Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation
  via Triplane
Kun Han Shanlin Sun Xiaohui Xie
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.