Distance Function

Distance functions, mathematical tools quantifying the separation between data points or objects, are central to numerous scientific and engineering fields. Current research emphasizes developing efficient and robust distance functions, particularly for complex data like point clouds, 3D shapes, and graphs, often leveraging neural networks and implicit surface representations (e.g., signed distance functions, ray distance functions) to learn these functions from data. This focus is driven by the need for accurate and computationally tractable distance measures in applications ranging from robotics and computer vision (e.g., collision detection, scene reconstruction) to machine learning (e.g., metric learning, clustering). The development of novel distance functions and associated algorithms continues to improve the performance and efficiency of various computational tasks across diverse disciplines.