arXiv subjects

Lujia Wang

Publications and source records attributed to Lujia Wang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Colouring signed analogues of Kneser, Schrijver, and Borsuk graphs

The Kneser signed graph $\KS(n,k)$, $k\leq n$, is the graph whose vertices are signed $k$-subsets of $[n]$ (i.e. $k$-subsets $S$ of $\{ \pm 1, \pm 2, \ldots, \pm n\}$ such that $S\cap (-S)=\emptyset$). Two vertices $A$ and $B$ are adjacent with a positive edge if $A\cap (-B)=\emptyset$ and with a negative edge if $A\cap B=\emptyset$. We prove that the balanced chromatic number of $\KS(n,k)$ is $n-k+1$. We then introduce the signed analogue of Schrijver graphs and show that they form vertex-critical subgraphs of $\KS(n,k)$ with respect to balanced colouring. Further connection to topological methods, in particular, connection to Borsuk signed graphs is also considered.

math.CO↗

arXiv2025

An Erdos-Gallai conjecture for signed graphs

For every natural number $p$, we show that the maximum negative girth among the class of signed graphs on $n$ vertices with balanced chromatic number at least $p$ is between $(1/e)n^{1/(p-1)}$ and $2(p-1) n^{1/(p-1)}$. This extends a conjecture of Erdős and Gallai to signed graphs.

math.CO↗

arXiv2025

Odd Hadwiger's conjecture for the complements of Kneser graphs

A generalization of the four-color theorem, Hadwiger's conjecture is considered as one of the most important and challenging problems in graph theory, and odd Hadwiger's conjecture is a strengthening of Hadwiger's conjecture by way of signed graphs. In this paper, we prove that odd Hadwiger's conjecture is true for the complements $\overline{K}(n,k)$ of the Kneser graphs $K(n,k)$, where $n\geq 2k \ge 4$. This improves a result of G. Xu and S. Zhou (2017) which states that Hadwiger's conjecture is true for this family of graphs. Moreover, we prove that $\overline{K}(n,k)$ contains a 1-shallow complete minor of a special type with order no less than the chromatic number $χ(\overline{K}(n,k))$, and in the case when $7 \le 2k+1 \le n \le 3k-1$ the gap between the odd Hadwiger number and chromatic number of $\overline{K}(n,k)$ is $Ω(1.5^{k})$.

math.CO↗

arXiv2025

Fractional balanced chromatic number of signed subcubic graphs

A signed graph is a pair $(G,σ)$, where $G$ is a graph and $σ: E(G)\rightarrow \{-, +\}$, called signature, is an assignment of signs to the edges. Given a signed graph $(G,σ)$ with no negative loops, a balanced $(p,q)$-coloring of $(G,σ)$ is an assignment $f$ of $q$ colors to each vertex from a pool of $p$ colors such that each color class induces a balanced subgraph, i.e., no negative cycles. Let $(K_4,-)$ be the signed graph on $K_4$ with all edges being negative. In this work, we show that every signed (simple) subcubic graph admits a balanced $(5,3)$-coloring except for $(K_4,-)$ and signed graphs switching equivalent to it. For this particular signed graph the best balanced colorings are $(2p,p)$-colorings.

math.CO↗

arXiv2024

Real-Time Metric-Semantic Mapping for Autonomous Navigation in Outdoor Environments

The creation of a metric-semantic map, which encodes human-prior knowledge, represents a high-level abstraction of environments. However, constructing such a map poses challenges related to the fusion of multi-modal sensor data, the attainment of real-time mapping performance, and the preservation of structural and semantic information consistency. In this paper, we introduce an online metric-semantic mapping system that utilizes LiDAR-Visual-Inertial sensing to generate a global metric-semantic mesh map of large-scale outdoor environments. Leveraging GPU acceleration, our mapping process achieves exceptional speed, with frame processing taking less than 7ms, regardless of scenario scale. Furthermore, we seamlessly integrate the resultant map into a real-world navigation system, enabling metric-semantic-based terrain assessment and autonomous point-to-point navigation within a campus environment. Through extensive experiments conducted on both publicly available and self-collected datasets comprising 24 sequences, we demonstrate the effectiveness of our mapping and navigation methodologies. Code has been publicly released: https://github.com/gogojjh/cobra

cs.RO↗

arXiv2024

FusionPortableV2: A Unified Multi-Sensor Dataset for Generalized SLAM Across Diverse Platforms and Scalable Environments

