The capability of autonomous exploration in complex, unknown environments is important in many robotic applications. While recent research on autonomous exploration have achieved much progress, there are still limitations, e.g., existing methods relying on greedy heuristics or optimal path planning are often hindered by repetitive paths and high computational demands. To address such limitations, we propose a novel exploration framework that utilizes the global topology information of observed environment to improve exploration efficiency while reducing computational overhead. Specifically, global information is utilized based on a skeletal topological graph representation of the environment geometry. We first propose an incremental skeleton extraction method based on wavefront propagation, based on which we then design an approach to generate a lightweight topological graph that can effectively capture the environment's structural characteristics. Building upon this, we introduce a finite state machine that leverages the topological structure to efficiently plan coverage paths, which can substantially mitigate the back-and-forth maneuvers (BFMs) problem. Experimental results demonstrate the superiority of our method in comparison with state-of-the-art methods. The source code will be made publicly available at: \url{https://github.com/Haochen-Niu/STGPlanner}.

Visual simultaneous localization and mapping (SLAM) systems face challenges in detecting loop closure under the circumstance of large viewpoint changes. In this paper, we present an object-based loop closure detection method based on the spatial layout and semanic consistency of the 3D scene graph. Firstly, we propose an object-level data association approach based on the semantic information from semantic labels, intersection over union (IoU), object color, and object embedding. Subsequently, multi-view bundle adjustment with the associated objects is utilized to jointly optimize the poses of objects and cameras. We represent the refined objects as a 3D spatial graph with semantics and topology. Then, we propose a graph matching approach to select correspondence objects based on the structure layout and semantic property similarity of vertices' neighbors. Finally, we jointly optimize camera trajectories and object poses in an object-level pose graph optimization, which results in a globally consistent map. Experimental results demonstrate that our proposed data association approach can construct more accurate 3D semantic maps, and our loop closure method is more robust than point-based and object-based methods in circumstances with large viewpoint changes.

Lossy compression algorithms are typically designed to achieve the lowest possible distortion at a given bit rate. However, recent studies show that pursuing high perceptual quality would lead to increase of the lowest achievable distortion (e.g., MSE). This paper provides nontrivial results theoretically revealing that, \textit{1}) the cost of achieving perfect perception quality is exactly a doubling of the lowest achievable MSE distortion, \textit{2}) an optimal encoder for the "classic" rate-distortion problem is also optimal for the perceptual compression problem, \textit{3}) distortion loss is unnecessary for training a perceptual decoder. Further, we propose a novel training framework to achieve the lowest MSE distortion under perfect perception constraint at a given bit rate. This framework uses a GAN with discriminator conditioned on an MSE-optimized encoder, which is superior over the traditional framework using distortion plus adversarial loss. Experiments are provided to verify the theoretical finding and demonstrate the superiority of the proposed training framework.

Matrix completion has attracted much interest in the past decade in machine learning and computer vision. For low-rank promotion in matrix completion, the nuclear norm penalty is convenient due to its convexity but has a bias problem. Recently, various algorithms using nonconvex penalties have been proposed, among which the proximal gradient descent (PGD) algorithm is one of the most efficient and effective. For the nonconvex PGD algorithm, whether it converges to a local minimizer and its convergence rate are still unclear. This work provides a nontrivial analysis on the PGD algorithm in the nonconvex case. Besides the convergence to a stationary point for a generalized nonconvex penalty, we provide more deep analysis on a popular and important class of nonconvex penalties which have discontinuous thresholding functions. For such penalties, we establish the finite rank convergence, convergence to restricted strictly local minimizer and eventually linear convergence rate of the PGD algorithm. Meanwhile, convergence to a local minimizer has been proved for the hard-thresholding penalty. Our result is the first shows that, nonconvex regularized matrix completion only has restricted strictly local minimizers, and the PGD algorithm can converge to such minimizers with eventually linear rate under certain conditions. Illustration of the PGD algorithm via experiments has also been provided. Code is available at https://github.com/FWen/nmc.