Fuzzy relation models play an important role in describing the complex relationships between the antecedent and consequent parts, but suffer from insufficient interpretability and accuracy, and rely on centralized modeling. This paper proposes a granular fuzzy relation model based on horizontal federated learning to enable distributed modeling of fuzzy relation models with privacy protection, while improving both interpretability and accuracy. In the first phase, fuzzy sets are designed with the aid of federated fuzzy clustering. In the second phase, the max-min fuzzy logic operation is employed to develop fuzzy relation models in federated learning. Based on the initial fuzzy relation issued by the global server, each client establishes the local fuzzy relation model using two federated learning strategies, namely gradient-based and average-based approaches, respectively. In the third phase, granular fuzzy relation models are generalized by introducing a granular parameter in specifying the level of information granularity, which is optimized by applying the Differential Evolution algorithm. The overall performance is measured by the product of two conflicting criteria, namely, coverage and specificity. The originality of proposed model lies in the realization of horizontal federated learning for granular fuzzy relation models. In this study, the granular version of fuzzy relation models incorporates richer semantic information, thereby enhancing both the interpretability and accuracy of the model. Meanwhile, each client can complete the training by simply interacting gradients or parameters instead of the original data and location, thus realizing privacy-protecting distributed modeling. Experimental results indicate better performance of the proposed method than that of centralized learning.

G-images, defined as graph-structured data with complex topologies, have played a significant role in various fields. Current research mainly focuses on denoising and segmenting observed G-images. However, due to sampling or information degradation, they often contain blurred texture information. Therefore, reconstructing and segmenting them accurately is a critical challenge. To address this issue, this work elaborates a feature-preserving FuzzyC-Means (FCM) algorithm by the aid of a wavelet frame transform, which is aimed at segmenting observed G-images with noise and blur. Given the superior performance of tight wavelet frames in feature extraction, this work leverages the proposed algorithm in a wavelet space, thus incorporating both the original and rectified features of G-images to maintain high robustness. To improve segmentation accuracy, it also uses the local binary pattern code to identify and enhance the blurred features. Additionally, to preserve the similarity between any vertex and its adjacent nodes, it introduces a Kullback-Leibler divergence term as a part of FCM’s objective function. Moreover, convergence analysis establishes that the entire sequence of iterates generated by the algorithm is globally convergent to a critical point. Finally, numerical experiments are conducted by comparing the proposed algorithm with other peers on both synthetic and real-world G-images with noise and blur of different levels. Experimental evidence shows that the proposed algorithm exhibits superior effectiveness and robustness compared to existing peers.

Image segmentation in the presence of mixed or unknown noise is a persistent challenge. Traditional Fuzzy$C$-Means (FCM) algorithms often struggle with complex noise, necessitating either prior knowledge of the noise characteristics or separate noise removal steps. To address this limitation, this work elaborates a novel residual-driven FCM framework, adaptively handling a wide variety of noise types within a unified model. The residual (the difference between the noisy and estimated clean images) is decomposed into two components, i.e., Gaussian-like noise and impulse noise, thus generating a weighted$\ell _{2}/\ell _{1}$-norm regularization term for the accurate estimation of mixed or unknown noise. An exponential function of the residual magnitude governs this adaptive weighting, promoting$\ell _{2}$-norm-based smoothing for Gaussian-like noise and$\ell _{1}$-norm-based robustness to impulse noise. The regularization term is integrated into FCM's objective function. To further enhance the robustness of the newly generated objective function, spatial constraints are used to refine the clustering process. Experimental results on synthetic, medical, and real-world images demonstrate the superior effectiveness and efficiency of the proposed algorithm compared to existing methods, significantly enhancing FCM's applicability and providing a more accurate solution in real-world or noisy scenarios.

