Laplace Beltrami Operator

The Laplace-Beltrami operator (LBO) is a fundamental tool in shape analysis, providing a way to extract intrinsic geometric information from surfaces and shapes regardless of their position or orientation. Current research focuses on extending the LBO's capabilities, including developing anisotropic and Finsler-based generalizations to handle more complex shapes and incorporating it into novel segmentation and shape matching algorithms, often leveraging its spectral properties. These advancements improve the robustness and accuracy of shape analysis techniques in computer vision applications, particularly for tasks involving partial shapes, noisy data, and the need for shape priors. The LBO's versatility makes it a powerful tool with broad applications across various fields.