arXiv subjects

Weiming Shen

Publications and source records attributed to Weiming Shen.

At least 55 records · Page 3Linked to original sources

arXiv2023

Blow-up sets of Ricci curvatures of complete conformal metrics

A version of the singular Yamabe problem in smooth domains in a closed manifold yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study the blow-up phenomena of Ricci curvatures of these metrics on domains whose boundary is close to a certain limit set of a lower dimension. We will characterize the blow-up set according to the Yamabe invariant of the underlying manifold. In particular, we will prove that all points in the lower dimension part of the limit set belong to the blow-up set on manifolds not conformally equivalent to the standard sphere and that all but one point in the lower dimension part of the limit set belong to the blow-up set on manifolds conformally equivalent to the standard sphere. In certain cases, the blow-up set can be the entire manifold. We will demonstrate by examples that these results are optimal.

math.DG↗

arXiv2023

V2X-Lead: LiDAR-based End-to-End Autonomous Driving with Vehicle-to-Everything Communication Integration

This paper presents a LiDAR-based end-to-end autonomous driving method with Vehicle-to-Everything (V2X) communication integration, termed V2X-Lead, to address the challenges of navigating unregulated urban scenarios under mixed-autonomy traffic conditions. The proposed method aims to handle imperfect partial observations by fusing the onboard LiDAR sensor and V2X communication data. A model-free and off-policy deep reinforcement learning (DRL) algorithm is employed to train the driving agent, which incorporates a carefully designed reward function and multi-task learning technique to enhance generalization across diverse driving tasks and scenarios. Experimental results demonstrate the effectiveness of the proposed approach in improving safety and efficiency in the task of traversing unsignalized intersections in mixed-autonomy traffic, and its generalizability to previously unseen scenarios, such as roundabouts. The integration of V2X communication offers a significant data source for autonomous vehicles (AVs) to perceive their surroundings beyond onboard sensors, resulting in a more accurate and comprehensive perception of the driving environment and more safe and robust driving behavior.

cs.RO↗

arXiv2023

2nd Place Winning Solution for the CVPR2023 Visual Anomaly and Novelty Detection Challenge: Multimodal Prompting for Data-centric Anomaly Detection

This technical report introduces the winning solution of the team Segment Any Anomaly for the CVPR2023 Visual Anomaly and Novelty Detection (VAND) challenge. Going beyond uni-modal prompt, e.g., language prompt, we present a novel framework, i.e., Segment Any Anomaly + (SAA$+$), for zero-shot anomaly segmentation with multi-modal prompts for the regularization of cascaded modern foundation models. Inspired by the great zero-shot generalization ability of foundation models like Segment Anything, we first explore their assembly (SAA) to leverage diverse multi-modal prior knowledge for anomaly localization. Subsequently, we further introduce multimodal prompts (SAA$+$) derived from domain expert knowledge and target image context to enable the non-parameter adaptation of foundation models to anomaly segmentation. The proposed SAA$+$ model achieves state-of-the-art performance on several anomaly segmentation benchmarks, including VisA and MVTec-AD, in the zero-shot setting. We will release the code of our winning solution for the CVPR2023 VAN.

cs.CV↗

arXiv2023

Segment Any Anomaly without Training via Hybrid Prompt Regularization

We present a novel framework, i.e., Segment Any Anomaly + (SAA+), for zero-shot anomaly segmentation with hybrid prompt regularization to improve the adaptability of modern foundation models. Existing anomaly segmentation models typically rely on domain-specific fine-tuning, limiting their generalization across countless anomaly patterns. In this work, inspired by the great zero-shot generalization ability of foundation models like Segment Anything, we first explore their assembly to leverage diverse multi-modal prior knowledge for anomaly localization. For non-parameter foundation model adaptation to anomaly segmentation, we further introduce hybrid prompts derived from domain expert knowledge and target image context as regularization. Our proposed SAA+ model achieves state-of-the-art performance on several anomaly segmentation benchmarks, including VisA, MVTec-AD, MTD, and KSDD2, in the zero-shot setting. We will release the code at \href{https://github.com/caoyunkang/Segment-Any-Anomaly}{https://github.com/caoyunkang/Segment-Any-Anomaly}.

cs.CV↗

arXiv2023

Complementary Pseudo Multimodal Feature for Point Cloud Anomaly Detection

Point cloud (PCD) anomaly detection steadily emerges as a promising research area. This study aims to improve PCD anomaly detection performance by combining handcrafted PCD descriptions with powerful pre-trained 2D neural networks. To this end, this study proposes Complementary Pseudo Multimodal Feature (CPMF) that incorporates local geometrical information in 3D modality using handcrafted PCD descriptors and global semantic information in the generated pseudo 2D modality using pre-trained 2D neural networks. For global semantics extraction, CPMF projects the origin PCD into a pseudo 2D modality containing multi-view images. These images are delivered to pre-trained 2D neural networks for informative 2D modality feature extraction. The 3D and 2D modality features are aggregated to obtain the CPMF for PCD anomaly detection. Extensive experiments demonstrate the complementary capacity between 2D and 3D modality features and the effectiveness of CPMF, with 95.15% image-level AU-ROC and 92.93% pixel-level PRO on the MVTec3D benchmark. Code is available on https://github.com/caoyunkang/CPMF.

cs.CV↗

arXiv2023

Meta-Learning Based Early Fault Detection for Rolling Bearings via Few-Shot Anomaly Detection

Early fault detection (EFD) of rolling bearings can recognize slight deviation of the health states and contribute to the stability of mechanical systems. In practice, very limited target bearing data are available to conduct EFD, which makes it hard to adapt to the EFD task of new bearings. To address this problem, many transfer learning based EFD methods utilize historical data to learn transferable domain knowledge and conduct early fault detection on new target bearings. However, most existing methods only consider the distribution drift across different working conditions but ignore the difference between bearings under the same working condition, which is called Unit-to-Unit Variability (UtUV). The setting of EFD with limited target data considering UtUV can be formulated as a Few-shot Anomaly Detection task. Therefore, this paper proposes a novel EFD method based on meta-learning considering UtUV. The proposed method can learn a generic metric based on Relation Network (RN) to measure the similarity between normal data and the new arrival target bearing data. Besides, the proposed method utilizes a health state embedding strategy to decrease false alarms. The performance of proposed method is tested on two bearing datasets. The results show that the proposed method can detect incipient faults earlier than the baselines with lower false alarms.

cs.LG↗

arXiv2023

An Early Fault Detection Method of Rotating Machines Based on Multiple Feature Fusion with Stacking Architecture

Early fault detection (EFD) of rotating machines is important to decrease the maintenance cost and improve the mechanical system stability. One of the key points of EFD is developing a generic model to extract robust and discriminative features from different equipment for early fault detection. Most existing EFD methods focus on learning fault representation by one type of feature. However, a combination of multiple features can capture a more comprehensive representation of system state. In this paper, we propose an EFD method based on multiple feature fusion with stacking architecture (M2FSA). The proposed method can extract generic and discriminiative features to detect early faults by combining time domain (TD), frequency domain (FD), and time-frequency domain (TFD) features. In order to unify the dimensions of the different domain features, Stacked Denoising Autoencoder (SDAE) is utilized to learn deep features in three domains. The architecture of the proposed M2FSA consists of two layers. The first layer contains three base models, whose corresponding inputs are different deep features. The outputs of the first layer are concatenated to generate the input to the second layer, which consists of a meta model. The proposed method is tested on three bearing datasets. The results demonstrate that the proposed method is better than existing methods both in sensibility and reliability.

cs.LG↗

arXiv2023

Collaborative Discrepancy Optimization for Reliable Image Anomaly Localization

Most unsupervised image anomaly localization methods suffer from overgeneralization because of the high generalization abilities of convolutional neural networks, leading to unreliable predictions. To mitigate the overgeneralization, this study proposes to collaboratively optimize normal and abnormal feature distributions with the assistance of synthetic anomalies, namely collaborative discrepancy optimization (CDO). CDO introduces a margin optimization module and an overlap optimization module to optimize the two key factors determining the localization performance, i.e., the margin and the overlap between the discrepancy distributions (DDs) of normal and abnormal samples. With CDO, a large margin and a small overlap between normal and abnormal DDs are obtained, and the prediction reliability is boosted. Experiments on MVTec2D and MVTec3D show that CDO effectively mitigates the overgeneralization and achieves great anomaly localization performance with real-time computation efficiency. A real-world automotive plastic parts inspection application further demonstrates the capability of the proposed CDO. Code is available on https://github.com/caoyunkang/CDO.

