Shape Space

Shape space research focuses on representing and analyzing the variations within collections of shapes, aiming to develop efficient methods for comparing, manipulating, and generating shapes. Current research emphasizes the use of Riemannian geometry and machine learning, including generative models (like LLMs and diffusion models), geodesic regression, and neural networks (e.g., autoencoders) to create and navigate these complex, often non-Euclidean spaces. This field is significant for its applications in diverse areas such as computer vision, biomedicine (e.g., analyzing brain shape changes), and archaeology (e.g., studying artifact evolution), enabling more sophisticated analysis and generation of shapes from various data sources.