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mathematical methods in pattern and image analysis

The proceedings contain 34 papers. The topics discussed include: nonlinear vector-valued diffusions with application to texture segmentation;road network extraction from digital imagery;a preliminary evaluation of 3D mesh animation coding techniques;video watermarking for mobile phone applications;automated 3D vascular segmentation in CT hepatic venography;face detection by optical decomposition;recall of patterns using binary and gray-scale auto-associative morphological memories;motion blur detecting by support vector machine;spatial random trees with applications to image classification;a solution to arc correction in cylindrical PET scanner;and image clustering algorithm using polynormal distributed data.

关键词： image processing

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An efficient no-reference image quality analysis based on statistical perceptual features

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IET image PROCESSING 2025年第1期19卷

作者： Al Sameera, B. N. Gaidhane, Vilas H. Birla Inst Technol & Sci Pilani Dept Elect & Elect Engn Dubai Campus Dubai U Arab Emirates

It is well known that image quality needs to be measured with human perception in many computer vision applications. However, these approaches are expensive and require more time for image quality analysis. Therefore, this paper proposes a robust and computationally efficient objective-mathematical model based on statistical perceptual features. The structural and textural features are computed using the modified regularized heaviside local binary pattern (RH-LBP) approach and the concept of entropy. The higher-order probability coefficients of images are considered to extract features that are highly correlated to the human visual system features. Further, the additivity property of Renyi entropy is used to show the randomness of the information combining two terms: One extracts the images spatial intensity changes, and therefore their texture qualities, and the other attain structural details. The features in the proposed approach are jointly optimized to achieve better robustness, monotonicity and match human assessments on image quality, while minimizing the computational complexity and run time. Experiments are conducted with three synthetically distorted datasets, KonIQ-10K, BIQ2021, and LIVE (wild), and two intentionally distorted datasets, TID2013 and CSIQ and are used to evaluate performance index. The proposed method offers competitive performance compared with state-of-the-art methods.

关键词： image processing image recognition image representation pattern recognition

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Fully-Connected Transformer for Multi-Source image Fusion

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 2025年第3期47卷 2071-2088页

作者： Wu, Xiao Cao, Zi-Han Huang, Ting-Zhu Deng, Liang-Jian Chanussot, Jocelyn Vivone, Gemine Univ Elect Sci & Technol China Sch Math Sci Chengdu 611731 Peoples R China Univ Grenoble Alpes Inria CNRS Grenoble INPLJK F-38000 Grenoble France Chinese Acad Sci Aerosp Informat Res Inst Beijing 100045 Peoples R China CNR IMAA Inst Methodol Environm Anal I-85050 Tito Italy Natl Biodivers Future Ctr NBFC I-90133 Palermo Italy

Multi-source image fusion combines the information coming from multiple images into one data, thus improving imaging quality. This topic has aroused great interest in the community. How to integrate information from different sources is still a big challenge, although the existing self-attention based transformer methods can capture spatial and channel similarities. In this paper, we first discuss the mathematical concepts behind the proposed generalized self-attention mechanism, where the existing self-attentions are considered basic forms. The proposed mechanism employs multilinear algebra to drive the development of a novel fully-connected self-attention (FCSA) method to fully exploit local and non-local domain-specific correlations among multi-source images. Moreover, we propose a multi-source image representation embedding it into the FCSA framework as a non-local prior within an optimization problem. Some different fusion problems are unfolded into the proposed fully-connected transformer fusion network (FC-Former). More specifically, the concept of generalized self-attention can promote the potential development of self-attention. Hence, the FC-Former can be viewed as a network model unifying different fusion tasks. Compared with state-of-the-art methods, the proposed FC-Former method exhibits robust and superior performance, showing its capability of faithfully preserving information.

