Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation via Triplane

TL;DR

This paper introduces HNDF, a hybrid neural diffeomorphic flow method that improves 3D shape representation and generation by explicitly modeling dense correspondences with triplane features and leveraging a 2D diffusion model for high-quality, topologically consistent shape synthesis.

Contribution

The paper proposes a novel hybrid supervision approach and a triplane-based diffeomorphic flow for better shape correspondence and generation, addressing limitations of existing DIF methods.

Findings

Effective dense correspondence modeling in 3D shapes.

High-quality, diverse shape generation with topological consistency.

Improved shape representation in medical imaging datasets.

Abstract

Deep Implicit Functions (DIFs) have gained popularity in 3D computer vision due to their compactness and continuous representation capabilities. However, addressing dense correspondences and semantic relationships across DIF-encoded shapes remains a critical challenge, limiting their applications in texture transfer and shape analysis. Moreover, recent endeavors in 3D shape generation using DIFs often neglect correspondence and topology preservation. This paper presents HNDF (Hybrid Neural Diffeomorphic Flow), a method that implicitly learns the underlying representation and decomposes intricate dense correspondences into explicitly axis-aligned triplane features. To avoid suboptimal representations trapped in local minima, we propose hybrid supervision that captures both local and global correspondences. Unlike conventional approaches that directly generate new 3D shapes, we further explore the idea of shape generation with deformed template shape via diffeomorphic flows, where the deformation is encoded by the generated triplane features. Leveraging a pre-existing 2D diffusion model, we produce high-quality and diverse 3D diffeomorphic flows through generated triplanes features, ensuring topological consistency with the template shape. Extensive experiments on medical image organ segmentation datasets evaluate the effectiveness of HNDF in 3D shape representation and generation.