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Abstract To address issues such as object‐background confusion and difficulties in multi‐scale object feature extraction in underwater scenarios, this article proposes an underwater organisms detection algorithm based on multi‐scale perception and representation enhancement. The key innovation of the proposed algorithm is the perception improvement of the deep learning model for underwater multi‐scale objects. First, for underwater large‐scale objects, omni‐dimensional dynamic convolution is embedded as an attention mechanism (AM) into the deep network to improve the network's sensitivity to large‐scale underwater objects. For underwater small‐scale objects, an information retention downsampling module is designed to reduce the effects of serious information loss. Then, a contextual transformer as an AM is introduced into shallow networks to strengthen the network's ability to extract features from small objects. The second innovation of the proposed algorithm is an underwater spatial pooling pyramid module which enhances the representation ability of the model. Furthermore, a lightweight decoupled head is designed to eliminate the conflict between classification and localization. The ablation experiment on the URPC dataset shows that the proposed models are effective for underwater object detection. The comparative experiments on the URPC and DUT‐USEG datasets demonstrate that the proposed algorithm achieves an advantage in detection performance compared with the mainstream detection algorithms and underwater detection algorithms.

Abstract Deep learning has made significant progress in the field of low‐light image enhancement. However, challenges remain, such as the substantial parameter consumption required for effective image enhancement. Inspired by multi‐scale geometric transformations in image detail enhancement, a novel model called the fixed‐directional filters network is proposed. Fixed‐directional filters network takes the original image as input and employs multiple branches for parallel processing. One branch uses conventional convolutional layers to extract features from the original image, while the other branches apply non‐linear mapping layers based on wavelet transforms. These wavelet transform branches capture the multi‐scale information of the image by combining different directions and convolutional kernels and utilize a trainable custom gamma mapping layer for non‐linear modulation to enhance specific regions of the image. The feature maps processed by each branch are merged through concatenation operations and then passed through convolutional layers to output the enhanced image. Using trainable mapping functions alone to enhance details significantly reduces the reliance on convolutional layers, effectively lowering the model's parameter count to only 13k parameters. Additionally, experiments demonstrate that fixed‐directional filters network significantly improves image quality, particularly in capturing image details and enhancing image contrast.

Abstract The surface quality of aluminium alloy castings is crucial to quality control. Aiming to address the challenges of limited samples and extensive computation in deep learning‐based surface defect detection for aluminium alloy castings, this paper proposes a surface defect detection method based on data enhancement and the Casting Real‐Time DEtection TRansformer. First, to tackle the issue of small sample sizes and uneven distribution in surface defect data sets of aluminium alloy castings, ECA‐MetaAconC Deep Convolution Generative Adversarial Networks is proposed for generating defects with fewer samples and employ the image augmentation (IMGAUG) library for sample enhancement. Second, building upon the Real‐Time DEtection TRansformer (RT‐DETR), a lightweight partial‐rep convolution is designed to decrease the network's parameter count. Simultaneously, the Deformable attention module and the DRBC3 module are introduced to enhance the neck network, thereby improving the model's capability to capture information and enhancing its detection performance. Compared to RT‐DETR, this method reduces the number of model parameters by 38.7%, increases mAP by 1.5%, and achieves a frame rate that is 1.58 times higher than the original model. The experimental results demonstrate that this method can effectively and accurately detect surface defects in aluminium alloy castings, satisfying industrial requirements.

Abstract Timely detection of hard exudates in fundus images can effectively avoid the severity of the disease, but the labelling of small and numerous lesion areas requires a lot of labour costs. This paper proposes a semi‐supervised segmentation network, which integrates pseudo‐labels and multi‐level features consistency correction. It achieves accurate segmentation of hard exudates by making full use of a small amount of labelled data and a large amount of unlabelled data. The network effectively extracts features from the unlabelled data through knowledge transfer of the teacher‐student model, and incorporates a Transformer network for auxiliary training to promote the quality of transfer. In addition, three unsupervised losses are introduced to improve the performance: the perturbation loss improves the robustness of the model to noise by adding different noises to the same input; the multi‐level feature consistency correction loss ensures the consistency of features of the student model at different scales; and the pseudo‐labelling cross‐supervision loss utilizes the generated pseudo‐labels for supervision between CNN and Transformer. By comparing the segmentation results with different proportion of the labelled data, it has better segmentation performance compared to other methods. The proposed methods can totally increase dice by 16.56% and mean intersection over union (MIoU) by 25.11%.

Abstract The non‐local imaging characteristics of computational ghost imaging (CGI) make it widely used in the field of information security. However, the information processing method based on traditional CGI has some problems in the process of multi‐image encryption, such as low efficiency and unsatisfactory reconstruction quality. Therefore, this article proposes to use wavelet transform and singular value decomposition technology to help computational ghost imaging to efficiently complete the coding and encryption of multiple images, and use alternating direction multiplier method (ADMM) in the process of image restoration to carry out high‐quality reconstruction of the original encrypted image. The results show that the scheme has good reconstruction effect, strong security and robustness even at a low sampling rate. It provides some reference for digital watermarking technology and cryptography.

