Local Geometry

Local geometry research focuses on understanding and leveraging the spatial relationships within data, particularly in complex, high-dimensional datasets like point clouds and generative model manifolds. Current efforts concentrate on developing algorithms and architectures, such as graph convolutional networks and transformers, that efficiently capture and utilize local geometric information for tasks ranging from point cloud denoising and registration to improving the quality and controllability of generative models. These advancements are crucial for improving the accuracy and efficiency of various applications, including 3D scene understanding, object recognition, and the generation of realistic synthetic data.