A Fuzzy$C$-Means (FCM) algorithm has been widely applied to image segmentation due to its simplicity and effectiveness. However, conventional FCM and its variants often struggle to maintain robustness and accuracy when dealing with complex noise environments, particularly Poisson and mixed Poisson-Gaussian noise. To address this shortcoming, this work proposes a novel Poisson-specific Residual-driven FCM (PRFCM) algorithm for robust image segmentation, which is the first work to develop a dedicated residual regularization mechanism that effectively realizes the robust estimation of Poisson noise (regarded as residual between noisy and noise-free images). It incorporates a weighted$\ell _{2}$-norm regularization term with respect to Poisson noise distribution into FCM. An iterative residual approximation method is introduced to solve the minimization problem about residual, thus simplifying PRFCM's optimization procedure and enhancing its computational efficiency. PRFCM is also extended to cope with mixed Poisson-Gaussian noise scenarios without compromising performance. Experimental results on both simulated and real-scene images demonstrate that the proposed approach outperforms other FCM-related methods in terms of segmentation accuracy, noise resilience, and structural preservation, especially in challenging noise conditions.

Recent advancements in image denoising algorithms have significantly improved visual performance. However, they also introduce new challenges for image quality assessment (IQA) indicators to provide evaluations that align with human visual perception. To address the limitations of current single-indicator methods, we propose a comprehensive IQA framework that integrates multiple indicators to achieve a holistic assessment of image quality. We first develop a large-scale denoised image dataset to show the diversity of distortions. Then, we employ structural equation modeling to establish correlations among three fundamental aspects of image quality, i.e., structural similarity, information loss, and perceptual gain. Through a series of regressions and iterative refinements, we eliminate indicators with low accuracy and high redundancy, thus resulting in a robust and optimal indicator system. Finally, we systematically validate the reliability and effectiveness of the proposed system through statistical analysis and evaluate its performance across three key tasks, i.e., image quality prediction, IQA indicator comparison, and denoising algorithm optimization. Experimental results demonstrate that the proposed system not only offers highly reliable and valid assessments but also provides valuable insights for the analysis and application of IQA indicators.

Modeling discriminative spectral-spatial features is a key to improving hyperspectral image classification performance. However, existing methods cannot fully characterize the spatial specificity of hyperspectral images, thus making them unable to fully explore the useful information within the image and further improve the discriminative power of features. To address this issue, this work proposes a dual heterogeneous network (DHNet) for hyperspectral image classification. Specifically, the network consists of spatial-specific and spectral-specific branches and captures spectral-spatial features with complementarity by combining convolution and spectral-spatial involution. To better characterize spatial specificity, the spectral-spatial involution modifies the weight parameters based on the center spectral information and neighborhood spatial information of various spatial locations. Besides, two feature calibration modules are proposed. Spatial-specific and spectral-specific weights are generated from the respective branches to calibrate the features captured by the other branches to improve the information interaction between the two branches. The center spectral mapping integrates the spectral features of the target pixel into the feature to suppress the influence of the neighboring disturbing pixels. Experimental results on four datasets indicate that DHNet achieves an accuracy improvement of 1.23%, 2.03%, 2.52%, and 1.77% over the state-of-the-art peers, respectively.

Graph-based methods have demonstrated strong performance in multi-view clustering (MVC) due to their capability to capture complex data structures. Among these, discrete spectral embedding learning has emerged as an effective strategy for directly producing clustering assignments, thereby avoiding potential suboptimality introduced by post-processing. However, most existing discrete MVC methods overlook the problem of skewed cluster assignments, which can significantly affect the quality and interpretability of clustering results in practical applications. To address this issue, we propose a novel framework for Balanced and Discrete Multi-view Clustering via Adaptive Graph Learning (BDMC-AGL). The proposed model jointly integrates adaptive graph construction and size-constrained spectral embedding learning into a unified optimization framework, enhancing the robustness of clustering while explicitly encouraging balanced partitioning. The introduction of size constraints into the discrete spectral embedding, however, poses a challenging optimization problem. To effectively solve it, we develop an efficient algorithm that guarantees convergence to a locally optimal solution. Extensive experiments conducted on eight benchmark datasets demonstrate that BDMC-AGL consistently outperforms state-of-the-art methods in terms of clustering accuracy and balance. Moreover, ablation studies validate the significant contribution of the size constraint mechanism in improving multi-view clustering performance. The source code is publicly available at: https://github.com/haha1206/BDMC-AGL.