Abstract The application of medical image segmentation technology enables accurate localization of human tissues, providing doctors with a reliable foundation for diagnosis. While deep learning methods have proven effective in this task, most current approaches rely on a single prediction framework, which overlooks Edge semantic features and results in flawed texture features. Moreover, existing supervised methods face challenges due to limited availability of high‐quality annotations in the field of medical imaging. In this article, a Semi‐supervised Contextual Cognitive Augmentation‐based Cross‐teaching Network is proposed. A Contextual Cognitive Enhancement Module is introduced consisting of two components: data augmentation and information extraction. The data augmentation component provides multi‐level data distribution by incorporating diverse perturbation strategies such as Discrete Cosine Transform and Gaussian noise. The information extraction component employs the Comprehensive Information Extraction module, which consists of Global Perception Information Extraction module and Multi‐channel Information Extraction module to extract perceptual information from images and enhance interaction between image channels, respectively. Additionally, a cross‐teaching strategy is adopted and a hybrid loss function is utilized to encourage knowledge sharing among the networks, leveraging the advantages of dual networks for improved performance. Experimental results demonstrate significant enhancements in multiclass medical image segmentation compared to several state‐of‐the‐art single‐framework networks.

Abstract Glaucoma is an eye disease that damages the optic nerve as a result of vision loss, it is the leading cause of blindness worldwide. Due to the time‐consuming, inaccurate, and manual nature of traditional methods, automation in glaucoma detection is important. This paper proposes an explainable artificial intelligence (XAI) based model for automatic glaucoma detection using pre‐trained convolutional neural networks (PCNNs) and machine learning classifiers (MLCs). PCNNs are used as feature extractors to obtain deep features that can capture the important visual patterns and characteristics from fundus images. Using extracted features MLCs then classify glaucoma and healthy images. An empirical selection of the CNN and MLC parameters has been made in the performance evaluation. In this work, a total of 1,865 healthy and 1,590 glaucoma images from different fundus datasets were used. The results on the ACRIMA dataset show an accuracy, precision, and recall of 98.03%, 97.61%, and 99%, respectively. Explainable artificial intelligence aims to create a model to increase the user's trust in the model's decision‐making process in a transparent and interpretable manner. An assessment of image misclassification has been carried out to facilitate future investigations.

Abstract Handwriting is a natural way to communicate and exchange ideas, but converting handwritten diagrams to application‐specific digital formats requires skill and time. Automatic handwritten document conversion can save time, but diagrams and text require different recognition engines. Since accurate segmentation of handwritten diagrams can improve the accuracy of later diagram recognition steps, the authors propose to solve the problem of segmentation of text and non‐text elements of handwritten diagrams using deep semantic segmentation. The model, DeepDP is a flexible U‐net style architecture that can be tuned in complexity to a level appropriate for a particular dataset and diagram type. Experiments on a public hand‐drawn flowchart dataset and a business process diagram dataset show excellent performance, with a per pixel accuracy of 98.6% on the public flowchart datasets and improvement over the 99.3% text stroke accuracy and 96.6% non‐text stroke accuracy obtained by state of the art methods that use online stroke information. On the smaller offline business process diagram dataset, the method obtains a per‐pixel accuracy of 96.9%.

Abstract Medical image registration is essential and a key step in many advanced medical image tasks. In recent years, medical image registration has been applied to many clinical diagnoses, but large deformation registration is still a challenge. Deep learning‐based methods typically have higher accuracy but do not involve spatial transformation, which ignores some desirable properties, including topology preservation and the invertibility of transformation, for medical imaging studies. On the other hand, diffeomorphic registration methods achieve a differentiable spatial transformation, which guarantees topology preservation and invertibility of transformation, but registration accuracy is low. Therefore, a diffeomorphic deformation registration with CNN is proposed, based on a symmetric architecture, simultaneously estimating forward and inverse deformation fields. CNN with Efficient Channel Attention is used to better capture the spatial relationship. Deformation fields are optimized explicitly and implicitly to enhance the invertibility of transformations. An extensive experimental evaluation is performed using two 3D datasets. The proposed method is compared with different state‐of‐the‐art methods. The experimental results show excellent registration accuracy while better guaranteeing the diffeomorphic transformation.

Abstract Although graph convolutional networks have achieved good performances in skeleton‐graph‐based action recognition, there are still some problems which include the incomplete utilization of skeleton graph features and the lacking of logical adjacency information between nodes in adjacency matrix. In this article, a human action recognition algorithm is proposed based on multiple features from the skeleton graph to solve these problems. More specifically, an improved adjacency matrix is constructed to make full use of the multiple skeleton graph features. These features include local differential features, multi‐scale edge features, features of the original skeleton graph, nodal features, and nodal motion features. Extensive results are conducted on four standard datasets (NTU RGB‐D 60, NTU RGB‐D 120, Kinetics, and Northwestern‐UCLA). The experimental results show that the proposed algorithm outperforms the SOTA action recognition algorithms.

