SampleLapNet: A Learnable Laplacian Approach for Task-Agnostic Point Cloud Downsampling

Advancements in 3D sensing technologies have led to an increased reliance on point cloud data for diverse applications ranging from autonomous navigation to environmental modeling. However, the sheer volume of data collected by these technologies poses significant challenges for real-time processing and analysis. This thesis introduces SampleLapNet, a novel neural network architecture designed to address the challenges of point cloud downsampling in a task-agnostic manner. By leveraging the Laplacian operator as a geometric measure of point importance, SampleLapNet learns to predict and preserve critical geometric features during the downsampling process, thereby ensuring minimal loss of relevant information. The architecture combines the robustness of transformer models with the efficiency of Laplacian-based importance scoring to facilitate efficient preprocessing that enhances subsequent point cloud analyses. We demonstrate the effectiveness of SampleLapNet through extensive experiments on benchmark datasets, showing significant improvements in downsampling efficiency without compromising the performance of downstream tasks such as semantic segmentation. This work not only proposes a method to reduce computational demands but also provides insights into the geometric processing of 3D data, suggesting pathways for future innovations in point cloud processing.