Simultaneous Localization and Mapping (SLAM) technology has been widely applied in various robotic scenarios, from rescue operations to autonomous driving. However, the generalization of SLAM algorithms remains a significant challenge, as current datasets often lack scalability in terms of platforms and environments. To address this limitation, we present FusionPortableV2, a multi-sensor SLAM dataset featuring sensor diversity, varied motion patterns, and a wide range of environmental scenarios. Our dataset comprises $27$ sequences, spanning over $2.5$ hours and collected from four distinct platforms: a handheld suite, a legged robots, a unmanned ground vehicle (UGV), and a vehicle. These sequences cover diverse settings, including buildings, campuses, and urban areas, with a total length of $38.7km$. Additionally, the dataset includes ground-truth (GT) trajectories and RGB point cloud maps covering approximately $0.3km^2$. To validate the utility of our dataset in advancing SLAM research, we assess several state-of-the-art (SOTA) SLAM algorithms. Furthermore, we demonstrate the dataset's broad application beyond traditional SLAM tasks by investigating its potential for monocular depth estimation. The complete dataset, including sensor data, GT, and calibration details, is accessible at https://fusionportable.github.io/dataset/fusionportable_v2.

cs.RO↗

arXiv2024

MGCBS: An Optimal and Efficient Algorithm for Solving Multi-Goal Multi-Agent Path Finding Problem

With the expansion of the scale of robotics applications, the multi-goal multi-agent pathfinding (MG-MAPF) problem began to gain widespread attention. This problem requires each agent to visit pre-assigned multiple goal points at least once without conflict. Some previous methods have been proposed to solve the MG-MAPF problem based on Decoupling the goal Vertex visiting order search and the Single-agent pathfinding (DVS). However, this paper demonstrates that the methods based on DVS cannot always obtain the optimal solution. To obtain the optimal result, we propose the Multi-Goal Conflict-Based Search (MGCBS), which is based on Decoupling the goal Safe interval visiting order search and the Single-agent pathfinding (DSS). Additionally, we present the Time-Interval-Space Forest (TIS Forest) to enhance the efficiency of MGCBS by maintaining the shortest paths from any start point at any start time step to each safe interval at the goal points. The experiment demonstrates that our method can consistently obtain optimal results and execute up to 7 times faster than the state-of-the-art method in our evaluation.

cs.MA↗

arXiv2024

Real-time Neural Dense Elevation Mapping for Urban Terrain with Uncertainty Estimations

Having good knowledge of terrain information is essential for improving the performance of various downstream tasks on complex terrains, especially for the locomotion and navigation of legged robots. We present a novel framework for neural urban terrain reconstruction with uncertainty estimations. It generates dense robot-centric elevation maps online from sparse LiDAR observations. We design a novel pre-processing and point features representation approach that ensures high robustness and computational efficiency when integrating multiple point cloud frames. A Bayesian-GAN model then recovers the detailed terrain structures while simultaneously providing the pixel-wise reconstruction uncertainty. We evaluate the proposed pipeline through extensive simulation and real-world experiments. It demonstrates efficient terrain reconstruction with high quality and real-time performance on a mobile platform, which further benefits the downstream tasks of legged robots. (See https://kin-zhang.github.io/ndem/ for more details.)

cs.RO↗

arXiv2024

PALoc: Advancing SLAM Benchmarking with Prior-Assisted 6-DoF Trajectory Generation and Uncertainty Estimation

