Spatial Transcriptomics

Nonrigid registration is conventionally divided into point set registration, which aligns sparse geometries, and image registration, which aligns continuous intensity fields on regular grids. This dichotomy is limiting for emerging scientific data such as spatial transcriptomics, where high-dimensional vector-valued functions, e.g., gene expression, are defined on irregular sparse manifolds. Researchers must therefore either sacrifice single-cell resolution through voxelization or ignore functional signals in favor of geometric alignment. We propose Domain Elastic Transform (DET), a grid-free probabilistic framework that jointly aligns geometry and function. By treating data as functions on irregular domains, DET registers high-dimensional signals directly without binning. Within a generalized Bayesian formulation, domain deformation is modeled as elastic motion guided by a joint spatial-functional likelihood. DET is fully unsupervised and scalable through registration on sampled points followed by displacement interpolation. We evaluate DET on MERFISH mouse-brain slices and Stereo-seq mouse-embryo atlases. On a 90-case MERFISH benchmark with severe perturbations and no prior initialization, DET achieved the strongest spatial overlap and topology among the evaluated pipelines, while an accelerated PASTE2 variant achieved the highest label-transfer ARI. In an atlas-scale MOSTA feasibility study without cross-stage ground truth, nonrigid refinement improved several within-pipeline anatomical-domain and boundary-consistency measures. These results suggest that grid-free function registration complements point-set, image-based, and optimal-transport approaches for high-dimensional scientific data. The DET implementation is available at https://github.com/ohirose/bcpd (since Mar, 2025).

Spatial Transcriptomics (ST) profiles thousands of gene expression values at discrete spots with precise coordinates on tissue sections, preserving spatial context essential for clinical and pathological studies. With rising sequencing throughput and advancing platforms, the expanding data volumes motivate large-scale ST pretraining. However, the fundamental unit for pretraining, i.e., what constitutes a single training sample, remains ill-posed. Existing choices fall into two camps: (1) treating each spot as an independent sample, which discards spatial dependencies and collapses ST into single-cell transcriptomics; and (2) treating an entire slide as a single sample, which produces prohibitively large inputs and drastically fewer training examples, undermining effective pretraining. To address this gap, we propose treating spatial transcriptomics as croppable images. Specifically, we define a multi-channel image representation with fixed spatial size by cropping patches from raw slides, thereby preserving spatial context while substantially increasing the number of training samples. Along the channel dimension, we define gene subset selection rules to control input dimensionality and improve pretraining stability. Extensive experiments show that the proposed image-like dataset construction for ST pretraining consistently improves downstream performance, outperforming conventional pretraining schemes. Ablation studies verify that both spatial patching and channel design are necessary, establishing a unified, practical paradigm for organizing ST data and enabling large-scale pretraining.