关键词： Algebra Imaging Pansharpening image representation Transformers mathematical models Computational efficiency Sensors image fusion Optimization Transformer multilinear algebra model-driven neural network multi-source image fusion multispectral and hyperspectral image fusion remote sensing pansharpening visible and infrared image fusion

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image Classification of Multimedia Platforms With Texture Algorithms and Neural Networks

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IEEE ACCESS 2025年 13卷 46478-46494页

作者： Sauzameda-Gonzalez, Mauricio Alvarez-Borrego, Josue Guerra-Rosas, Esperanza Ctr Invest Cient & Educ Super Ensenada CICESE Ensenada 22860 Baja California Mexico Univ Autonoma Baja California Fac Ingn Arquitectura & Diseno Ensenada 22860 Baja California Mexico

In this paper, a methodology for real-time image classification on multimedia platforms has been developed. For this purpose, six feedforward neural network models were trained with images from two databases, which were preprocessed by three texture extraction methods: local binary pattern-uniform (LBP-U), gray level co-occurrence matrix (GLCM), and wavelet image scattering (WIS). The databases used consist of 157,448 images of the sections with the thumbnails of the platform content (mosaics) representing 14 classes and 38,214 images with the descriptions of the available content (descriptors) representing 11 classes, where all images have a resolution of 1280 x 720 pixels. The six models (three for mosaics and three for descriptors) were validated with images from the databases, which were not part of the training process, to obtain their performance metrics. The training and validation process was performed 30 times, and the average results were compared. The most outstanding models for each database were the neural networks trained with the wavelet image scattering method, with metrics of 99.97 +/- 0.01 % accuracy, 99.99 +/- 0.01 % specificity, 99.84 +/- 0.06 % sensitivity, 99.59 +/- 0.13 % precision and 99.71 +/- 0. 08 % of F1 score with a response time of 0.7349 seconds for the model trained with mosaics and with metrics of 99.90 +/- 0.03 % of accuracy, 99.94 +/- 0.02 % of specificity, 99.58 +/- 0.15 % of sensitivity, 98.63 +/- 0.55 % of precision and 99.09 +/- 0.30 % of F1 score with a response time of 0.6227 seconds for the model trained with descriptor images. The results are very significant due to the high efficiency obtained and confirm the effectiveness of the models with the WIS method for the classification of multimedia platform images with the characteristics of the databases used. It is suggested that the remaining methods be adjusted to improve their performance.

关键词： Gray-scale mathematical models Symmetric matrices Scattering Real-time systems image classification Statistical analysis Object recognition Multimedia databases Histograms Classification method neural networks texture analysis methods local binary pattern grayscale co-occurrence matrix performance metrics

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MMBIA IEEE Computer Society Workshop on mathematical methods in Biomedical image analysis In conjunction with Computer Vision and pattern Recognition (CVPR) 8-9 December 2001 Kauai, Hawaii, USA http://***/mmbia2001

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Medical image analysis 2001年第2期5卷 171-171页

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SinDiffusion: Learning a Diffusion Model From a Single Natural image

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 2025年第5期47卷 3412-3423页

作者： Wang, Weilun Bao, Jianmin Zhou, Wengang Chen, Dongdong Chen, Dong Yuan, Lu Li, Houqiang Univ Sci & Technol China MoE Key Lab Brain inspired Intelligent Percept & C Hefei 230027 Peoples R China Microsoft Res Asia Beijing 100080 Peoples R China Microsoft Cloud AI Redmond WA 98052 USA

We present SinDiffusion, leveraging denoising diffusion models to capture internal distribution of patches from a single natural image. The default approach of previous GAN-based methods on this problem is to train multiple models at progressive growing scales, which leads to the accumulation of errors and causes characteristic artifacts in generated results. In this paper, we uncover that multiple models at progressive growing scales are not essential for learning from a single image and propose SinDiffusion, a single diffusion-based model trained on a single scale, which is better-suited for this task. Furthermore, we identify that a patch-level receptive field is crucial and effective for diffusion models to capture the image's patch statistics, therefore we redesign an patch-wise denoising network for SinDiffusion. Coupling these two designs enables SinDiffusion to generate more photorealistic and diverse images from a single image compared with GAN-based approaches. SinDiffusion can also be applied to various applications, i.e., text-guided image generation, and image outpainting beyond the capability of SinGAN. Extensive experiments on a wide range of images demonstrate the superiority of SinDiffusion for modeling the patch distribution.

