Anatomica: Localized Control over Geometric and Topological Properties for Anatomical Diffusion Models

TL;DR

Anatomica addresses the problem of controllably generating 3D multi-class anatomical segmentations by enabling localized geometric and topological constraints during inference. It combines cuboidal substructure parsing (V-parsing and L-parsing) with differentiable geometric moments and persistent homology-based penalties to steer diffusion sampling, and it integrates neural-field decoding for efficient latent-space partial decoding. The approach yields competitive geometric fidelity and improved topological control across cardiac, aorta, spine, and coronary datasets, with favorable speedups from partial decoding strategies. By enabling flexible, plug-and-play geo-topological guidance without retraining, Anatomica supports synthetic data augmentation and virtual clinical trials at scale.

Abstract

We present Anatomica: an inference-time framework for generating multi-class anatomical voxel maps with localized geo-topological control. During generation, we use cuboidal control domains of varying dimensionality, location, and shape to slice out relevant substructures. These local substructures are used to compute differentiable penalty functions that steer the sample towards target constraints. We control geometric features such as size, shape, and position through voxel-wise moments, while topological features such as connected components, loops, and voids are enforced through persistent homology. Lastly, we implement Anatomica for latent diffusion models, where neural field decoders partially extract substructures, enabling the efficient control of anatomical properties. Anatomica applies flexibly across diverse anatomical systems, composing constraints to control complex structures over arbitrary dimensions and coordinate systems, thereby enabling the rational design of synthetic datasets for virtual trials or machine learning workflows.

Figures (10)

• Figure 1: Anatomica is a compositional diffusion-guidance framework for generating segmentations based on anatomical features that are localized within cuboidal control domains.Left: We generate voxel maps according to localized target geometry (size, shape, and position) visualized as red ellipsoids. Right: We generate voxel maps according to target topology (components, loops, and voids).
• Figure 2: Differentiable measurement of anatomical properties from multi-class voxel maps.A: We differentiably parse relevant substructures from anatomical voxel maps for localized measurement. B: We spatially transform cuboidal primitives (template domains) into control domains that slice into anatomical structures (V-parsing). C: The substructure is then differentiably measured in terms of geometric properties; as well as D: persistent homology-based topological properties.
• Figure 3: Efficient parsing of anatomical substructures during diffusion guidance.A: During guidance, we parse relevant substructures directly from the clean latent prediction with a neural field decoder (L-parsing). B: In coarse L-parsing, we use a coarse grid to decode globally defined substructures at low spatial resolution. C: In localized L-parsing, we use a similar grid size but spatially transform the template point grid to decode localized substructures at high spatial resolution.
• Figure 4: Geometric Control Tasks. We define a variety of relevant tasks by varying the selected tissues, template domain grid size, and control domain-specific spatial transforms.
• Figure 5: Qualitative evaluation of geometric control experiments. We generate anatomical segmentations based on target domains (black frames) and geometric features (red ellipsoids) for four cardiac tasks. Sample geometry shown as green ellipsoids.