Machine vision plays a crucial role in Earth observation. As a fundamental and challenging task in vision systems, image registration faces new challenges due to increasing collaborative and customization applications. The prevalence of more false matches and low-precision matches is particularly evident in complex and changeable scenarios. In this article, we propose a robust image registration method via topology sort and vision consistence. Initial candidate matches are established via the nearest neighbor ratio of image intensity descriptors. A topological sort across the proximity structure around the point pairs is defined to assess the reliability of candidate matched pairs, effectively eliminating more false matches while retaining highly reliable point pairs. To preserve more point pairs, we develop a spatial visual inspection mechanism to further determine the potential matches from the remaining pairs that do not satisfy the previous topological constraint. During vision inspection, the spatial transformation model is simultaneously estimated. Experimental results on public datasets show that the proposed method outperforms state-of-the-art approaches in both matching accuracy and visual effect.

Single hyperspectral image super-resolution aims to enhance the spatial resolution of a hyperspectral image without relying on any auxiliary information. Despite the abundant spectral information, the inherent high-dimensionality in hyperspectral images still remains a challenge for memory efficiency. Recently, recursion-based methods have been proposed to reduce memory requirements. However, these methods utilize the reconstruction features as feedback embedding to explore context information, leading to sub-optimal performance as they ignore the complementarity of different hierarchical levels of information in the context. Additionally, existing methods equivalently compensate the previous feedback information to the current band, resulting in an indistinct and untargeted introduction of the context. In this paper, we propose a hierarchical context measurement network to construct corresponding measurement strategies for different hierarchical information, capturing comprehensive and powerful complementary knowledge from the context. Specifically, a feature-wise similarity measurement module is designed to calculate global cross-layer relationships between the middle features of the current band and those of the context, so as to explore the embedded middle features discriminatively through generated global dependencies. Furthermore, considering the pixel-wise correspondence between the reconstruction features and the super-resolved results, we propose a pixel-wise similarity measurement module for the complementary reconstruction features embedding, exploring detailed complementary information within the embedded reconstruction features by dynamically generating a spatially adaptive filter for each pixel. Experimental results reported on three benchmark hyperspectral datasets reveal that the proposed method outperforms other state-of-the-art peers in both visual and metric evaluations.

Hyperspectral image classification methods based on graph convolution network have received extensive attention. However, the traditional distance metric is difficult to fully represent the spectral variability and uncertainty in hyperspectral images. In order to alleviate this problem, a multi-scale fuzzy graph convolutional network is constructed for hyperspectral image classification. In detail, the SLIC algorithm is used to perform superpixel segmentation of hyperspectral images. Each superpixel is regarded as a graph node, and a fuzzy measurement mechanism is introduced to measure the similarity between two nodes to describe the uncertainty between pixels in the hyperspectral image, so as to construct a fuzzy graph convolution. Subsequently, the fuzzy graph convolution is extended to multi-scale to capture the rich contextual information within the hyperspectral image. In the training process, the pixel-level features are integrated into the superpixel-level graph update process to establish the connection between the pixel level and the superpixel level. Finally, experimental results on two publicly available hyperspectral image datasets show that the proposed network outperforms other representative peers.

Since a noisy image has inferior characteristics, the direct use of Fuzzy C -Means (FCM) to segment it often produces poor image segmentation results. Intuitively, using its ideal value (noise-free image) benefits FCM's robustness enhancement. Therefore, the realization of accurate noise estimation in FCM is a new and important task. To date, only two noise-estimation-based FCM algorithms have been proposed for image segmentation, that is: 1) deviation-sparse FCM (DSFCM) and 2) our earlier proposed residual-driven FCM (RFCM). In this article, we make a thorough comparative study of DSFCM and RFCM. We demonstrate that an RFCM framework can realize more accurate noise estimation than DSFCM when different types of noise are involved. It is mainly thanks to its utilization of noise distribution characteristics instead of noise sparsity used in DSFCM. We show that DSFCM is a particular case of RFCM, thus signifying that they are the same when only impulse noise is involved. With a spatial information constraint, we demonstrate RFCM's superior effectiveness and efficiency over DSFCM in terms of supporting experiments with different levels of single, mixed, and unknown noise.