关键词： Diffusion models image synthesis Training Noise reduction Periodic structures Translation mathematical models Art Noise Generative adversarial networks Denoising diffusion probabilistic models single image generation image manipulation

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Small-Sample GIS Partial Discharge-Type Identification Method Based on Fusion of 1-D AT-DRSN and IDRN Models

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IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 2025年第2期32卷 877-886页

作者： Yin, Baiqiang Zeng, Yahong Wang, Ruoyu Zuo, Lei Li, Bing Cheng, Zhen Hefei Univ Technol Sch Elect Engn & Automat Hefei 230009 Peoples R China

Different types of partial discharges (PDs) in gas-insulated switchgear (GIS) cause different degrees of GIS insulation damage, and correct PD identification is critical to GIS insulation status. This article proposes a multimodel fusion PD pattern recognition method based on 1-D adaptive transfer deep residual shrinkage network (AT-DRSN) and improved deep residual network (IDRN), which fully utilizes PD time-domain waveform images generated from field inspection. First, the finite-difference time-domain (FDTD) method and mathematical models are used to simulate GIS PDs, and the time-domain waveform image datasets of four typical PD defects are established. Second, the network model is built based on time-domain feature sequences and time-order feature parameters, respectively, and effectively combined with the transfer learning method, and finally, the AT-DRSN and IDRN models are weighted and fused for PD pattern recognition. The results show that the model proposed in this article can effectively achieve high-precision diagnosis of small-sample GIS PDs, with a recognition accuracy of 98.3%, and the accuracy under strong noise is still greater than 95%, which has higher accuracy and anti-interference performance compared with other methods and is of reference value for small-sample PD recognition in the field.

关键词： Feature extraction Partial discharges mathematical models pattern recognition Metals Time-domain analysis Accuracy Deep learning gas-insulated switchgear (GIS) partial discharge (PD) pattern recognition transfer learning

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Cross-Optical Property image Translation for Face Anti-Spoofing: From Visible to Polarization

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2025年 20卷 1192-1205页

作者： Tian, Yu Zhang, Kunbo Huang, Yalin Wang, Leyuan Liu, Yue Sun, Zhenan Beijing Inst Technol Sch Opt & Photon Beijing 100081 Peoples R China Chinese Acad Sci Inst Automat Key Lab Multimodal Artificial Intelligence Syst New Lab Pattern Recognit NLPR Beijing 100190 Peoples R China Hunan Univ Sch Elect & Informat Engn Changsha 410082 Peoples R China Beijing Univ Posts & Telecommun Sch Artificial Intelligence Beijing 100876 Peoples R China

Despite the development of spectral sensors and spectral data-driven learning methods which have led to significant advances in face anti-spoofing (FAS), the singular dimensionality of spectral information often results in poor robustness and weak generalization. Polarization, another fundamental property of light, can reveal intrinsic differences between genuine and fake faces with advantaged performance in precision, robustness, and generalizability. In this paper, we propose a facial image translation method from visible light (VIS) to polarization (VPT), capable of generating valuable polarimetric optical characteristics for facial presentation attack detection using VIS spectrum information input only. Specifically, the VPT method adopts a multi-stream network structure, comprising a main network and two branch networks, to translate VIS images into degree of polarization (DoP) images and Stokes polarization parameters ${S}_methods$ and ${S}_methods$ . To further improve image translation quality, we introduce a frequency-domain consistency loss as a complement to the existing spatial losses to narrow the gap in the frequency domain. The physical mapping relations for the DoP and Stokes parameters are employed, and the Stokes loss is designed to ensure that the generated polarization modalities conform to objective physical laws. Extensive experiments on the CASIA-Polar and CASIA-SURF datasets demonstrate the superiority of VPT over other baseline methods in terms of polarization image quality and its remarkable performance in the FAS task. This work leverages the inherent physical advantages of polarization information in material discrimination tasks while addressing hardware limitations in polarization image collection, proposing a novel solution for face recognition system security control.