Abstract To tackle challenges in road multi‐object detection, such as object occlusion, small object detection, and multi‐scale object detection difficulties, a new YOLOv8n‐RSFM structure is proposed. The key improvement of this structure lies in the introduction of the transformer decoder head, which optimizes the matching between the ground truth and predicted boxes, thereby effectively addressing issues of object overlap and multi‐scale detection. Additionally, a small object detection layer is incorporated to retain crucial information beneficial for detecting small objects, significantly improving the detection accuracy for small targets. To enhance learning capacity and reduce redundant computations, the FasterNet backbone is employed to replace CSPDarknet53, thus accelerating the training process. Finally, the INNER‐MPDIoU loss function is introduced to replace the original algorithm's complete IoU to accelerate the convergence and obtain more accurate regression results. A series of experiments were conducted on different datasets. The experimental results show that the proposed model YOLOv8N‐RSFM outperforms the original model YOLOv8n in small target detection. On the VisDrone, TinyPerson, and VSCrowd datasets, the mean accuracy percentage improved by 7.9%, 12.3%, and 4.5%, respectively.

Abstract Image hiding is a task that embeds secret images in digital images without being detected. The performance of image hiding has been greatly improved by using the invertible neural network. However, current image hiding methods are less robust in the face of Joint Photographic Experts Group (JPEG) compression. The secret image cannot be extracted from the stego image after JPEG compression of the stego image. Some methods show good robustness for some certain JPEG compression quality factors but poor robustness for other common JPEG compression quality factors. An image‐hiding network (RIHINNet) that is robust to all common JPEG compression quality factors is proposed. First of all, the loss function is redesigned; thus, the secret image is hidden as much as possible in the area that is less likely to be changed after JPEG compression. Second, the classifier is designed, which can help the model to select the extractor according to the range of JPEG compression degree. Finally, the interval robustness of the secret image extraction is improved through the design of a denoising module. Experimental results show that this RIHINNet outperforms other state‐of‐the‐art image‐hiding methods in the face of JPEG compressed noise with random compression quality factors, with more than 10 dB peak signal‐to‐noise ratio improvement in secret image recovery on ImageNet, COCO and DIV2K datasets.

Abstract Side‐scan sonar (SSS) detection is a key method in underwater environmental security and subsea resource development. However, many detection approaches primarily concentrate on tracking the evolution path of optical image object detection tasks when using acoustic images, resulting in complex structures and limited versatility. To tackle this issue, we introduce a pioneering dual‐domain multi‐frequency network (D2MFNet) meticulously crafted to harness the distinct characteristics of SSS image detection. In D2MFNet, a novel method for optimizing and improving the detection sensitivity in different frequency ranges called multi‐frequency combined attention mechanism (MFCAM) is proposed. This mechanism amplifies the relevance of dual‐domain features across different channels and spaces. Moreover, we introduce a dual‐domain feature pyramid network (D2FPN) significantly augments the depth and breadth of feature information in underwater small datasets. The methods offer plug‐and‐play functionality with substantial performance enhancements. Extensive experiments are conducted to validate the efficacy of the proposed techniques, and the results showcase their state‐of‐the‐art performance. MFCAM improves the mAP by 16.9% in the KLSG dataset and 15.5% in the SCTD dataset. The mAP of D2FPN was improved by 8.4% in the KLSG dataset and by 9.8% in the SCTD dataset. The code and models will be publicly available at https://dagshub.com/estrellaww00/D2MFNet.

Abstract Invertible colour‐to‐grey algorithms protect the colour of an image against illegal usage and distribution. These schemes hide the colour information into a grayscale version of the image, making colour recovery without proper authorization challenging. A previous study proposed the incorporation of content security by distorting the protected image to hinder illegal structure restoration. This work addresses the limitations of this method, significantly improving both processing time and the quality of the recovered colour image. Specifically, processing times are reduced from 45 h to 9 s, and the mean PSNR value is increased by up to 2.23 dB. Furthermore, this proposal achieves competitive results compared to existing approaches that do not implement content security, obtaining mean peak signal‐to‐noise ratio (PSNR) and structural similarity index measure (SSIM) values above 42.32 dB and 0.992, respectively. Finally, quantitative results are supported by visual comparisons.

Abstract To effectively address common issues such as cattle being obscured by fences and images prone to colour shifts and high brightness in a ranch setting, this paper proposes an algorithm for counting cows based on multi‐scale perception and image correlation. The algorithm first adjusts the model output scale to enhance cattle detection under current conditions. It incor‐porates efficient Partial Convolution (PConv) to replace 3 × 3 convolutions in the Neck segment of the YOLOv7 network, boost‐ing computational speed and reducing complexity. To streamline feature fusion, Dynamic Head (DyHead) unifies multiple at‐tentional operations in the Neck segment, enhancing efficiency. Additionally, it introduces a novel bounding box similarity metric Minimum Point DioU (MPDIoU) based on minimum point distance, encompassing factors from existing loss functions, while simplifying computations. Experimental results demonstrate the algorithm significantly improves detection, achieving 98.8% accuracy, 99.0% recall, and a 92.1% mAP value. Compared with mainstream SOTA models, Precision increases by 0.4%, Recall by 2.0%, and mAP value by 2.2%. Model size decreases by 23.9%, parameter count by 23.0%, and computational load by 6.1%. the algorithm shows improvements across all indices, meeting the challenge of real‐time cattle counting in ranches under complex conditions.