Anatomically diffused tissues (ADTs) refer to soft tissues containing many anatomical regions that are spatially dispersed and structurally irregular. In magnetic resonance images, ADTs exhibit blurred morphology and heterogeneous texture, making the accurate extraction of their 3D anatomy challenging. Center-free fuzzy C-means (FCM) can effectively partition nonlinear or nonspherical clusters, providing a promising scheme for ADT segmentation. It solves the uncertainty arising from unreliable center estimation by introducing a similarity criterion. However, the similarity criterion is sensitive to the number of target objects and their adjacent members in the images. Moreover, memberships of the existing algorithms are susceptible to losing real ADT details. To handle these issues, we propose an edge-preserving constrained center-free FCM algorithm for segmenting 3D ADTs in magnetic resonance images. To overcome the sensitivity of the similarity criterion, a novel object-to-cluster similarity measure is first proposed to utilize refined member-toobject adjacency. Specifically, the similarity measure focuses on members in the feature space, which share approximately homogeneous characteristics with each target object. Gradient-domain edge-preserving filtering is then combined with the improved similarity criterion to construct the novel objective function of center-free FCM. With the assistance of the designed imagedriven edge-preserving regularization, the gradient information of clusters is constrained, eventually approaching that of ADTs in the guidance image. Experiments are conducted on two public brain datasets and one local intrahepatic vein dataset. The results demonstrate that the proposed algorithm is more effective for ADT segmentation than the state-of-the-art peers, exhibiting superior generalization capability.

Feature selection in a traditional binary classification algorithm is always used in the stage of dataset preprocessing, which makes the obtained features not necessarily the best ones for the classification algorithm, thus affecting the classification performance. For a traditional rule-based binary classification algorithm, classification rules are usually deterministic, which results in the fuzzy information contained in the rules being ignored. To do so, this article employs iterative feature selection in fuzzy rule-based binary classification. The proposed algorithm combines feature selection based on fuzzy correlation family with rule mining based on biclustering. It first conducts biclustering on the dataset after feature selection. Then it conducts feature selection again for the biclusters according to the feedback of biclusters evaluation. In this way, an iterative feature selection framework is built. During the iteration process, it stops until the obtained bicluster meets the requirements. In addition, the rule membership function is introduced to extract vectorized fuzzy rules from the bicluster and construct weak classifiers. The weak classifiers with good classification performance are selected by adaptive boosting and the strong classifier is constructed by “weighted average.” Finally, we perform the proposed algorithm on different datasets and compare it with other peers. Experimental results show that it achieves good classification performance and outperforms its peers.

Myocardial scar regions appear in cardiac magnetic resonance images of patients with myocardial infarction. Implantable cardioverter defibrillators (ICDs) can be used to effectively prevent arrhythmias and even death caused by myocardial infarction. Whether or not to implant an ICD and deciding the precise location of implantation are huge clinical challenges. This work proposes a noise-estimation-dominated fuzzy segmentation strategy for ICD implantation. It achieves accurate noise estimation in cardiac magnetic resonance image segmentation by weighting mixed noise distributions and adding a spatial information constraint. To be specific, a weightedl2-norm regularization term is proposed to form a universal noiseestimation-based FuzzyC-Means algorithm that can perform accurate segmentation of images subject to mixed or unknown noise. Through region growth and flood fill in order, the region and volume of myocardial scars are precisely obtained. Thus, the ICD implantation is accurately estimated. Finally, a criterion for ICD implantation estimation is reported. Experimental results on different myocardial infarction datasets show that the proposed strategy is more effective and efficient than its peers.

The distribution of ground objects in hyperspectral images predominantly reveals spatial indications of both order and disorder, encapsulating a wealth of texture information. This texture information encompasses not only local structural details but also global statistical priors of an image. Nevertheless, convolutional-neural-network-based methods for hyperspectral image classification (HIC) primarily use skip connections to incorporate shallow features abundant in texture information into deeper layers. They face challenges in effectively capturing the statistical properties of texture information, and the traditional method of modeling statistical attributes struggles to seamlessly integrate into parameter learning of convolutional neural networks (CNNs). To do so, this work proposes a statistical texture awareness network (STANet) for HIC. It achieves the exploration of learnable texture features. Through multilevel quantization and quantization encoding, a statistical texture learning module (STLM) is constructed to represent texture information from low-level features in a statistical manner. As a result, it augments the discriminatory power of such features. In addition, a complete feature fusion module (CFFM) is designed to intelligently combine multiscale contextual semantic and statistical texture features, thereby bolstering the discrimination of spectral-spatial ones. Experimental results reported for three public datasets demonstrate the superior performance of the proposed network over other peers.

