# Hamiltonian operator for spectral shape analysis

arXiv: https://arxiv.org/abs/1611.01990 · HTML: https://mlsanity.com/paper/1611.01990/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2016.

## Built on by (most cited first, 10 of 10)

- [SRIF: Semantic Shape Registration Empowered by Diffusion-based Image Morphing and Flow Estimation](https://mlsanity.com/paper/2409.11682/) (2024)
- [Non-Isometric Shape Matching via Functional Maps on Landmark-Adapted Bases](https://mlsanity.com/paper/2205.04800/) (2022)
- [Disentangling Geometric Deformation Spaces in Generative Latent Shape Models](https://mlsanity.com/paper/2103.00142/) (2021)
- [Hearing the shape of an arena with spectral swarm robotics](https://mlsanity.com/paper/2403.17147/) (2024)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)
- [Smoothness and effective regularizations in learned embeddings for shape matching](https://mlsanity.com/paper/2112.07289/) (2021)
- [Partial Shape Similarity via Alignment of Multi-Metric Hamiltonian Spectra](https://mlsanity.com/paper/2207.03018/) (2022)
- [LBONet: Supervised Spectral Descriptors for Shape Analysis](https://mlsanity.com/paper/2411.08272/) (2024)
- [Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach](https://mlsanity.com/paper/2108.02161/) (2021)
- [NHO: A Neural Hamiltonian Operator for Anchor-based Region Localization and Dense Correspondence](https://mlsanity.com/paper/2609.37048/) (2026)

## Abstract (arXiv)

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.