Geodesic Distance

Geodesic distance, the shortest distance between two points along a curved surface or manifold, is a fundamental concept with applications across diverse fields. Current research focuses on developing efficient algorithms for computing geodesic distances, particularly in complex spaces like those represented by graphs or high-dimensional data manifolds, often employing techniques like graph neural networks or Riemannian geometry. These advancements improve the accuracy and speed of geodesic computations, impacting applications ranging from image processing and computer vision to protein folding and change point detection in time series data. The robustness of geodesic distance calculations to noise and outliers is also a key area of investigation, leading to more reliable results in real-world scenarios.