A Mathematical Review of Shape Space Analysis in Machine Learning

This survey presents a mathematical framework for analyzing geometric data, integrating differential geometry, statistics, and machine learning. It outlines a unified pipeline for shape representation, geodesic metrics, statistical analysis, and geometry-aware learning, enabling the study of shape variability and structural trajectories across populations and time. Applications span biology, medicine, anthropology, and computer vision, highlighting challenges in handling nonlinear and unaligned geometric variation.