cs.CV↗

arXiv2023

SCCAM: Supervised Contrastive Convolutional Attention Mechanism for Ante-hoc Interpretable Fault Diagnosis with Limited Fault Samples

In real industrial processes, fault diagnosis methods are required to learn from limited fault samples since the procedures are mainly under normal conditions and the faults rarely occur. Although attention mechanisms have become popular in the field of fault diagnosis, the existing attention-based methods are still unsatisfying for the above practical applications. First, pure attention-based architectures like transformers need a large number of fault samples to offset the lack of inductive biases thus performing poorly under limited fault samples. Moreover, the poor fault classification dilemma further leads to the failure of the existing attention-based methods to identify the root causes. To address the aforementioned issues, we innovatively propose a supervised contrastive convolutional attention mechanism (SCCAM) with ante-hoc interpretability, which solves the root cause analysis problem under limited fault samples for the first time. The proposed SCCAM method is tested on a continuous stirred tank heater and the Tennessee Eastman industrial process benchmark. Three common fault diagnosis scenarios are covered, including a balanced scenario for additional verification and two scenarios with limited fault samples (i.e., imbalanced scenario and long-tail scenario). The comprehensive results demonstrate that the proposed SCCAM method can achieve better performance compared with the state-of-the-art methods on fault classification and root cause analysis.

cs.LG↗

arXiv2023

SCLIFD:Supervised Contrastive Knowledge Distillation for Incremental Fault Diagnosis under Limited Fault Data

Intelligent fault diagnosis has made extraordinary advancements currently. Nonetheless, few works tackle class-incremental learning for fault diagnosis under limited fault data, i.e., imbalanced and long-tailed fault diagnosis, which brings about various notable challenges. Initially, it is difficult to extract discriminative features from limited fault data. Moreover, a well-trained model must be retrained from scratch to classify the samples from new classes, thus causing a high computational burden and time consumption. Furthermore, the model may suffer from catastrophic forgetting when trained incrementally. Finally, the model decision is biased toward the new classes due to the class imbalance. The problems can consequently lead to performance degradation of fault diagnosis models. Accordingly, we introduce a supervised contrastive knowledge distillation for incremental fault diagnosis under limited fault data (SCLIFD) framework to address these issues, which extends the classical incremental classifier and representation learning (iCaRL) framework from three perspectives. Primarily, we adopt supervised contrastive knowledge distillation (KD) to enhance its representation learning capability under limited fault data. Moreover, we propose a novel prioritized exemplar selection method adaptive herding (AdaHerding) to restrict the increase of the computational burden, which is also combined with KD to alleviate catastrophic forgetting. Additionally, we adopt the cosine classifier to mitigate the adverse impact of class imbalance. We conduct extensive experiments on simulated and real-world industrial processes under different imbalance ratios. Experimental results show that our SCLIFD outperforms the existing methods by a large margin.

cs.LG↗

arXiv2022

FastATDC: Fast Anomalous Trajectory Detection and Classification

Automated detection of anomalous trajectories is an important problem with considerable applications in intelligent transportation systems. Many existing studies have focused on distinguishing anomalous trajectories from normal trajectories, ignoring the large differences between anomalous trajectories. A recent study has made great progress in identifying abnormal trajectory patterns and proposed a two-stage algorithm for anomalous trajectory detection and classification (ATDC). This algorithm has excellent performance but suffers from a few limitations, such as high time complexity and poor interpretation. Here, we present a careful theoretical and empirical analysis of the ATDC algorithm, showing that the calculation of anomaly scores in both stages can be simplified, and that the second stage of the algorithm is much more important than the first stage. Hence, we develop a FastATDC algorithm that introduces a random sampling strategy in both stages. Experimental results show that FastATDC is 10 to 20 times faster than ATDC on real datasets. Moreover, FastATDC outperforms the baseline algorithms and is comparable to the ATDC algorithm.

