Convex Hull

A convex hull is the smallest convex polygon or polyhedron encompassing a given set of points, a fundamental concept in computational geometry with applications across diverse fields. Current research focuses on efficient algorithms for approximating convex hulls in high-dimensional spaces, particularly for large datasets where exact computation is intractable, employing techniques like mathematical programming, support vector machines, and Delaunay triangulations. These advancements are crucial for improving uncertainty quantification in machine learning models, enabling efficient data valuation and selection for trustworthy AI, and enhancing applications such as vehicle pose estimation and adaptive video streaming. Furthermore, convex hull analysis is increasingly used to address challenges in areas like federated learning and weakly supervised learning.