Near-Optimal Algorithms for Shortest Paths in Weighted Unit-Disk Graphs

We revisit a classical graph-theoretic problem, the single-source shortest-path (SSSP) problem, in weighted unit-disk graphs. We first propose an exact (and deterministic) algorithm which solves the problem in O(n log^2 n) time using linear space, where n is the number of the vertices of the graph. This significantly improves the previous deterministic algorithm by Cabello and Jejcic [CGTA\u2715] which uses O(n^{1+delta}) time and O(n^{1+delta}) space (for any small constant delta>0) and the previous randomized algorithm by Kaplan et al. [SODA\u2717] which uses O(n log^{12+o(1)} n) expected time and O(n log^3 n) space. More specifically, we show that if the 2D offline insertion-only (additively-)weighted nearest-neighbor problem with k operations (i.e., insertions and queries) can be solved in f(k) time, then the SSSP problem in weighted unit-disk graphs can be solved in O(n log n+f(n)) time. Using the same framework with some new ideas, we also obtain a (1+epsilon)-approximate algorithm for the problem, using O(n log n + n log^2(1/epsilon)) time and linear space. This improves the previous (1+epsilon)-approximate algorithm by Chan and Skrepetos [SoCG\u2718] which uses O((1/epsilon)^2 n log n) time and O((1/epsilon)^2 n) space. Because of the Omega(n log n)-time lower bound of the problem (even when approximation is allowed), both of our algorithms are almost optimal

PourIt!: Weakly-supervised Liquid Perception from a Single Image for Visual Closed-Loop Robotic Pouring

Liquid perception is critical for robotic pouring tasks. It usually requires the robust visual detection of flowing liquid. However, while recent works have shown promising results in liquid perception, they typically require labeled data for model training, a process that is both time-consuming and reliant on human labor. To this end, this paper proposes a simple yet effective framework PourIt!, to serve as a tool for robotic pouring tasks. We design a simple data collection pipeline that only needs image-level labels to reduce the reliance on tedious pixel-wise annotations. Then, a binary classification model is trained to generate Class Activation Map (CAM) that focuses on the visual difference between these two kinds of collected data, i.e., the existence of liquid drop or not. We also devise a feature contrast strategy to improve the quality of the CAM, thus entirely and tightly covering the actual liquid regions. Then, the container pose is further utilized to facilitate the 3D point cloud recovery of the detected liquid region. Finally, the liquid-to-container distance is calculated for visual closed-loop control of the physical robot. To validate the effectiveness of our proposed method, we also contribute a novel dataset for our task and name it PourIt! dataset. Extensive results on this dataset and physical Franka robot have shown the utility and effectiveness of our method in the robotic pouring tasks. Our dataset, code and pre-trained models will be available on the project page.Comment: ICCV202