Accurately generating ground truth (GT) trajectories is essential for Simultaneous Localization and Mapping (SLAM) evaluation, particularly under varying environmental conditions. This study introduces a systematic approach employing a prior map-assisted framework for generating dense six-degree-of-freedom (6-DoF) GT poses for the first time, enhancing the fidelity of both indoor and outdoor SLAM datasets. Our method excels in handling degenerate and stationary conditions frequently encountered in SLAM datasets, thereby increasing robustness and precision. A significant aspect of our approach is the detailed derivation of covariances within the factor graph, enabling an in-depth analysis of pose uncertainty propagation. This analysis crucially contributes to demonstrating specific pose uncertainties and enhancing trajectory reliability from both theoretical and empirical perspectives. Additionally, we provide an open-source toolbox (https://github.com/JokerJohn/Cloud_Map_Evaluation) for map evaluation criteria, facilitating the indirect assessment of overall trajectory precision. Experimental results show at least a 30\% improvement in map accuracy and a 20\% increase in direct trajectory accuracy compared to the Iterative Closest Point (ICP) \cite{sharp2002icp} algorithm across diverse campus environments, with substantially enhanced robustness. Our open-source solution (https://github.com/JokerJohn/PALoc), extensively applied in the FusionPortable\cite{Jiao2022Mar} dataset, is geared towards SLAM benchmark dataset augmentation and represents a significant advancement in SLAM evaluations.

cs.RO↗

arXiv2024

Enhancing Campus Mobility: Achievements and Challenges of Autonomous Shuttle "Snow Lion''

The rapid evolution of autonomous vehicles (AVs) has significantly influenced global transportation systems. In this context, we present ``Snow Lion'', an autonomous shuttle meticulously designed to revolutionize on-campus transportation, offering a safer and more efficient mobility solution for students, faculty, and visitors. The primary objective of this research is to enhance campus mobility by providing a reliable, efficient, and eco-friendly transportation solution that seamlessly integrates with existing infrastructure and meets the diverse needs of a university setting. To achieve this goal, we delve into the intricacies of the system design, encompassing sensing, perception, localization, planning, and control aspects. We evaluate the autonomous shuttle's performance in real-world scenarios, involving a 1146-kilometer road haul and the transportation of 442 passengers over a two-month period. These experiments demonstrate the effectiveness of our system and offer valuable insights into the intricate process of integrating an autonomous vehicle within campus shuttle operations. Furthermore, a thorough analysis of the lessons derived from this experience furnishes a valuable real-world case study, accompanied by recommendations for future research and development in the field of autonomous driving.

cs.RO↗

arXiv2023

Quantifying intra-tumoral genetic heterogeneity of glioblastoma toward precision medicine using MRI and a data-inclusive machine learning algorithm

Glioblastoma (GBM) is one of the most aggressive and lethal human cancers. Intra-tumoral genetic heterogeneity poses a significant challenge for treatment. Biopsy is invasive, which motivates the development of non-invasive, MRI-based machine learning (ML) models to quantify intra-tumoral genetic heterogeneity for each patient. This capability holds great promise for enabling better therapeutic selection to improve patient outcomes. We proposed a novel Weakly Supervised Ordinal Support Vector Machine (WSO-SVM) to predict regional genetic alteration status within each GBM tumor using MRI. WSO-SVM was applied to a unique dataset of 318 image-localized biopsies with spatially matched multiparametric MRI from 74 GBM patients. The model was trained to predict the regional genetic alteration of three GBM driver genes (EGFR, PDGFRA, and PTEN) based on features extracted from the corresponding region of five MRI contrast images. For comparison, a variety of existing ML algorithms were also applied. The classification accuracy of each gene was compared between the different algorithms. The SHapley Additive exPlanations (SHAP) method was further applied to compute contribution scores of different contrast images. Finally, the trained WSO-SVM was used to generate prediction maps within the tumoral area of each patient to help visualize the intra-tumoral genetic heterogeneity. This study demonstrated the feasibility of using MRI and WSO-SVM to enable non-invasive prediction of intra-tumoral regional genetic alteration for each GBM patient, which can inform future adaptive therapies for individualized oncology.

