🤖 AI Summary
This paper addresses the challenge of locally controlling geometric and topological attributes in multi-class anatomical voxel map generation. Methodologically, it proposes a controllable latent diffusion framework featuring: (1) cubic control domains for substructure-level spatial localization; (2) the first integration of persistent homology into the diffusion process, enabling differentiable topological loss functions to precisely constrain global features—including connected components, cycles, and voids; and (3) voxel moment guidance for geometric shape control, coupled with a neural field decoder for efficient local editing. The approach jointly optimizes multi-dimensional geometric–topological constraints under arbitrary coordinate systems, preserving anatomical plausibility while significantly enhancing generation controllability and interpretability. Experimental results demonstrate superior fidelity and structural compliance compared to prior methods. This work establishes a novel paradigm for medical image synthesis and in silico experimentation.
📝 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.