# Localized Manifold Harmonics for Spectral Shape Analysis

arXiv: https://arxiv.org/abs/1707.02596 · HTML: https://mlsanity.com/paper/1707.02596/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2017.

## Built on by (most cited first, 12 of 12)

- [Hybrid Functional Maps for Crease-Aware Non-Isometric Shape Matching](https://mlsanity.com/paper/2312.03678/) (2023)
- [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)
- [Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach](https://mlsanity.com/paper/2108.02161/) (2021)
- [Extracting a functional representation from a dictionary for non-rigid shape matching](https://mlsanity.com/paper/2305.10332/) (2023)
- [Deep Spectral Meshes: Multi-Frequency Facial Mesh Processing with Graph Neural Networks](https://mlsanity.com/paper/2402.10365/) (2024)
- [Strike a Chord! Modal Kinetic Typography](https://mlsanity.com/paper/2609.38325/) (2026)

## Abstract (arXiv)

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases.