Generalized Geodesic

Generalized geodesics, shortest paths on curved spaces, are central to various scientific fields, aiming to efficiently compute these paths and leverage their properties for diverse applications. Current research focuses on developing novel algorithms and model architectures, such as neural networks and optimal transport methods, to compute geodesics in complex spaces like manifolds and shape spaces, often incorporating geometric insights to improve accuracy and efficiency. These advancements have significant implications for diverse fields, including image processing, molecular docking, machine learning, and medical imaging, enabling improved data analysis, model training, and more accurate predictions. The ability to efficiently compute and utilize generalized geodesics is driving progress in numerous scientific and engineering domains.