Abstract Image denoising is one of the fundamental problems in image processing. Convolutional neural network (CNN) based denoising approaches have achieved better performance than traditional methods, such as STROLLR and BM3D. However, CNNs can easily bring unexplainable artifacts to denoised images. In this article, a Deep Learning‐Informed Diffusion Equation (DLI‐DE) framework utilizing the image prior or the image gradient prior for image denoising is proposed. The image priors and gradient priors are learned from CNN models and used as coefficients in diffusion equations. The solution of DLI‐DE is infinitely smooth from the uniqueness of existence theorem, which guarantees that the denoised image is free of artifacts. Good properties of DLI‐DE also ensure high‐quality of denoising. The experimental analysis confirms that the denoising performance of DLI‐DE is comparable to that of contemporary CNN‐based denoising methods such as TNRD and DnCNN, while effectively preventing artifacts.

Abstract This study evaluates the effectiveness of three loss functions Asymmetric Unified Focal Loss (AUFL), Dice Similarity Coefficient Loss (DSCL), and Cross‐Entropy (CE) for segmenting COVID‐19 lung infections in computed tomography images. Detailed analyses using the intersection over union metric assessed each function's accuracy. AUFL achieved an average Dice Similarity Coefficient (DSC) of 85.18% ± 8.86%, outperforming DSCL 85.18% ± 8.86%, which had the same average DSC but less precise segmentation, and CE, which had an average DSC of 78.31% ± 11.93%. Segmentations using AUFL demonstrated more defined contours and better alignment with actual anatomical structures than those obtained with DSCL and CE. Observations revealed that AUFL‐generated segmentations had more precise boundaries and were more consistent with the expected anatomical regions of lung infections. This study is the first to quantitatively and qualitatively compare the effectiveness of AUFL, DSCL, and CE in segmenting COVID‐19 lung infections, providing concrete evidence of AUFL's superiority in segmentation performance and reliability for clinical applications. The findings underscore the importance of selecting appropriate loss functions to enhance segmentation in medical imaging, highlighting their crucial role in improving image‐based diagnostics and treatment. The study emphasizes the need for ongoing research to optimize these segmentation techniques further.

Abstract Image quality is significantly impacted by rain, posing challenges in fields like surveillance, autonomous driving, and outdoor robotics. The field of image deraining, particularly for single image, has attracted considerable attention to improve image clarity in inclement weather. To overcome the inherent complexity of the single‐image rain removal task, we proposed a novel architecture of the attention mechanism and gated recurrent network (AMGR‐Net) that combines spatial and channel attention mechanisms with gated recurrent units. AMGR‐Net contains multiple modules, each of which uses convolution kernels and attention mechanisms to enhance feature extraction. AMGR‐Net demonstrates superior performance over state‐of‐the‐art methods in both synthetic and real‐world image datasets, as evidenced by higher peak signal to noise ratio and structural similarity index measurement scores. The integration of spatial attention significantly enhances feature expression, enabling more effective rain streak removal and detail preservation. Furthermore, this method also shows promising results in the application of stripe noise removal from meteorological satellite cloud images.

Abstract In pedestrian detection task, numerous predicted boxes and their corresponding scores are generated and these scores are used to filter these predicted boxes by non‐maximum suppression. This paper analysed the training process of the popular anchor‐based pedestrian detection models (e.g. YOLO and Faster RCNN), and found that the score of the predicted box reflects the overlap between the corresponding anchor and the ground truth, rather than the predicted box itself. Due to the many‐to‐one strategy adopted by anchor‐based methods, multiple predicted boxes could be generated around one predicted box. This study refers to the number of other predicted boxes around the target predicted box as its local density. When a predicted box has a higher local density, it should have a greater overlap with the ground truth. Therefore, this study proposed the fused score by introducing local density into the score. The experiments showed that replacing the score with the fused score can effectively improve the model's detection accuracy. The code and experiments will soon be open‐sourced at https://github.com/zefeichen/FusedScore.

Abstract With the emergence of computer‐aided diagnostic (CAD) systems, the speed of histopathological image analysis and the accuracy of cancer detection have considerably improved. However, the appearance of histopathological slides can vary depending on the consistency of tissue thickness, stain concentrations, and equipment, thus affecting the judgment of CAD systems. This study proposes a palette‐based colour normalization method for histopathology images is proposed to solve the problem of colour differences between histopathology images. The method builds a graphical user interface based on an improved palette generation algorithm and colour transfer definitions, through which the user can complete the corresponding colour modification to achieve colour normalization. The evaluation of the metrics on histopathological images shows that our method is able to achieve higher image quality and better preservation of structural information of the source image compared with four other colour normalization algorithms. The peak signal‐to‐noise ratio values obtained by the proposed method on two publicly available datasets were 24.1914 and 21.3666, and the structural similarity index matrix values were 0.9871 and 0.9760. The proposed method provides new ideas for the development and design of CAD systems.

