arXiv subjects

Lidong Wang

Publications and source records attributed to Lidong Wang.

15 recordsLinked to original sources

arXiv2026

Shadowing property and transitivity of a set-valued map and its inverse limit

We study the properties of shadowing, transitivity, weakly mixing, mixing, chain transitivity and chain mixing of a set-valued map and its generalized inverse limit. Concerning shadowing, we prove that for a surjective upper semi-continuous set-valued map $F$ on a compact metric space, $F$ has shadowing if and only if the shift map on the generalized inverse limit $\underleftarrow{\lim}\,\underleftarrow{F}$ of its inverse set-valued map has shadowing; dually, $\underleftarrow{F}$ has shadowing if and only if the shift map on $\underleftarrow{\lim}F$ has shadowing. We further show that the shadowing of $F$ and that of $\underleftarrow{F}$ are always equivalent; consequently $F$, $\underleftarrow{F}$ and the shift maps on $\underleftarrow{\lim}\,\underleftarrow{F}$ and on $\underleftarrow{\lim}F$ all have shadowing simultaneously. In particular, $F$ has shadowing if and only if the shift map on its directly induced generalized inverse limit $\underleftarrow{\lim}F$ has shadowing. This strengthens a recent theorem established under continuity and openness assumptions. We show that if the shift map on the generalized inverse limit is transitive (resp. weakly mixing, mixing, chain transitive, chain mixing), then the set-valued map is transitive (resp. weakly mixing, mixing, chain transitive, chain mixing). For a set-valued map with shadowing, the properties of total transitivity, weak mixing, mixing, specification and chain mixing are mutually equivalent.

math.DS↗

arXiv2026

Constructions of two-dimensional optical orthogonal codes of weight three

The study of optical orthogonal codes has been motivated by an application in an optical code-division multiple access system. This paper focuses on optimal two-dimensional optical orthogonal codes with autocorrelation and cross-correlation both equal to $1$. By examining the structures of $n$-cyclic group divisible packings and semi-cyclic incomplete holey group divisible designs, we present new combinatorial constructions for two-dimensional $(m\times n,k,1)$-optical orthogonal codes. As a consequence, the exact number of codewords of an optimal two-dimensional $(m\times n,3,1)$-optical orthogonal code is determined for any positive integers $m$ and $n$.

math.CO↗

arXiv2026

Real-IAD Variety: Pushing Industrial Anomaly Detection Dataset to a Modern Era

Industrial Anomaly Detection (IAD) is a cornerstone for ensuring operational safety, maintaining product quality, and optimizing manufacturing efficiency. However, the advancement of IAD algorithms is severely hindered by the limitations of existing public benchmarks. Current datasets often suffer from restricted category diversity and insufficient scale, leading to performance saturation and poor model transferability in complex, real-world scenarios. To bridge this gap, we introduce Real-IAD Variety, the largest and most diverse IAD benchmark. It comprises 198,950 high-resolution images across 160 distinct object categories. The dataset ensures unprecedented diversity by covering 28 industries, 24 material types, 22 color variations, and 27 defect types. Our extensive experimental analysis highlights the substantial challenges posed by this benchmark: state-of-the-art multi-class unsupervised anomaly detection methods suffer significant performance degradation (ranging from 10% to 20%) when scaled from 30 to 160 categories. Conversely, we demonstrate that zero-shot and few-shot IAD models exhibit remarkable robustness to category scale-up, maintaining consistent performance and significantly enhancing generalization across diverse industrial contexts. This unprecedented scale positions Real-IAD Variety as an essential resource for training and evaluating next-generation foundation IAD models.

cs.CV↗

arXiv2025

Once Is Enough: Lightweight DiT-Based Video Virtual Try-On via One-Time Garment Appearance Injection

Video virtual try-on aims to replace the clothing of a person in a video with a target garment. Current dual-branch architectures have achieved significant success in diffusion models based on the U-Net; however, adapting them to diffusion models built upon the Diffusion Transformer remains challenging. Initially, introducing latent space features from the garment reference branch requires adding or modifying the backbone network, leading to a large number of trainable parameters. Subsequently, the latent space features of garments lack inherent temporal characteristics and thus require additional learning. To address these challenges, we propose a novel approach, OIE (Once is Enough), a virtual try-on strategy based on first-frame clothing replacement: specifically, we employ an image-based clothing transfer model to replace the clothing in the initial frame, and then, under the content control of the edited first frame, utilize pose and mask information to guide the temporal prior of the video generation model in synthesizing the remaining frames sequentially. Experiments show that our method achieves superior parameter efficiency and computational efficiency while still maintaining leading performance under these constraints.

cs.CV↗

arXiv2025

Pro-AD: Learning Comprehensive Prototypes with Prototype-based Constraint for Multi-class Unsupervised Anomaly Detection