Visual grounding in remote sensing (RSVG) images aims to detect specific objects associated with referring expressions in remote sensing images. Existing methods typically combine outputs of pretrained visual and linguistic backbones to locate referred objects. However, due to the lack of interaction with the language modality during the visual feature extraction process, the visual backbone may suffer from attention drift, limiting RSVG’s performance. To avoid this, we propose a novel RSVG framework, namely, language-guided progressive visual attention (LPVA), which achieves precise attention on referred objects by adjusting visual features with a progressive attention (PA) module and a multilevel feature enhancement (MFE) decoder. Specifically, the former can dynamically generate multiscale weights and biases, enabling the visual backbone to gradually focus on expression-related features at spatial and channel levels. The latter is designed to aggregate visual contextual information of the referred objects to enhance features’ distinctiveness while simultaneously suppressing information of irrelevant regions. To thoroughly examine the localization capability of RSVG models, we construct a new large-scale benchmark dataset, namely, OPT-RSVG, which poses challenges in comprehensive understanding among complex scenarios. Experimental results show that the proposed method pushes the accuracy score to 82.27% (6.29% absolute improvement) on the DIOR-RSVG dataset and 78.03% on the OPT-RSVG dataset, thus setting new records. The source codes of the proposed method and OPT-RSVG dataset are available athttps://github.com/like413/OPT-RSVG.

Single hyperspectral image super-resolution aims to improve the spatial resolution of a hyperspectral image without relying on auxiliary information. By taking advantage of the high similarity among neighbor bands, some recent methods have employed a recursive structure to super-resolve a hyperspectral image band-by-band. They are usually memory-efficient and perform well. However, they tend to introduce feedback information without distinction so as to weaken the utilization of complementary information in the context. Additionally, the spectral structure is inevitably destroyed when spatial information is extracted from neighbor bands, which hampers the effective exploration of spectral information in the subsequent process. To this end, we propose a two-stage network based on neighbor spectra maintenance and context affinity enhancement, which is composed of two sub-networks: neighbor network and context network. The former utilizes several neighbor bands to generate the neighbor spatial-spectral feature, incorporating a parallel processing scheme designed to reduce spectral distortion. Then we construct a relationship representation between the neighbor feature and feedback context information in the context network. By referring to the representation, the contents with higher complementarity will be highlighted in this stage. Experimental results on five public hyperspectral image datasets demonstrate that the proposed network not only outperforms state-of-the-art methods in terms of spatial reconstruction accuracy and spectral fidelity, but also requires less memory usage.

Atmospheric turbulence can often introduce phase errors into a propagating light field, thus resulting in anisoplanatic and temporally varying blur and distortion of images. Restoring such images degraded by atmospheric turbulence is extremely ill-posed, due to multiple plausible solutions for a given input image. Most methods offer a deterministic estimation of clean images and require high-computational costs. To address these challenges, this article proposes a fast turbulence mitigation network (FTMNet). It is a lightweight model for atmospheric turbulence mitigation. Differing other methods, it does not employ a strategy for producing a single deterministic reconstruction. Instead, it leverages the Monte Carlo method to enhance restoration performance and produces a different and reasonable set of reconstructed images for a given input. As a result, FTMNet effectively mitigates atmospheric turbulence effect while maintaining low-inference time and computational resource requirements. Experimental results demonstrate that FTMNet shows high-inference speed, reaching 90 fps, and outperforms the state-of-the-art peers.