Abstract Chinese stroke segmentation is a crucial and challenging task for various downstream applications such as font generation, aesthetic evaluation etc. Conventional semantic segmentation techniques typically face difficulties in accurately segmenting strokes, as intersection regions in Chinese characters can belong to multiple strokes simultaneously, and these approaches often lack a holistic understanding of character composition. This paper proposes a character stroke segmentation framework named Stroke‐Seg that integrates with various semantic segmentation architectures, demonstrating adaptability to different backbone networks to tackle the above tasks. A multi‐label output strategy is proposed to effectively classify strokes in intersection areas, overcoming the limitations of traditional semantic segmentation approaches. Additionally, a prior knowledge vector is incorporated into the input layer to provide character‐specific information on stroke composition, enhancing the ability of the framework to precisely identify and segment strokes. The effectiveness of the proposed framework is demonstrated through evaluations of a comprehensive dataset (brush calligraphy stroke segmentation dataset). Evaluations show that the proposed framework significantly improves the capability of semantic segmentation networks, achieving a remarkable improvement of up to 19.9% in the true stroke rate, compared to traditional stroke segmentation techniques. The Stroke‐Seg framework integrated with TransUNet demonstrates its high performance with an impressive 98.2% true stroke rate. Furthermore, the proposed framework combined with FCN still achieves good performance while consuming the least amount of computational resources and memory, demonstrating its potential for lightweight design.

Abstract This research work presents a novel secured spatial steganography algorithm consisting of three stages. In the first stage, a secret message is divided into three parts, each is encrypted using a tan logistic map encryption key with a unique seed value. In the second stage, the encrypted parts are transformed into quick response codes, serving as a layer of channel coding. Subsequently, the quick response codes are decoded back into bit‐streams. To enhance security, a uniquely‐seeded Mersenne Twister key is generated and employed to apply DNA coding onto each bit‐stream. The resulting bit‐streams are then embedded in the least significant bits of the RGB channels of a cover image. Finally, the RGB channels are merged to form a single stego image. A comprehensive set of experimental analyses is conducted to evaluate the performance of the proposed secure steganography algorithm. The experimental results demonstrate the algorithm's robustness against various attacks and its ability to achieve high embedding capacity while maintaining imperceptibility. The proposed algorithm offers a promising solution for secure information hiding in the spatial domain, with potential applications in areas such as data transmission, digital forensics, and covert communication.

Abstract Diffusion models are increasingly applied in low‐light image enhancement tasks due to their exceptional capability to model data distributions, but most current methods focus only on the original pixel space and neglect the potential of Fourier frequency information. In this article, SFDiff is proposed, a novel low‐light image enhancement method that integrates Fourier frequency information into the diffusion process. Specifically, Fourier transforms are applied at both the image and feature levels to separately enhance the amplitude and phase components, which restores global illumination degradation and positional information. Then a Spatial‐Frequency Fusion (SFF) block is used to fully integrate and interact with the information across spatial and frequency domains. Since illumination degradation is primarily manifested in the amplitude component, a loss function based on maximum likelihood learning is employed to constrain the amplitude component at each step of the sampling process, ensuring that the reverse process maintains an optimal trajectory. Owing to the streamlined network design and the fact that the Fourier transform requires no extra parameters, SFDiff achieves a reduction in parameters of over 35% compared to several state‐of‐the‐art (SOTA) diffusion models and delivers high‐quality enhancement results on multiple real‐world datasets. The code is available at https://github.com/MrWan001/SFDiff.

Abstract Due to the powerful ability in capturing the global information, transformer has become an alternative architecture of CNNs for hyperspectral image classification. However, general transformer mainly considers the global spectral information while ignores the multiscale spatial information of the hyperspectral image. In this paper, we propose a multiscale spectral–spatial convolutional transformer (MultiFormer) for hyperspectral image classification. First, the developed method utilizes multiscale spatial patches as tokens to formulate the spatial transformer and generates multiscale spatial representation of each band in each pixel. Second, the spatial representation of all the bands in a given pixel are utilized as tokens to formulate the spectral transformer and generate the multiscale spectral–spatial representation of each pixel. Besides, a modified spectral–spatial CAF module is constructed in the MultiFormer to fuse cross‐layer spectral and spatial information. Therefore, the proposed MultiFormer can capture the multiscale spectral–spatial information and provide better performance than most of other architectures for hyperspectral image classification. Experiments are conducted over commonly used real‐world datasets and the comparison results show the superiority of the proposed method.

Abstract Melanoma, a highly prevalent and lethal form of skin cancer, has a significant impact globally. The chances of recovery for melanoma patients substantially improve with early detection. Currently, deep learning (DL) methods are gaining popularity in assisting with the early identification of melanoma. Despite their high performance, relying solely on an image classifier undermines the credibility of the application and makes it difficult to understand the rationale behind the model's predictions highlighting the need for Explainable AI (XAI). This study provides a survey on skin cancer identification using DL techniques utilized in studies from 2017 to 2024. Compared to existing survey studies, the authors address the latest related studies covering several public skin cancer image datasets and focusing on segmentation, classification based on convolutional neural networks and vision transformers, and explainability. The analysis and the comparisons of the existing studies will be beneficial for the researchers and developers in this area, to identify the suitable techniques to be used for automated skin cancer image classification. Thereby, the survey findings can be used to implement support applications advancing the skin cancer diagnosis process.

Abstract Insulators, as typical equipment for distribution networks, provide good electrical insulation between live conductors and earth. Timely and accurate detection is essential for insulator detection issues. However, as the complexity of neural networks increases, the detection efficiency is often lower. Therefore, this paper proposes a fast insulator positioning and defect detection method. Firstly, for insulator target localization, the SqueezeNet network is improved using ECA attention mechanism. In addition, to address the issue of low defect detection accuracy, a joint algorithm has been proposed. The integration of convolutional variational autoencoder (CVAE) and generative adversarial network (GAN) solve their own shortcomings due to different image focus angles. The target localization accuracy reaches 94.30%, and the defect detection accuracy reaches 89.60%. It solves the problems of difficulty in locating small targets in a large field of view and inaccurate detection due to a small number of abnormal samples. This method has been tried and tested in practical distribution network systems.

