Geodesic Regression

Geodesic regression is a statistical method used to model data evolving on curved spaces, often representing shapes or images, by finding the "best-fitting" curve along the manifold's geodesics (shortest paths). Current research focuses on improving the efficiency and robustness of geodesic regression, particularly through the development of novel algorithms like neural ordinary differential equations and the incorporation of techniques from manifold learning, such as principal geodesic analysis. Applications span diverse fields, including medical image analysis (e.g., brain tumor segmentation and tracking changes in brain shape during menstruation), computer vision (e.g., keypoint estimation on deformable shapes), and analysis of topological data structures (e.g., merge trees). These advancements enable more accurate and efficient analysis of complex, high-dimensional data with non-linear relationships.