Tissue tearing degrades optimal-transport and diffeomorphic registration of spatial transcriptomics beyond displacement magnitude: a multi-seed deformation benchmark and a supervised graph cross-attention proof-of-concept
Discuss this preprint
Start a discussion What are Sciety discussions?Listed in
This article is not in any list yet, why not save it to one of your lists.Abstract
Background
Three-dimensional reconstruction from serial spatial-transcriptomics (ST) sections requires registering adjacent slices, but physical sectioning introduces tears — discontinuous, non-isometric deformations. Leading methods rely on priors that tears strain: PASTE/PASTE2 use Fused Gromov–Wasserstein optimal transport (OT), which assumes near-isometric preservation of within-slice distances, while STalign and CODA use diffeomorphic (LDDMM) mapping, which cannot change tissue topology. Learned-deformation ST methods are emerging (STaCker, INST-Align), but OT/diffeomorphic behaviour under tearing has not been systematically characterised.
Methods
On the spatialLIBD human DLPFC Visium dataset (Maynard et al., 2021; 3 donors), we build a controlled benchmark — known smooth warps, single-block rigid tears (expression unchanged), and an identity self-control — at severities of 0–8 spot pitches, scored against an approximate array-position ground truth (∼8 px residual). We evaluate three unsupervised incumbents — PASTE2 (OT, over five warp seeds), STalign (diffeomorphic LDDMM), and GPSA (Gaussian-process warp) — add a magnitude-matched smooth control, and test a minimal graph model, Sutura (per-slice graph encoder →cross-attention correspondence → per-spot displacement; spatial coupling is local kNN message passing only, no explicit smoothness penalty). Sutura is trained supervised on each tissue’s ground truth; all baselines are unsupervised. Generalisation is assessed by leave-one-donor-out across all three donors.
Results
OT registration is robust to smooth warps but degrades reproducibly under tearing: nearest-correspondence (argmax) error 722 ± 5 →855 ± 27 px and layer accuracy 64.9% → 60.5% (mean ± 95% CI, 5 seeds). The effect is not merely displacement magnitude: at a matched mean displacement ( ∼2000 px), a smooth warp costs 769 px / 60.2% accuracy whereas a tear costs 863 px / 57.5% — an extra ∼100 px and ∼3 points attributable to the discontinuity. STalign (LDDMM) and GPSA (GP warp) both collapse at severe tears (866 px and 931 px respectively), confirming tear-collapse is field-wide across three independent method families. Trained and evaluated on the same donor, Sutura fits torn-tissue correspondence to a median 99 →106 px (5-seed), but under leave-one-donor-out is 1236 ±2→ 1584 ± 52 px — ∼1.8–3.6× worse than PASTE2 on every unseen donor. A contrastive correspondence loss halves the gap on two of three donors (to 816→949 and 749→ 826 px, ∼1.1–1.2× PASTE2 at worst-case tear) but is modest on the third and never surpasses PASTE2.
Conclusion
Tearing is a real, magnitude-controlled failure mode of all three incumbent method classes. A learned model fits it in-sample but donor-invariant generalisation remains open. The contrastive fix roughly halves the held-out gap on two of three donors and nears PASTE2 at worst-case tear, but does not surpass it: donor-invariance is improved, not solved. The durable contribution is the benchmark, the characterisation across three method families, and an honest negative with a diagnosed mechanism.