Abstract Coal Mining enterprises deploy numerous monitoring devices to ensure safe and efficient production using target detection technologies. However, deploying deep detection models on edge devices poses challenges due to high computational loads, impacting detection speed and accuracy. A mining target detection dataset has been created to address these issues, featuring key targets in coal mining scenes such as miners, safety helmets, and coal gangue. A model is proposed to improve real‐time performance for edge mining detection tasks. Detection performance is enhanced by incorporating a Pixel‐wise Normalization Spatial Attention Module (PN‐SAM) into the MobileNet‐v3 bneck structure and replacing the h‐swish activation function with Mish, providing more prosperous gradient information transfer. The proposed model, YOLO‐v4‐LSAM, shows a 3.2% mAP improvement on the VOC2012 dataset and a 2.4% improvement on the mining target dataset compared to YOLO‐v4‐Tiny, demonstrating its effectiveness in mining environments. These enhancements enable more accurate and efficient detection in resource‐constrained edge environments, contributing to safer and more reliable monitoring in coal mining operations.

Abstract Multi‐organ segmentation from abdominal CT scans is crucial for various medical examinations and diagnoses. Despite the remarkable achievements of existing deep‐learning‐based methods, accurately segmenting small organs remains challenging due to their small size and low contrast. This article introduces a novel knowledge‐guided cascaded framework that utilizes two types of knowledge—image intrinsic (anatomy) and clinical expertise (radiology)—to improve the segmentation accuracy of small abdominal organs. Specifically, based on the anatomical similarities in abdominal CT scans, the approach employs entropy‐based registration techniques to map high‐quality segmentation results onto inaccurate results from the first stage, thereby guiding precise localization of small organs. Additionally, inspired by the practice of annotating images from multiple perspectives by radiologists, novel Multi‐View Fusion Convolution (MVFC) operator is developed, which can extract and adaptively fuse features from various directions of CT images to refine segmentation of small organs effectively. Simultaneously, the MVFC operator offers a seamless alternative to conventional convolutions within diverse model architectures. Extensive experiments on the Abdominal Multi‐Organ Segmentation (AMOS) dataset demonstrate the superiority of the method, setting a new benchmark in the segmentation of small organs.

Abstract License plate recognition is crucial in Intelligent Transportation Systems (ITS) for vehicle management, traffic monitoring, and security inspection. In highway scenarios, this task faces challenges such as diversity, blurriness, occlusion, and illumination variation of license plates. This article explores Recurrent Neural Networks based on Connectionist Temporal Classification (RNN‐CTC) for license plate recognition in challenging highway conditions. Four neural network models: ResNet50, ResNeXt, InceptionV3, and SENet, all combined with RNN‐CTC are comparatively evaluated. Furthermore, a novel architecture named ResNet50 Deep Fusion Network using Connectionist Temporal Classification (ResNet50‐DFN‐CTC) is proposed. Comparative and ablation experiments are conducted using the Highway License Plate Dataset of Southeast University (HLPD‐SU). Results demonstrate the superior performance of ResNet50‐DFN‐CTC in challenging highway conditions, achieving 93.158% accuracy with a processing time of 7.91 ms, outperforming other tested models. This research contributes to advancing license plate recognition technology for real‐world highway applications under adverse conditions.

Abstract Image steganography aims to hide secret data in the cover media for covert communication. Though many deep‐learning‐based image steganography methods have been presented, these approaches suffer from the inefficiency of building long‐distance connections between the cover and secret images, leading to noticeable modification traces and poor steganalysis resistance. To improve the visual imperceptibility of generated stego images, it is essential to establish a global correlation between the cover and secret images. In this way, the secret image can be dispersed throughout the cover image globally. To bridge this gap, a novel image steganography framework called HiiT is proposed, which takes advantage of CNN and Transformer to learn both the local and global pixel correlation in image hiding. Specifically, a new Transformer structure called Inception Transformer is proposed, which incorporates the Inception Net in the attention‐based Transformer architecture. The Inception Net can learn different scaled image features using multiple convolution kernels, while the attention mechanism can learn the global pixel correlation. By this, the proposed Inception Transformer learns the long‐distance pixel dependency between the cover and secret images. Furthermore, we propose a ‘Skip Connection’ mechanism in the proposed Inception Transformer, which merges the low‐level visual features and high‐level semantic features and achieves better model performance. In detail, The HiiT generates higher‐quality stego images with 45.46 PSNR and 0.9915 SSIM. Besides, accurately restored secret images achieve 47.27 PSNR and 0.9952 SSIM. Extensive experimental results show the proposed HiiT significantly improves the image‐hiding performance compared with state‐of‐the‐art methods.

