Neural operator improves matching between partial and full 3D shapes
NHO: A Neural Hamiltonian Operator for Anchor-based Region Localization and Dense Correspondance
Computer Vision and Pattern Recognition
Summary
Matching incomplete 3D shapes to their full versions is challenging because only a few matching points are known, and the rest must be figured out. The authors present a method called NHO that uses math-inspired tools combined with neural networks to find corresponding regions and detailed matches on the shapes. It uses an iterative process where guesses about the shape's matching regions and dense correspondences improve each other, making the final matches more accurate. Their tests show this method works well even if the shapes are scaled or rotated.
What this means in practice
- •For 3d model developers: Localize and match partial scans to full 3D models for accurate mesh alignment and object reconstruction.
- •For medical imaging specialists: Match partial anatomical scans to complete organ shapes to help with diagnostics and treatment planning.
Authors
Jing Li, Yawei Luo, Xiangze Meng, Ying Li, Tieru Wu, Rui Ma
Abstract
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.