基于三平面的混合神经微分同胚流用于形状表示与生成
Hybrid Neural Diffeomorphic Flow for Shape Representation and Generation via Triplane
AI总结：
本文提出HNDF方法，通过混合神经微分同胚流和三平面特征分解实现三维形状的稠密对应学习与拓扑保持的形状生成，并利用二维扩散模型提升生成质量与多样性。
摘要：
深度隐式函数（DIFs）因其紧凑性和连续表示能力而在三维计算机视觉中受到广泛关注。然而，处理DIF编码形状之间的稠密对应关系和语义关系仍然是一个关键挑战，限制了它们在纹理迁移和形状分析中的应用。此外，近期利用DIFs进行三维形状生成的工作往往忽视了对应关系和拓扑保持。本文提出HNDF（混合神经微分同胚流），一种隐式学习底层表示并将复杂的稠密对应关系分解为显式轴对齐三平面特征的方法。为了避免陷入局部最优的次优表示，我们提出了一种混合监督方法，同时捕获局部和全局对应关系。与直接生成新三维形状的传统方法不同，我们进一步探索了通过微分同胚流对模板形状进行变形来生成形状的思路，其中变形由生成的三平面特征编码。利用现有的二维扩散模型，我们通过生成的三平面特征产生高质量且多样化的三维微分同胚流，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评估了HNDF在三维形状表示和生成方面的有效性。
英文摘要：
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.
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