NHO: A Neural Hamiltonian Operator for Anchor-based Region Localization and Dense Correspondance

2026-09-29

AI Summary

This study addresses the challenge of localizing partial shapes and recovering dense correspondences to complete shapes under sparse anchor conditions in non-rigid settings. To this end, it proposes a novel paradigm based on neural Hamiltonian operators that integrates sparse anchors with intrinsic geometry. Specifically, an intrinsic neural field parameterizes the potential function subject to spectral and geometric constraints, while a localized feature space is constructed to encode regional support. Furthermore, a reciprocal refinement mechanism between operator estimation and correspondence recovery is introduced to resolve spatial ambiguities. The proposed method achieves competitive accuracy on both tasks and demonstrates strong robustness to uniform scaling and rotation.

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.

Problem

• non-rigid shape correspondence
• partial-to-full matching
• region localization
• dense correspondence
• sparse anchors

Innovation

• Neural Hamiltonian Operator
• Intrinsic Neural Field
• Reciprocal Refinement
• Dense Correspondence
• Region Localization