Shape Function

Shape functions are mathematical representations used to describe the geometry of objects or data, with applications ranging from 3D modeling and surface reconstruction to machine learning and scientific modeling. Current research focuses on developing efficient and accurate methods for learning and representing these functions, employing techniques like neural networks (e.g., implicit surface representations, GAMs), optimized discretization strategies (e.g., Centroidal Voronoi Tesselation), and novel algorithms for fitting additive models. These advancements improve the accuracy, interpretability, and efficiency of shape analysis across diverse fields, impacting areas such as medical image analysis, computer vision, and the discovery of scientific laws from complex data.