# LBONet: Supervised Spectral Descriptors for Shape Analysis

arXiv: https://arxiv.org/abs/2411.08272 · HTML: https://mlsanity.com/paper/2411.08272/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 76 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [MVTN: Multi-View Transformation Network for 3D Shape Recognition](https://mlsanity.com/paper/2011.13244/) (2020)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Primal-Dual Mesh Convolutional Neural Networks](https://mlsanity.com/paper/2010.12455/) (2020)
- [CNNs on Surfaces using Rotation-Equivariant Features](https://mlsanity.com/paper/2006.01570/) (2020)
- [Isospectralization, or how to hear shape, style, and correspondence](https://mlsanity.com/paper/1811.11465/) (2018)
- [Field Convolutions for Surface CNNs](https://mlsanity.com/paper/2104.03916/) (2021)
- [Correspondence-Free Region Localization for Partial Shape Similarity via Hamiltonian Spectrum Alignment](https://mlsanity.com/paper/1906.06226/) (2019)
- [Hamiltonian operator for spectral shape analysis](https://mlsanity.com/paper/1611.01990/) (2016)
- [Finsler-Laplace-Beltrami Operators with Application to Shape Analysis](https://mlsanity.com/paper/2404.03999/) (2024)
- [Geodesic convolutional neural networks on Riemannian manifolds](https://mlsanity.com/paper/1501.06297/) (2015)

## Built on by (most cited first, 1 of 1)

- [Learning Eigenstructures of Unstructured Data Manifolds](https://mlsanity.com/paper/2512.01103/) (2025)

## Abstract (arXiv)

The Laplace-Beltrami operator has established itself in the field of non-rigid shape analysis due to its many useful properties such as being invariant under isometric transformation, having a countable eigensystem forming an orthornormal basis, and fully characterizing geodesic distances of the manifold. However, this invariancy only applies under isometric deformations, which leads to a performance breakdown in many real-world applications. In recent years emphasis has been placed upon extracting optimal features using deep learning methods,however spectral signatures play a crucial role and still add value. In this paper we take a step back, revisiting the LBO and proposing a supervised way to learn several operators on a manifold. Depending on the task, by applying these functions, we can train the LBO eigenbasis to be more task-specific. The optimization of the LBO leads to enormous improvements to established descriptors such as the heat kernel signature in various tasks such as retrieval, classification, segmentation, and correspondence, proving the adaption of the LBO eigenbasis to both global and highly local learning settings.