LBONet: Supervised Spectral Descriptors for Shape Analysis.

Area of Science:

• Differential Geometry
• Computer Vision
• Machine Learning

Background:

• The Laplace-Beltrami operator (LBO) is crucial for non-rigid shape analysis due to its invariance under isometric transformations.
• Its performance degrades with non-isometric deformations, limiting real-world applications.
• While deep learning excels at feature extraction, spectral signatures remain valuable.

Purpose of the Study:

• To develop a supervised framework for learning task-specific operators on manifolds.
• To adapt the LBO's eigenbasis for improved performance in diverse shape analysis tasks.
• To enhance established shape descriptors by optimizing the LBO.

Main Methods:

• Proposing a supervised learning approach to customize LBO operators.
• Training task-specific LBO eigenbases.
• Evaluating optimized LBO on retrieval, classification, segmentation, and correspondence tasks.

Main Results:

• Significant improvements in established descriptors like the heat kernel signature.
• Demonstrated adaptation of the LBO eigenbasis for both global and local learning settings.
• Validation of the supervised LBO optimization for enhanced shape analysis.

Conclusions:

• Supervised learning offers a powerful way to adapt the LBO for specific shape analysis challenges.
• Optimized LBO significantly boosts performance across multiple computer vision tasks.
• This method bridges the gap between traditional spectral methods and modern deep learning.