Prototype-based reconstruction methods for unsupervised anomaly detection utilize a limited set of learnable prototypes which only aggregates insufficient normal information, resulting in undesirable reconstruction. However, increasing the number of prototypes may lead to anomalies being well reconstructed through the attention mechanism, which we refer to as the "Soft Identity Mapping" problem. In this paper, we propose Pro-AD to address these issues and fully utilize the prototypes to boost the performance of anomaly detection. Specifically, we first introduce an expanded set of learnable prototypes to provide sufficient capacity for semantic information. Then we employ a Dynamic Bidirectional Decoder which integrates the process of the normal information aggregation and the target feature reconstruction via prototypes, with the aim of allowing the prototypes to aggregate more comprehensive normal semantic information from different levels of the image features and the target feature reconstruction to not only utilize its contextual information but also dynamically leverage the learned comprehensive prototypes. Additionally, to prevent the anomalies from being well reconstructed using sufficient semantic information through the attention mechanism, Pro-AD introduces a Prototype-based Constraint that applied within the target feature reconstruction process of the decoder, which further improves the performance of our approach. Extensive experiments on multiple challenging benchmarks demonstrate that our Pro-AD achieve state-of-the-art performance, highlighting its superior robustness and practical effectiveness for Multi-class Unsupervised Anomaly Detection task.

cs.CV↗

arXiv2025

Real-IAD D3: A Real-World 2D/Pseudo-3D/3D Dataset for Industrial Anomaly Detection

The increasing complexity of industrial anomaly detection (IAD) has positioned multimodal detection methods as a focal area of machine vision research. However, dedicated multimodal datasets specifically tailored for IAD remain limited. Pioneering datasets like MVTec 3D have laid essential groundwork in multimodal IAD by incorporating RGB+3D data, but still face challenges in bridging the gap with real industrial environments due to limitations in scale and resolution. To address these challenges, we introduce Real-IAD D3, a high-precision multimodal dataset that uniquely incorporates an additional pseudo3D modality generated through photometric stereo, alongside high-resolution RGB images and micrometer-level 3D point clouds. Real-IAD D3 features finer defects, diverse anomalies, and greater scale across 20 categories, providing a challenging benchmark for multimodal IAD Additionally, we introduce an effective approach that integrates RGB, point cloud, and pseudo-3D depth information to leverage the complementary strengths of each modality, enhancing detection performance. Our experiments highlight the importance of these modalities in boosting detection robustness and overall IAD performance. The dataset and code are publicly accessible for research purposes at https://realiad4ad.github.io/Real-IAD D3

cs.CV↗

arXiv2025

DiffV2IR: Visible-to-Infrared Diffusion Model via Vision-Language Understanding

The task of translating visible-to-infrared images (V2IR) is inherently challenging due to three main obstacles: 1) achieving semantic-aware translation, 2) managing the diverse wavelength spectrum in infrared imagery, and 3) the scarcity of comprehensive infrared datasets. Current leading methods tend to treat V2IR as a conventional image-to-image synthesis challenge, often overlooking these specific issues. To address this, we introduce DiffV2IR, a novel framework for image translation comprising two key elements: a Progressive Learning Module (PLM) and a Vision-Language Understanding Module (VLUM). PLM features an adaptive diffusion model architecture that leverages multi-stage knowledge learning to infrared transition from full-range to target wavelength. To improve V2IR translation, VLUM incorporates unified Vision-Language Understanding. We also collected a large infrared dataset, IR-500K, which includes 500,000 infrared images compiled by various scenes and objects under various environmental conditions. Through the combination of PLM, VLUM, and the extensive IR-500K dataset, DiffV2IR markedly improves the performance of V2IR. Experiments validate DiffV2IR's excellence in producing high-quality translations, establishing its efficacy and broad applicability. The code, dataset, and DiffV2IR model will be available at https://github.com/LidongWang-26/DiffV2IR.

cs.CV↗

arXiv2025

PA-CLIP: Enhancing Zero-Shot Anomaly Detection through Pseudo-Anomaly Awareness

In industrial anomaly detection (IAD), accurately identifying defects amidst diverse anomalies and under varying imaging conditions remains a significant challenge. Traditional approaches often struggle with high false-positive rates, frequently misclassifying normal shadows and surface deformations as defects, an issue that becomes particularly pronounced in products with complex and intricate surface features. To address these challenges, we introduce PA-CLIP, a zero-shot anomaly detection method that reduces background noise and enhances defect detection through a pseudo-anomaly-based framework. The proposed method integrates a multiscale feature aggregation strategy for capturing detailed global and local information, two memory banks for distinguishing background information, including normal patterns and pseudo-anomalies, from true anomaly features, and a decision-making module designed to minimize false positives caused by environmental variations while maintaining high defect sensitivity. Demonstrated on the MVTec AD and VisA datasets, PA-CLIP outperforms existing zero-shot methods, providing a robust solution for industrial defect detection.