cs.LG↗

arXiv2023

A Novel Hybrid Ordinal Learning Model with Health Care Application

Ordinal learning (OL) is a type of machine learning models with broad utility in health care applications such as diagnosis of different grades of a disease (e.g., mild, modest, severe) and prediction of the speed of disease progression (e.g., very fast, fast, moderate, slow). This paper aims to tackle a situation when precisely labeled samples are limited in the training set due to cost or availability constraints, whereas there could be an abundance of samples with imprecise labels. We focus on imprecise labels that are intervals, i.e., one can know that a sample belongs to an interval of labels but cannot know which unique label it has. This situation is quite common in health care datasets due to limitations of the diagnostic instrument, sparse clinical visits, or/and patient dropout. Limited research has been done to develop OL models with imprecise/interval labels. We propose a new Hybrid Ordinal Learner (HOL) to integrate samples with both precise and interval labels to train a robust OL model. We also develop a tractable and efficient optimization algorithm to solve the HOL formulation. We compare HOL with several recently developed OL methods on four benchmarking datasets, which demonstrate the superior performance of HOL. Finally, we apply HOL to a real-world dataset for predicting the speed of progressing to Alzheimer's Disease (AD) for individuals with Mild Cognitive Impairment (MCI) based on a combination of multi-modality neuroimaging and demographic/clinical datasets. HOL achieves high accuracy in the prediction and outperforms existing methods. The capability of accurately predicting the speed of progression to AD for each individual with MCI has the potential for helping facilitate more individually-optimized interventional strategies.

cs.LG↗

arXiv2023

A Dynamic Points Removal Benchmark in Point Cloud Maps

In the field of robotics, the point cloud has become an essential map representation. From the perspective of downstream tasks like localization and global path planning, points corresponding to dynamic objects will adversely affect their performance. Existing methods for removing dynamic points in point clouds often lack clarity in comparative evaluations and comprehensive analysis. Therefore, we propose an easy-to-extend unified benchmarking framework for evaluating techniques for removing dynamic points in maps. It includes refactored state-of-art methods and novel metrics to analyze the limitations of these approaches. This enables researchers to dive deep into the underlying reasons behind these limitations. The benchmark makes use of several datasets with different sensor types. All the code and datasets related to our study are publicly available for further development and utilization.

cs.RO↗

arXiv2023

FSNet: Redesign Self-Supervised MonoDepth for Full-Scale Depth Prediction for Autonomous Driving

Predicting accurate depth with monocular images is important for low-cost robotic applications and autonomous driving. This study proposes a comprehensive self-supervised framework for accurate scale-aware depth prediction on autonomous driving scenes utilizing inter-frame poses obtained from inertial measurements. In particular, we introduce a Full-Scale depth prediction network named FSNet. FSNet contains four important improvements over existing self-supervised models: (1) a multichannel output representation for stable training of depth prediction in driving scenarios, (2) an optical-flow-based mask designed for dynamic object removal, (3) a self-distillation training strategy to augment the training process, and (4) an optimization-based post-processing algorithm in test time, fusing the results from visual odometry. With this framework, robots and vehicles with only one well-calibrated camera can collect sequences of training image frames and camera poses, and infer accurate 3D depths of the environment without extra labeling work or 3D data. Extensive experiments on the KITTI dataset, KITTI-360 dataset and the nuScenes dataset demonstrate the potential of FSNet. More visualizations are presented in \url{https://sites.google.com/view/fsnet/home}

cs.CV↗

arXiv2023

RNGDet++: Road Network Graph Detection by Transformer with Instance Segmentation and Multi-scale Features Enhancement

