LBONet: Supervised Spectral Descriptors for Shape Analysis

TL;DR

This paper introduces a supervised learning approach to optimize the Laplace-Beltrami operator for shape analysis, enhancing spectral descriptors' performance in various tasks like retrieval and segmentation.

Contribution

It proposes a method to learn task-specific operators on manifolds, improving spectral descriptors beyond traditional isometry-invariant properties.

Findings

Enhanced descriptors outperform traditional ones in shape retrieval and classification.

Optimized operators improve segmentation and correspondence accuracy.

Task-specific LBO eigenbasis adapts to both global and local learning settings.

Abstract

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.