Functional Map

Functional maps are a mathematical framework for representing and comparing shapes, primarily focusing on establishing correspondences between points on different shapes, even under non-rigid deformations. Current research emphasizes learning-based approaches, often integrating deep learning architectures (like those based on ARFlow or DiffusionNet) with spectral methods and optimal transport techniques to improve accuracy and efficiency, particularly for non-isometric shapes and partial data. This work has significant implications for various fields, including computer vision (shape matching, image registration), medical imaging (cardiovascular analysis), and robotics (object tracking, 3D scene reconstruction), by enabling more robust and accurate analysis of complex geometric data.