Single hyperspectral image super-resolution aims to reconstruct a high-resolution hyperspectral image from a low-resolution one, which does not use any auxiliary images. For now, existing super-resolution methods often ignore the difference between the features of neighbor and non-neighbor spectral bands, leaving the feature exploration untargeted. As a result, the complementary information of such bands has not been effectively exploited. To do so, we propose an asymmetric dual-direction quasi-recursive network for single hyperspectral image super-resolution, which separately explores the features among neighbor and non-neighbor bands via forward and backward units. By considering the high similarity among neighbor bands, each forward unit thoroughly exploits spatial-spectral features among such bands through two kinds of correspondence aggregation modules. It also preserves a spectral structure by a spectral band grouping strategy and a spatial-spectral consistency module. Owning to the inconsecutive spectra among non-neighbor bands, backward units focus on extracting spatial features in such bands. With the aid of a global feature context fusion module, the information of global non-neighbor context and neighbor bands are adaptively fused, thus improving information completeness and complementarity. Experimental results reported for natural and remote sensing hyperspectral image datasets demonstrate the proposed network not only outperforms the state-of-the-art methods in terms of reconstruction quality and noise suppression, but also requires a smaller memory footprint.

In this article, we elaborate on a Kullback-Leibler (KL) divergence-based Fuzzy C -Means (FCM) algorithm by incorporating a tight wavelet frame transform and morphological reconstruction (MR). To make membership degrees of each image pixel closer to those of its neighbors, a KL divergence term on the partition matrix is introduced as a part of FCM, thus resulting in KL divergence-based FCM. To make the proposed FCM robust, a filtered term is augmented in its objective function, where MR is used for image filtering. Since tight wavelet frames provide redundant representations of images, the proposed FCM is performed in a feature space constructed by tight wavelet frame decomposition. To further improve its segmentation accuracy (SA), a segmented feature set is reconstructed by minimizing the inverse process of its objective function. Each reconstructed feature is reassigned to the closest prototype, thus modifying abnormal features produced in the reconstruction process. Moreover, a segmented image is reconstructed by using tight wavelet frame reconstruction. Finally, supporting experiments coping with synthetic, medical, and real-world images are reported. The experimental results exhibit that the proposed algorithm works well and comes with better segmentation performance than other peers. In a quantitative fashion, its average SA improvements over its peers are 4.06%, 3.94%, and 4.41%, respectively, when segmenting synthetic, medical, and real-world images. Moreover, the proposed algorithm requires less time than most of the FCM-related algorithms.

G-images refer to image data defined on irregular graph domains. This article elaborates on a similarity-preserving FuzzyC-Means (FCM) algorithm for G-image segmentation and aims to develop techniques and tools for segmenting G-images. To preserve the membership similarity between an arbitrary image pixel and its neighbors, a Kullback–Leibler divergence term on partition matrix is introduced as a part of FCM. As a result, similarity-preserving FCM is developed by considering spatial information of image pixels for its robustness enhancement. Due to superior characteristics of a wavelet space, the proposed FCM is performed in this space rather than the Euclidean one used in conventional FCM to secure its high robustness. Experiments on synthetic and real-world G-images demonstrate that it indeed achieves higher robustness and performance than the state-of-the-art segmentation algorithms. Moreover, it requires less computation than most of them.

In this article, we develop a residual-sparse FuzzyC-Means (FCM) algorithm for image segmentation, which furthers FCM's robustness by realizing the favorable estimation of the residual (e.g., unknown noise) between an observed image and its ideal version (noise-free image). To achieve a sound tradeoff between detail preservation and noise suppression, morphological reconstruction is used to filter the observed image. By combining the observed and filtered images, a weighted sum image is generated. Tight wavelet frame decomposition is used to transform the weighted sum image into its corresponding feature set. Taking such feature set as data for clustering, we impose an$\ell _0$regularization term on residual to FCM's objective function, thus resulting in residual-sparse FCM, where spatial information is introduced for improving its robustness and making residual estimation more reliable. To further enhance segmentation accuracy of the proposed FCM, we employ morphological reconstruction to smoothen the labels generated by clustering. Finally, based on the prototypes and smoothed labels, a segmented image is reconstructed by using tight wavelet frame reconstruction. Experimental results regarding synthetic, medical, and real-world images show that the proposed algorithm is effective and efficient, and outperforms its peers.

