ohirose/bcpd

Domain Elastic Transform / Bayesian Coherent Point Drift

What it solves

This software suite provides tools for non-rigid registration of point clouds and functions on irregular domains. It solves the problem of aligning two different geometric structures or high-dimensional signals (like spatial transcriptomics data) that may be deformed, rotated, or noisy, allowing for shape analysis, 3D model reconstruction, and functional alignment.

How it works

The suite implements several probabilistic frameworks based on Bayesian inference:

  • Domain Elastic Transform (DET): A grid-free framework that registers functions on irregular domains by combining geometric and functional alignment, treating data as functions rather than requiring voxelization.
  • Bayesian Coherent Point Drift (BCPD): A generalization of the Coherent Point Drift algorithm that uses a motion coherence prior to ensure smooth deformations when aligning sparse point clouds.
  • Geodesic-Based BCPD (GBCPD): Enhances BCPD by using a surface coherence matrix (combining Gaussian and geodesic kernels) to better separate closely located boundaries and handle complex topological cuts.
  • Dependent Landmark Drift (DLD): Uses a statistical shape model to constrain deformations, mapping a learned mean shape to a target point cloud to resist noise and artifacts.

To handle massive datasets (millions of points), the "++" variants (e.g., BCPD++) use downsampling, displacement field interpolation, the Nystrom method for low-rank matrix approximation, and k-d tree searches for efficient point correspondence.

Who it’s for

It is designed for researchers and engineers working with scientific data, specifically those dealing with spatial transcriptomics, digital images, audio signals, 3D shape analysis, and 3D model reconstruction.

Highlights

  • Grid-free registration: DET allows for the registration of high-dimensional signals on irregular domains without binning or voxelization.
  • High scalability: The "++" framework enables the processing of millions of points on standard hardware.
  • Topological awareness: GBCPD uses geodesic kernels to maintain structural integrity across complex interfaces.
  • Robust shape fitting: DLD leverages prior shape knowledge via statistical models to handle noisy data.

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