ohirose/bcpd

What it solves

This project provides a suite of probabilistic algorithms for registering (aligning) point clouds and high-dimensional functions. It solves the problem of non-rigid alignment where shapes or signals may be deformed, noisy, or structurally complex, enabling applications in 3D model reconstruction, shape analysis, and the alignment of scientific data like spatial transcriptomics.

How it works

The software implements several Bayesian frameworks to handle different types of data:

• Domain Elastic Transform (DET): A grid-free framework that registers high-dimensional signals (functions) on irregular domains without requiring voxelization.
• Bayesian Coherent Point Drift (BCPD): A generalization of the Coherent Point Drift algorithm that uses a motion coherence prior to ensure smooth, non-rigid deformation of point clouds.
• Geodesic-Based BCPD (GBCPD): Enhances BCPD by using a geodesic exponential kernel, which helps separate boundaries that are spatially close but topologically distant.
• Dependent Landmark Drift (DLD): Uses a statistical shape model instead of a motion coherence prior to fit a learned mean shape to a target point cloud.

To handle massive datasets (millions of points), the project uses an "++" acceleration framework involving downsampling, displacement field interpolation, the Nyström method for low-rank matrix approximation, and k-d tree searches for efficient point correspondence.

Who it’s for

This tool is designed for researchers and engineers working in 3D computer vision, shape analysis, spatial transcriptomics, and signal processing who need to align complex, non-rigid datasets.

Highlights

• Scalability: Capable of handling millions of points on standard hardware via optimized acceleration modes.
• Versatility: Supports both geometric point set registration and functional signal registration.
• Robustness: Includes geodesic kernels to handle complex topological cuts and statistical shape models for noise-resilient fitting.
• Flexible Transformations: Supports similarity, affine, rigid, and non-rigid transformation models.