Domain Elastic Transform: Bayesian Function Registration for High-Dimensional Scientific Data

• URL: http://arxiv.org/abs/2603.21235v1
• Date: Sun, 22 Mar 2026 13:47:29 GMT
• Title: Domain Elastic Transform: Bayesian Function Registration for High-Dimensional Scientific Data
• Abstract summary: We propose Domain Elastic Transform, a grid-free probabilistic framework that unifies geometric and functional alignment.<n>We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood.<n>We demonstrate that DET achieves 92% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle.
• Score: 8.674184859651135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. However, this dichotomy creates a critical bottleneck for emerging scientific data, such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular, sparse manifolds. Consequently, researchers currently face a forced choice: either sacrifice single-cell resolution via voxelization to utilize image-based tools, or ignore the critical functional signal to utilize geometric tools. To resolve this dilemma, we propose Domain Elastic Transform (DET), a grid-free probabilistic framework that unifies geometric and functional alignment. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. We formulate the problem within a rigorous Bayesian framework, modeling domain deformation as an elastic motion guided by a joint spatial-functional likelihood. The method is fully unsupervised and scalable, utilizing feature-sensitive downsampling to handle massive atlases. We demonstrate that DET achieves 92\% topological preservation on MERFISH data where state-of-the-art optimal transport methods struggle ($<$5\%), and successfully registers whole-embryo Stereo-seq atlases across developmental stages -- a task involving massive scale and complex nonrigid growth. The implementation of DET is available on {https://github.com/ohirose/bcpd} (since Mar, 2025).

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