Elastic Shape Analysis

Elastic shape analysis focuses on comparing and analyzing the shapes of objects, particularly surfaces and graphs, while accounting for variations in their representation (e.g., different mesh structures or node arrangements). Current research emphasizes developing efficient algorithms, often leveraging Riemannian geometry and machine learning techniques like neural networks, to perform tasks such as shape registration, interpolation, and statistical analysis on unregistered or incomplete data. These advancements are improving the accuracy and speed of shape analysis across diverse applications, including medical imaging, computer graphics, and engineering design, by enabling more robust and efficient comparisons of complex shapes.