)

Full Example

Below is a simple example that demonstrates how to use alphamorph to transform a point cloud:

import numpy as np
import matplotlib.pyplot as plt
from alphamorph.geometry import generate_point_cloud, distort_point_cloud
from alphamorph.alpha import compute_alpha_shape
from alphamorph.apply import alphamorph_apply
from alphamorph.plotting import plot_point_cloud, create_color_list


np.random.seed(42)

# Generate an original point cloud and a distorted version
original_points = generate_point_cloud(num_points=2000)
color_list = create_color_list(original_points)
noisy_points = distort_point_cloud(original_points, noise_scale=0.2, num_bins=15)



# Compute alpha shapes and apply alphamorph transformation
alpha = 2.5
original_hull_indices, original_hull_points = compute_alpha_shape(original_points, alpha)
reconstructed_hull_indices, reconstructed_hull_points = compute_alpha_shape(noisy_points, alpha)
new_points = alphamorph_apply(original_points, alpha=alpha)
new_points_hull_points = new_points[reconstructed_hull_indices]

# Plot
fig, axes = plt.subplots(1, 3, figsize=(12, 6))
plot_point_cloud(axes[0], original_points, 'Original', color_list=color_list, hull_points=original_hull_points)
plot_point_cloud(axes[1], noisy_points, 'Noisy', color_list=color_list, hull_points=reconstructed_hull_points)
plot_point_cloud(axes[2], new_points, 'Noisy + Alphamorph', color_list=color_list, hull_points=new_points_hull_points)
plt.tight_layout()
plt.savefig('alphamorph_example.png')
plt.show()

Example Results