Abstract Infrared and visible image fusion involves merging the advantages of infrared and visible images to generate a composite image that encompasses thermal radiation as well as intricate texture details. Infrared and visible image fusion has garnered increasing attention, with numerous fusion methods proposed. However, how to fairly perceive the performance of fused image remains a contentious topic. This paper is dedicated to solving this problem from two perspectives (e.g., subjective and objective aspects). Firstly, an infrared and visible fusion image quality assessment dataset was constructed, including 60 pairs of infrared and visible images captured in various scenes, along with 540 fusion images with different types and degrees of distortions. Additionally, a subjective evaluation dataset of 16,200 subjective scores by 30 participants was further provided for the fused image. Secondly, to overcome the challenging assessment for infrared and visible fusion images without a real reference image, an interesting multi‐domain pseudo‐reference image quality assessment model (MPIQAM) is proposed, by comprehensively considering the thermal radiation information distortion, texture information distortion, and overall naturalness of the fused image. The proposed MPIQAM was compared with 18 mainstream objective metrics, and the experimental findings showcased a commendable level of competitiveness.

Abstract With the advent of the digital era, millions of facial images are shared online daily, posing severe privacy threats. Generative face anonymization (GFA) methods generate virtual faces to conceal original identities, protecting sensitive information while preserving utility. However, deep learning based user identity linkage (UIL) methods can link similar faces to the same identity and leverage the linked profiles for malicious purposes, including localization and behaviour prediction. These UIL methods pose a significant challenge to the diversity of virtual faces, a challenge that existing GFA methods have not adequately addressed. To address this research gap, we propose Style Diversification‐based Generative Face Anonymization (SD‐GFA), a framework that generates virtual faces with diverse identities and high visual quality. SD‐GFA features an equalized control module to balance input faces and user‐specified keys, a face generation module with a re‐connection strategy for high‐quality synthesis, and a maximum probability simulation module to enhance diversity. Our experiments demonstrate that SD‐GFA effectively mitigates linkage risk by improving the diversity of virtual faces, while also enhancing their utility and visual quality. This study provides a robust solution to enhance the security of anonymized faces shared on the internet.

Abstract Photon‐counting detector‐based computed tomography (PCD‐CT) is an advanced realization of spectral CT, the multi‐energy projection data is captured from the same object, hence, CT images can provide additional spectral resolution, making it possible to perform material decomposition. However, multiple projections may have a low signal‐to‐noise ratio (SNR), such that CT images suffer from noise. To handle this problem, a spectral CT image reconstruction method based on anisotropic sparse transformation (AST) is proposed. To increase the quality of reconstruction, AST through an anisotropic guided filter (AGF) and L0 quasi norm is proposed. Then, as a new regularization, AST is introduced into an iterative reconstruction process, generating an AST‐based method. Moreover, to utilize the correlation among projection data, the average image serves as the guidance image of AGF, it varies with the iterative index, resulting in a technique of dynamic average image (DAI). The AST‐based model involves L0 quasi norm minimization, hence an effective strategy is employed to solve the corresponding problem. A series of experiments were performed. The experiment showed that, compared to other listed methods, the result of the AST‐based method can achieve better visualization and higher quantitative indexes, hence it has application potential in the medical imaging field.

Abstract In response to the inadequate utilization of prior information in current mural inpainting processes, leading to issues such as semantically unreliable inpaintings and the presence of artifacts in the inpainting area, a Dunhuang mural inpainting method based on reference guidance and multi‐scale feature fusion is proposed. First, the simulated broken mural, the mask image, and the reference mural are input into the model to complete the multi‐level embedding of patches and align the multi‐scale fine‐grained features of damaged murals and reference murals. Following the patch embedding module, a hybrid residual module is added based on hybrid attention to fully extract mural features. In addition, by continuing the residual concatenation of outputs of the hierarchical embedding module improves the ability of the model to represent deeper features, and improves the robustness and generalisation of the model. Second, the encoded features are fed into the decoder to generate decoded features. Finally, the convolutional tail is employed to propagate them and complete the mural painting. Experimental validation on the Dunhuang mural dataset demonstrates that, compared to other algorithms, this model exhibits higher evaluation metrics in the inpainting of extensively damaged murals and demonstrates overall robustness. In terms of visual effects, the results of this model in the inpainting process exhibit finer textures, richer semantic information, more coherent edge structures, and a closer resemblance to authentic murals.

Abstract In practical production applications, the efficiency and success rate of gesture recognition directly affect the user experience and work efficiency. However, the existing gesture recognition models have the problem of a large number of model parameters and high computational complexity, which makes them unable to meet the needs of end‐to‐end industrial deployment. To solve these problems, this article proposes a gesture recognition model based on YOLOv8. First, FasterNet is adopted as the backbone of YOLOv8, which significantlydecrease the number of parameters and made the model more lightweight. By reducing the number of parameters, the computational complexity of the model can be reduced while maintaining the performance of the model, and the operation efficiency of the model can be improved. Second, recombination convolution ScConv is introduced to replace common convolution operations to further improve the model's efficiency. Recombination convolution can reduce the computation and make up for the loss of precision to some extent. Finally, the MDPIoU loss function is used to optimize target location and prediction, to improve the accuracy of the model. The MDPIoU loss function can better deal with the problem of target boundary frame positioning and prediction so that the model can locate and predict gestures more accurately in gesture recognition tasks. Experiments on a data set containing 10 types of gestures show that the number of parameters and floating point calculations of the improved network model are reduced by 45% and 42.7%, respectively, while the accuracy is unchanged. The improved model can be deployed on edge terminals, providing efficient and accurate gesture recognition.