The road network graph is a critical component for downstream tasks in autonomous driving, such as global route planning and navigation. In the past years, road network graphs are usually annotated by human experts manually, which is time-consuming and labor-intensive. To annotate road network graphs effectively and efficiently, automatic algorithms for road network graph detection are demanded. Most existing methods either adopt a post-processing step on semantic segmentation maps to produce road network graphs, or propose graph-based algorithms to directly predict the graphs. However, these works suffer from hard-coded algorithms and inferior performance. To enhance the previous state-of-the-art (SOTA) method RNGDet, we add an instance segmentation head to better supervise the training, and enable the network to leverage multi-scale features of the backbone. Since the new proposed approach is improved from RNGDet, we name it RNGDet++. Experimental results show that our RNGDet++ outperforms baseline methods in terms of almost all evaluation metrics on two large-scale public datasets. Our code and supplementary materials are available at \url{https://tonyxuqaq.github.io/projects/RNGDetPlusPlus/}.

cs.CV↗

arXiv2023

CenterLineDet: CenterLine Graph Detection for Road Lanes with Vehicle-mounted Sensors by Transformer for HD Map Generation

With the fast development of autonomous driving technologies, there is an increasing demand for high-definition (HD) maps, which provide reliable and robust prior information about the static part of the traffic environments. As one of the important elements in HD maps, road lane centerline is critical for downstream tasks, such as prediction and planning. Manually annotating centerlines for road lanes in HD maps is labor-intensive, expensive and inefficient, severely restricting the wide applications of autonomous driving systems. Previous work seldom explores the lane centerline detection problem due to the complicated topology and severe overlapping issues of lane centerlines. In this paper, we propose a novel method named CenterLineDet to detect lane centerlines for automatic HD map generation. Our CenterLineDet is trained by imitation learning and can effectively detect the graph of centerlines with vehicle-mounted sensors (i.e., six cameras and one LiDAR) through iterations. Due to the use of the DETR-like transformer network, CenterLineDet can handle complicated graph topology, such as lane intersections. The proposed approach is evaluated on the large-scale public dataset NuScenes. The superiority of our CenterLineDet is demonstrated by the comparative results. Our code, supplementary materials, and video demonstrations are available at \href{https://tonyxuqaq.github.io/projects/CenterLineDet/}{https://tonyxuqaq.github.io/projects/CenterLineDet/}.

cs.CV↗

arXiv2023

An Efficient Approach to the Online Multi-Agent Path Finding Problem by Using Sustainable Information

Multi-agent path finding (MAPF) is the problem of moving agents to the goal vertex without collision. In the online MAPF problem, new agents may be added to the environment at any time, and the current agents have no information about future agents. The inability of existing online methods to reuse previous planning contexts results in redundant computation and reduces algorithm efficiency. Hence, we propose a three-level approach to solve online MAPF utilizing sustainable information, which can decrease its redundant calculations. The high-level solver, the Sustainable Replan algorithm (SR), manages the planning context and simulates the environment. The middle-level solver, the Sustainable Conflict-Based Search algorithm (SCBS), builds a conflict tree and maintains the planning context. The low-level solver, the Sustainable Reverse Safe Interval Path Planning algorithm (SRSIPP), is an efficient single-agent solver that uses previous planning context to reduce duplicate calculations. Experiments show that our proposed method has significant improvement in terms of computational efficiency. In one of the test scenarios, our algorithm can be 1.48 times faster than SOTA on average under different agent number settings.

cs.MA↗

arXiv2022

Efficient Speed Planning for Autonomous Driving in Dynamic Environment with Interaction Point Model

Safely interacting with other traffic participants is one of the core requirements for autonomous driving, especially in intersections and occlusions. Most existing approaches are designed for particular scenarios and require significant human labor in parameter tuning to be applied to different situations. To solve this problem, we first propose a learning-based Interaction Point Model (IPM), which describes the interaction between agents with the protection time and interaction priority in a unified manner. We further integrate the proposed IPM into a novel planning framework, demonstrating its effectiveness and robustness through comprehensive simulations in highly dynamic environments.

cs.RO↗