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Abstract This paper explicates a solution to building correspondences between molecular-scale transcriptomics and tissue-scale atlases. This problem arises in atlas construction and cross-specimen/technology alignment where specimens per emerging technology remain sparse and conventional image representations cannot efficiently model the high dimensions from subcellular detection of thousands of genes. We address these challenges by representing spatial transcriptomics data as generalized functions encoding position and high-dimensional feature (gene, cell type) identity. We map onto low-dimensional atlas ontologies by modeling regions as homogeneous random fields with unknown transcriptomic feature distribution. We solve simultaneously for the minimizing geodesic diffeomorphism of coordinates through LDDMM and for these latent feature densities. We map tissue-scale mouse brain atlases to gene-based and cell-based transcriptomics data from MERFISH and BARseq technologies and to histopathology and cross-species atlases to illustrate integration of diverse molecular and cellular datasets into a single coordinate system as a means of comparison and further atlas construction. 

Abstract Spatial transcriptomics (ST) technologies enable high throughput gene expression characterization within thin tissue sections. However, comparing spatial observations across sections, samples, and technologies remains challenging. To address this challenge, we develop STalign to align ST datasets in a manner that accounts for partially matched tissue sections and other local non-linear distortions using diffeomorphic metric mapping. We apply STalign to align ST datasets within and across technologies as well as to align ST datasets to a 3D common coordinate framework. We show that STalign achieves high gene expression and cell-type correspondence across matched spatial locations that is significantly improved over landmark-based affine alignments. Applying STalign to align ST datasets of the mouse brain to the 3D common coordinate framework from the Allen Brain Atlas, we highlight how STalign can be used to lift over brain region annotations and enable the interrogation of compositional heterogeneity across anatomical structures. STalign is available as an open-source Python toolkit athttps://github.com/JEFworks-Lab/STalignand as Supplementary Software with additional documentation and tutorials available athttps://jef.works/STalign.