NHO：一种用于锚点区域定位与稠密对应的神经哈密顿算子

中文摘要 AI 辅助

非刚性部分到整体的形状对应，从稀疏锚点出发，需要识别完整表面上的对应区域，并恢复部分形状与该区域之间的稠密对应。我们提出NHO，将稀疏锚点与部分形状的内在几何相结合，学习一个神经哈密顿算子，其局部化特征空间同时编码区域支撑和用于稠密对应的内在坐标。NHO将哈密顿势参数化为内在神经场，并利用锚点证据以及谱和几何约束对其进行优化。为解决稀疏锚点留下的空间模糊性，我们引入了算子估计与对应恢复之间的相互细化。在每一轮中，当前特征空间提供谱坐标，并将其匹配限制在其诱导的支撑区域内，而几何上可靠的对应则为更新势提供额外证据。细化后，聚合的特征函数能量产生最终定位，恢复的映射初始化稠密对应细化。实验表明，在两项任务上均具有竞争力的精度，以及对均匀缩放和旋转的鲁棒性。

英文摘要

Non-rigid partial-to-full shape correspondence from sparse anchors requires identifying the corresponding region on the full surface and recovering dense correspondences between the partial shape and that region. We present NHO, which combines sparse anchors with the intrinsic geometry of the partial shape to learn a neural Hamiltonian operator whose localized eigenspace encodes both the region support and intrinsic coordinates for dense correspondence. NHO parameterizes the Hamiltonian potential as an intrinsic neural field and optimizes it using anchor evidence together with spectral and geometric constraints. To resolve the spatial ambiguity left by sparse anchors, we introduce reciprocal refinement between operator estimation and correspondence recovery. At each round, the current eigenspace provides spectral coordinates and restricts matching to its induced support, while geometrically reliable correspondences provide additional evidence for updating the potential. After refinement, aggregated eigenfunction energy yields the final localization, and the recovered map initializes dense correspondence refinement. Experiments demonstrate competitive accuracy on both tasks and robustness to uniform scaling and rotation.

发表机构

• Jilin University（吉林大学）
• Zhejiang University（浙江大学）
• North China University of Technology（北方工业大学）

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