PhD Proposal: Efficient and Robust Point Cloud Embedding: Theories, Algorithms and Applications

https://umd.zoom.us/j/8594561040
This thesis proposal seeks to advance point cloud embedding by focusing on two critical areas: computational and memory efficiency, and robustness to noise and density variations. Existing methods, such as PointNet and KPConv, rely heavily on data-driven approaches that require extensive training to capture geometric features. These approaches, while effective in certain respects, fall short in terms of inherent robustness against environmental noise and data density fluctuations, and often require substantial computational resources. These limitations restrict their application in scenarios where speed and resource constraints are critical, such as in event camera stream processing and drone navigation.In response, this proposal introduces novel methodologies that utilize kernel methods to enhance both the efficiency and robustness of point cloud embeddings, grounded in a strong theoretical framework. It further explores the application of these advanced embeddings in two distinct domains: real-time processing of event camera streams and numeric encoding in tabular data. These case studies demonstrate the versatility and potential impact of the proposed methods across various technological fields.The thesis is structured to methodically address these challenges, presenting a comprehensive approach from foundational theories and algorithms to practical applications. This includes detailed discussions on the mathematical modeling of point clouds, development of efficient and robust embedding techniques using kernel methods, and their implementation in diverse settings.