cs.CV↗

arXiv2022

Devaney Chaos on a Set-valued Map and Its Inverse Limit

We study relationships between a set-valued map and its inverse limits about the notion of periodic point set, transitivity, sensitivity and Devaney chaos. Density of periodic point set of a set-valued map and its inverse limits implies each other. Sensitivity of a set-valued map and its inverse limits does not imply each other. Transitivity and Devaney chaos of generalized inverse limits implies the corresponding property of a set-valued map.

math.DS↗

arXiv2022

Generalized perfect difference families and their application to variable-weight geometric orthogonal codes

Motivated by the application in geometric orthogonal codes (GOCs), Wang et al. introduced the concept of generalized perfect difference families (PDFs), and established the equivalence between GOCs and a certain type of generalized PDFs recently. Based on the relationship, we discuss the existence problem of generalized $(n\times m,K,1)$-PDFs in this paper. By using some auxiliary designs such as semi-perfect group divisible designs and several recursive constructions, we prove that a generalized $(n\times m, \{3,4\}, 1)$-PDF exists if and only if $nm\equiv1\pmod{6}$. The existence of a generalized $(n\times m, \{3,4,5\}, 1)$-PDF is also completely solved possibly except for a few values. As a consequence, some variable-weight perfect $(n\times m,K,1)$-GOCs are obtained.\vspace{0.2cm} {\bf Keywords}: generalized perfect difference family, generalized perfect difference packing, geometric orthogonal code, semi-perfect group divisible design

math.CO↗

arXiv2021

Ordinal sum of two binary operations being a t-norm on bounded lattice

The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm. Some necessary and sufficient conditions are presented in this paper for ensuring that an ordinal sum on a bounded lattice of two binary operations is, in fact, a t-norm. In particular, the results presented here provide an answer to an open problem put forward by Ertuğrul and Yeşilyurt [Ordinal sums of triangular norms on bounded lattices, Inf. Sci., 517 (2020) 198-216].

math.GM↗

arXiv2020

Maximum $w$-cyclic holely group divisible packings with block size three and applications to optical orthogonal codes

In this paper we investigate combinatorial constructions for $w$-cyclic holely group divisible packings with block size three (briefly by $3$-HGDPs). For any positive integers $u,v,w$ with $u\equiv0,1~(\bmod~3)$, the exact number of base blocks of a maximum $w$-cyclic $3$-HGDP of type $(u,w^v)$ is determined. This result is used to determine the exact number of codewords in a maximum three-dimensional $(u\times v\times w,3,1)$ optical orthogonal code with at most one optical pulse per spatial plane and per wavelength plane.

math.CO↗

arXiv2019

Optimal optical orthogonal signature pattern codes with weight three and cross-correlation constraint one

Optical orthogonal signature pattern codes (OOSPCs) have attracted wide attention as signature patterns of spatial optical code division multiple access networks. In this paper, an improved upper bound on the size of an $(m,n,3,λ_a,1)$-OOSPC with $λ_a=2,3$ is established. The exact number of codewords of an optimal $(m,n,3,λ_a,1)$-OOSPC is determined for any positive integers $m,n\equiv2\ ({\rm mod }\ 4)$ and $λ_a\in\{2,3\}$.

math.CO↗

arXiv2018

Optimal $2$-D $(n\times m,3,2,1)$-optical orthogonal codes and related equi-difference conflict avoiding codes

This paper focuses on constructions for optimal $2$-D $(n\times m,3,2,1)$-optical orthogonal codes with $m\equiv 0\ ({\rm mod}\ 4)$. An upper bound on the size of such codes is established. It relies heavily on the size of optimal equi-difference $1$-D $(m,3,2,1)$-optical orthogonal codes, which is closely related to optimal equi-difference conflict avoiding codes with weight $3$. The exact number of codewords of an optimal $2$-D $(n\times m,3,2,1)$-optical orthogonal code is determined for $n=1,2$, $m\equiv 0 \pmod{4}$, and $n\equiv 0 \pmod{3}$, $m\equiv 8 \pmod{16}$ or $m\equiv 32 \pmod{64}$ or $m\equiv 4,20 \pmod{48}$.

math.CO↗

arXiv2016

Determination of sizes of optimal three-dimensional optical orthogonal codes of weight three with the AM-OPP restriction

In this paper, we further investigate the constructions on three-dimensional $(u\times v\times w,k,1)$ optical orthogonal codes with the at most one optical pulse per wavelength/time plane restriction (briefly AM-OPP $3$-D $(u\times v\times w,k,1)$-OOCs) by way of the corresponding designs. Several new auxiliary designs such as incomplete holey group divisible designs and incomplete group divisible packings are introduced and therefore new constructions are presented. As a consequence, the exact number of codewords of an optimal AM-OPP $3$-D $(u\times v\times w,3,1)$-OOC is finally determined for any positive integers $v,w$ and $u\geq3$.

cs.IT↗