A grid-free probabilistic framework for nonrigid registration of high-dimensional vector-valued functions on irregular manifolds.
March 24, 2026
Original Paper
Domain Elastic Transform: Bayesian Function Registration for High-Dimensional Scientific Data
arXiv · 2603.21235
The Takeaway
In fields like spatial transcriptomics, researchers currently have to choose between losing resolution via voxelization or ignoring functional signals. This method allows for the direct registration of massive, high-dimensional atlases without binning, achieving 92% topological preservation where previous optimal transport methods failed.
From the 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 s