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.

翻译：深度隐式函数（DIFs）因其紧凑性和连续表征能力在三维计算机视觉领域广受欢迎。然而，如何建立DIF编码形状间的密集对应关系和语义关联仍是关键挑战，制约了其在纹理迁移和形状分析中的应用。此外，近期基于DIF的三维形状生成研究往往忽视对应关系保持与拓扑结构保留。本文提出HNDF（混合神经微分同胚流）方法，通过隐式学习底层表征，将复杂的密集对应关系显式分解为轴向对齐的三平面场特征。为避免陷入局部最优的次优表征，我们提出混合监督策略，同时捕捉局部与全局对应关系。不同于直接生成新三维形状的传统方法，我们进一步探索基于微分同胚流形变模板形状的生成范式，其中形变由生成的三平面场特征编码。借助预训练的二维扩散模型，我们通过生成的三平面场特征产生高质量且多样的三维微分同胚流，确保与模板形状的拓扑一致性。在医学图像器官分割数据集上的大量实验验证了HNDF在三维形状表征与生成中的有效性。