The conventional fuzzy C-means (FCM) algorithm is not robust to noise and its rate of convergence is generally impacted by data distribution. Consequently, it is challenging to develop FCM-related algorithms that have good performance and require less computing time. In this article, we elaborate on a comprehensive FCM-related algorithm for image segmentation. To make FCM robust, we first utilize a morphological grayscale reconstruction (MGR) operation to filter observed images before clustering, which guarantees noise-immunity and image detail-preservation. Since real images can generally be approximated by sparse coefficients in a tight wavelet frame system, feature spaces of observed and filtered images can be obtained. Taking such features to be clustered, we investigate an improved FCM model in which a sparse regularization term is introduced into the objective function of FCM. We design a three-step iterative algorithm to solve the sparse regularization-based FCM model, which is constructed by the Lagrangian multiplier method, hard-threshold operator, and normalization operator, respectively. Such an algorithm can not only perform well for image segmentation, but also come with high computational efficiency. To further enhance the segmentation accuracy, we use MGR to filter the label set generated by clustering. Finally, a large number of supporting experiments and comparative studies with other FCM-related algorithms available in the literature are provided. The obtained results for synthetic, medical and color images indicate that the proposed algorithm has good ability for multiphase image segmentation, and performs better than other alternative FCM-related algorithms. Moreover, the proposed algorithm requires less time than most of the existing algorithms.

In recent years, image processing in a Euclidean domain has been well studied. Practical problems in computer vision and geometric modeling involve image data defined in irregular domains, which can be modeled by huge graphs. In this paper, a wavelet frame-based fuzzy C -means (FCM) algorithm for segmenting images on graphs is presented. To enhance its robustness, images on graphs are first filtered by using spatial information. Since a real image usually exhibits sparse approximation under a tight wavelet frame system, feature spaces of images on graphs can be obtained. Combining the original and filtered feature sets, this paper uses the FCM algorithm for segmentation of images on graphs contaminated by noise of different intensities. Finally, some supporting numerical experiments and comparison with other FCM-related algorithms are provided. Experimental results reported for synthetic and real images on graphs demonstrate that the proposed algorithm is effective and efficient, and has a better ability for segmentation of images on graphs than other improved FCM algorithms existing in the literature. The approach can effectively remove noise and retain feature details of images on graphs. It offers a new avenue for segmenting images in irregular domains.

Image denoising technologies in a Euclidean domain have achieved good results and are becoming mature. However, in recent years, many real-world applications encountered in computer vision and geometric modeling involve image data defined in irregular domains modeled by huge graphs, which results in the problem on how to solve image denoising problems defined on graphs. In this paper, we propose a novel model for removing mixed or unknown noise in images on graphs. The objective is to minimize the sum of a weighted fidelity term and a sparse regularization term that additionally utilizes wavelet frame transform on graphs to retain feature details of images defined on graphs. Specifically, the weighted fidelity term with ℓ1-norm and ℓ2-norm is designed based on a analysis of the distribution of mixed noise. The augmented Lagrangian and accelerated proximal gradient methods are employed to achieve the optimal solution to the problem. Finally, some supporting numerical results and comparative analyses with other denoising algorithms are provided. It is noted that we investigate image denoising with unknown noise or a wide range of mixed noise, especially the mixture of Poisson, Gaussian, and impulse noise. Experimental results reported for synthetic and real images on graphs demonstrate that the proposed method is effective and efficient, and exhibits better performance for the removal of mixed or unknown noise in images on graphs than other denoising algorithms in the literature. The method can effectively remove mixed or unknown noise and retain feature details of images on graphs. It delivers a new avenue for denoising images in irregular domains.

This issue marks the beginning of the IEEE Transactions on Neural Networks and Learning Systems (TNNLS). By adding "Learning Systems" to the title, we now state explicitly the scope of the Transactions to include neural networks as well as related learning systems. This issue marks a new era in the history of our Transactions. The Transactions is now ready to face the challenges of the next 10-20 years. With the evolution of the fields of neural networks in particular and computational intelligence in general, the IEEE Transactions on Neural Networks and Learning Systems will continue to grow and to succeed in this ever-changing world. Also included are a few comments about the review process of TNN manuscripts and the introduction of 14 new TNNLS Associate Editors. Short biographies are included for the new Associate Editors.