cs.LG↗

arXiv2021

Hidden Path Selection Network for Semantic Segmentation of Remote Sensing Images

Targeting at depicting land covers with pixel-wise semantic categories, semantic segmentation in remote sensing images needs to portray diverse distributions over vast geographical locations, which is difficult to be achieved by the homogeneous pixel-wise forward paths in the architectures of existing deep models. Although several algorithms have been designed to select pixel-wise adaptive forward paths for natural image analysis, it still lacks theoretical supports on how to obtain optimal selections. In this paper, we provide mathematical analyses in terms of the parameter optimization, which guides us to design a method called Hidden Path Selection Network (HPS-Net). With the help of hidden variables derived from an extra mini-branch, HPS-Net is able to tackle the inherent problem about inaccessible global optimums by adjusting the direct relationships between feature maps and pixel-wise path selections in existing algorithms, which we call hidden path selection. For the better training and evaluation, we further refine and expand the 5-class Gaofen Image Dataset (GID-5) to a new one with 15 land-cover categories, i.e., GID-15. The experimental results on both GID-5 and GID-15 demonstrate that the proposed modules can stably improve the performance of different deep structures, which validates the proposed mathematical analyses.

eess.IV↗

arXiv2021

Automated Allocation of Detention Rooms Based on Inverse Graph Partitioning

Room allocation is a challenging task in detention centers since lots of related people need to be held separately with limited rooms. It is extremely difficult and risky to allocate rooms manually, especially for organized crime groups with close connections. To tackle this problem, we develop an intelligent room allocation system for detention centers to provide optimized room allocation schemes automatically. We first formalize the detention room allocation problem as inverse graph partitioning, which can measure the quality of room allocation schemes. Then, we propose two heuristic algorithms to achieve the global optimization and local optimization of detention room allocation. Experiment results on real-world datasets show that the proposed algorithms significantly outperform manual allocation and suggest that the system is of great practical application value.

cs.SI↗

arXiv2020

The Loewner-Nirenberg Problem in Cones

We study asymptotic behaviors of solutions to the Loewner-Nirenberg problem in finite cones and establish optimal asymptotic expansions in terms of the corresponding solutions in infinite cones. The spherical domains over which cones are formed are allowed to have singularities. An elliptic operator on such spherical domains with coefficients singular on boundary play an important role. Due to the singularity of the spherical domains, extra cares are needed for the study of the global regularity of the eigenfunctions and solutions of the associated singular Dirichlet problem.

math.AP↗

arXiv2020

On The Negativity of Ricci Curvatures of Complete Conformal Metrics

A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study whether these metrics have negative Ricci curvatures. Affirmatively, we prove that these metrics indeed have negative Ricci curvatures in bounded convex domains in the Euclidean space. On the other hand, we provide a general construction of domains in compact manifolds and demonstrate that the negativity of Ricci curvatures does not hold if the boundary is close to certain sets of low dimension. The expansion of the Green's function and the positive mass theorem play essential roles in certain cases.

math.DG↗

arXiv2019

Learning to Calibrate Straight Lines for Fisheye Image Rectification

This paper presents a new deep-learning based method to simultaneously calibrate the intrinsic parameters of fisheye lens and rectify the distorted images. Assuming that the distorted lines generated by fisheye projection should be straight after rectification, we propose a novel deep neural network to impose explicit geometry constraints onto processes of the fisheye lens calibration and the distorted image rectification. In addition, considering the nonlinearity of distortion distribution in fisheye images, the proposed network fully exploits multi-scale perception to equalize the rectification effects on the whole image. To train and evaluate the proposed model, we also create a new largescale dataset labeled with corresponding distortion parameters and well-annotated distorted lines. Compared with the state-of-the-art methods, our model achieves the best published rectification quality and the most accurate estimation of distortion parameters on a large set of synthetic and real fisheye images.

cs.CV↗

arXiv2019

Boundary layer separation and local behavior for the Steady Prandtl equation

In the case of favorable pressure gradient, Oleinik proved the global existence of classical solution for the 2-D steady Prandtl equation for a class of positive data. In the case of adverse pressure gradient, an important physical phenomena is the boundary layer separation. In this paper, we prove the boundary layer separation for a large class of Oleinik's data and confirm Goldstein's hypothesis concerning the local behavior of the solution near the separation, which gives a partial answer to open problem 5 proposed by Oleinik and Samokin in \cite{Olei}.

math.AP↗

arXiv2018

The Rigidity and Gap Theorem for Liouville's Equation

In this paper, we study the properties of the first global term in the polyhomogeneous expansions for Liouville's equation. We obtain rigidity and gap results for the boundary integral of the global coefficient. We prove that such a boundary integral is always nonpositive, and is zero if and only if the underlying domain is a disc. More generally, we prove some gap theorems relating such a boundary integral to the number of components of the boundary. The conformal structure plays an essential role.

math.DG↗