关键词： Face recognition Translation Feature extraction Vibrations Faces Optical imaging Frequency-domain analysis mathematical models Optical reflection Lighting Cross-property translation polarization face anti-spoofing generative model

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Enhancing Object Detection With Fourier Series

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IEEE TRANSACTIONS ON pattern analysis AND MACHINE INTELLIGENCE 2025年第4期47卷 2581-2596页

作者： Liu, Jin Lu, Zhongyuan Cen, Yaorong Hu, Hui Shao, Zhenfeng Hong, Yong Jiang, Ming Xu, Miaozhong Wuhan Univ State Key Lab Informat Engn Surveying Mapping & Re Wuhan 430079 Peoples R China Wuhan Xiongchu Gaojing Technol Co Ltd Wuhan 430000 Peoples R China Wuhan Univ Elect Informat Sch Wuhan 430079 Peoples R China Aviat Ind Corp China Res Inst Leihua Elect Technol Beijing 100028 Peoples R China

Traditional object detection models often lose the detailed outline information of the object. To address this problem, we propose the Fourier Series Object Detection (FSD). It encodes the object's outline closed curve into two one-dimensional periodic Fourier series. The Fourier Series Model (FSM) is constructed to regress the Fourier series for each object in the image. Thus, during inference, the detailed outline information of each object can be retrieved. We introduce Rolling Optimization Matching for Fourier loss to ensure that the model's learning process is not affected by the sequence of the starting points of the labeled contour points, speeding up the training process. The FSM demonstrates improved feature extraction and descriptive capabilities for non-rectangular or elongated object regions. The model achieves AP50 = 73.3% on the DOTA 1.5 dataset, which surpasses the state-of-the-art (SOTA) method by 6.44% at 66.86%. On the UCAS dataset, the model achieves AP50 = 97.25%, also surpassing the performance indicators of the SOTA methods. Furthermore, we introduce the object's Fourier power spectrum to describe outline features and the Fourier vector to indicate its direction. This enhances the scene semantic representation of the object detection model and paves a new pathway for the evolution of object detection methodologies.

关键词： Fourier series Object detection Shape mathematical models Transformers Optimization Vectors Predictive models image segmentation Gaussian distribution closed curve of arbitrary shape and directional vector

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Range-Null Space Decomposition With Frequency-Oriented Mamba for Spectral Superresolution

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2025年 18卷 10292-10306页

作者： Weng, Meimei Liu, Jianjun Yang, Jinlong Wu, Zebin Xiao, Liang Jiangnan Univ Sch Artificial Intelligence & Comp Sci Jiangsu Prov Engn Lab Pattern Recognit & Computat Wuxi 214122 Peoples R China Nanjing Univ Sci & Technol Sch Comp Sci Nanjing 210094 Peoples R China

Spectral superresolution (SSR) is a technique aimed at reconstructing hyperspectral images (HSIs) from images with low spectral resolution. Previous methods combining mathematical models with deep learning have shown promising performance for HSI reconstruction. However, these methods still have limitations when dealing with complex scenes, especially in terms of data consistency and realness. To address these issues, we propose a model-driven SSR network that integrates range-null space decomposition with deep learning. Specifically, we solve for the range space (R-Space) part and null space (N-Space) part to reconstruct the desired HSI with consistency and realness. The R-Space is primarily iteratively derived from the input multispectral image to ensure reliable data consistency, while the N-Space reflects the true distribution of the target HSI, and its proper representation helps improve visual quality. To enhance N-Space exploration, we construct a frequency-oriented N-Space learning module that leverages Mamba and self-attention to separately extract spatial and spectral information in the frequency domain. In addition, we introduce a structure tensor term and a multikernel maximum mean discrepancy term in the loss function to constrain R-Space and N-space, respectively. Experimental results show that the proposed method achieves excellent performance.

关键词： image reconstruction Transformers Superresolution Hyperspectral imaging Feature extraction Frequency-domain analysis Data mining Convolution Visualization Optimization Hyperspectral image (HSI) Mamba range-null space decomposition (RNSD) spectral superresolution (SSR)

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