Abstract Research on low‐light image enhancement focuses on improving image quality in dim conditions. Recently, deep learning has driven significant advancements, with many studies using neural networks to enhance low‐light images. However, most focus on complex network designs to increase nonlinearity, often neglecting the implicit information from local image transformations. This paper introduces an improved U‐net‐based method for low‐light enhancement, retaining the original encoding network and adding branch links in the decoding network. The method uses attention feature fusion to handle image noise and gradients separately, adjusting brightness through a gradient‐adaptive transform. This approach optimizes performance using loss functions like peak signal‐to‐noise ratio and colour consistency. Unlike previous methods, the approach emphasizes extracting implicit information from image gradients, achieving enhancement that aligns with the original brightness distribution. The result is enhanced images with high detail similarity to the original, achieved through end‐to‐end inference in experiments.

Abstract Aiming at the problem of low detection accuracy caused by overlapping occlusion and noise disturbance, a contraband detection algorithm for X‐ray security inspection images based on global semantic enhancement is proposed to achieve accurate contraband target detection by enhancing global semantic information. First, the disturbance suppression module is used to weaken the noise disturbance at different positions by local suppression and aggregate finer detail information. Then, the parallel cascade search module is used to capture long‐range dependencies and strengthen the representation of global semantic information, which helps the model identify contraband under overlapping occlusion. Finally, the contribution of different features is adaptively adjusted through the feature‐weighted fusion module, which promotes the effective fusion of multi‐scale features and improves the accuracy of model detection. The method in this article has been extensively evaluated and experimented on three mainstream benchmark datasets: SIXray, OPIXray, and PIDray. The mAPs of three datasets reach 93.5%, 91.9%, and 85.9%, respectively. The experimental results fully demonstrate that the method in this article has better performance compared with the latest method, which can meet the practical application requirements of real‐time target detection.

Abstract Unsupervised anomaly detection, often approached as a one‐class classification problem, is a critical task in computer vision. Knowledge distillation has emerged as a promising technique for enhancing anomaly detection accuracy, especially with the advent of reverse distillation networks that employ encoder–decoder architectures. This study introduces a novel reverse knowledge distillation framework known as RDMS, which incorporates a pretrained teacher encoding module, a multi‐level feature fusion connection module, and a student decoding module consisting of three independent decoders. RDMS is designed to distill distinct features from the teacher encoder, mitigating overfitting issues associated with similar or identical teacher–student structures. The model achieves an average of 99.3% image‐level AUROC and 98.34% pixel‐level AUROC on the MVTec‐AD dataset and demonstrates state‐of‐the‐art performance on the more challenging BTAD dataset. The RDMS model's high accuracy in anomaly detection and localization underscores the potential of multi‐student reverse distillation to advance unsupervised anomaly detection capabilities. The source code is available at https://github.com/zihengchen777/RDMS

Abstract POSIT is a numerical system consists of sign, regime, exponential, and fraction bits to overcome some limitations of the IEEE‐754 floating point (FP) representation. This work proposes a technique to hide critical information in the least significant bits (LSBs) of the POSIT FP representation by exploiting approximate computing (AC). The proposed technique, called information hiding using POSIT and LSB (IHUPL), explores the opportunities offered by both the POSIT representation and the AC to hide information with a minimum loss in accuracy and other performance metrics. IHUPL offers two options for hiding information: either by embedding one digit of each character into each pixel or by embedding all the digits of the character at the same time into each pixel of the alpha‐red, green, blue, or black/white image. Experimental results are evaluated for benchmark images and showed that IHUPL enhanced the accuracy of embedding data into LSB of POSIT FP by an average of 5%, the image quality improvement rates of IHUPL are 19% and 16% for options 1 and 2, respectively. Besides the encoding method using IHUPL, the paper outlines an extraction decoding technique that saves the original replacement bits in a key‐image to recover the hidden security message.

Abstract The technology for face‐to‐sketch synthesis transforms optical face images into a sketch‐style format. However, traditional style losses are insufficient to discern the modal differences between optical and sketch domain images, leading to unclear images. At the same time, generated images lack clarity due to traditional approaches' disregard for high‐frequency texture. To address these issues, a modality separation approach for facial sketch synthesis is proposed. First, a modality separation structure is proposed, using a quicksort algorithm to merge features of optical and sketch images as target modality (positive samples), ensuring the generated images' feature distribution matches real sketches. By controlling the Euclidean distance between generated images (anchors) and both target and filtered modality (positive and negative samples), irrelevant information is effectively filtered out. Next, an edge‐promoting module feeds processed blurry sketch images into the discriminator to enhance robustness. Lastly, a detail optimization module uses Laplacian filtering to extract high‐frequency texture from optical face images for local enhancement. Experimental validation on CUHK, AR, and XM2VTS datasets shows that this method outperforms mainstream sketch face synthesis methods in terms of Fréchet inception distance and learned perceptual image patch similarity, producing more realistic and natural images with richer texture details.

Abstract This research investigates advanced approaches in medical image analysis, specifically focusing on segmentation and classification techniques, as well as their integration into multi‐task architectures for lung infections. This research begins by explaining key architectural models used in segmentation and classification tasks. The study extends to the enhancement of these architectures through attention modules and conditional random fields. Relevant datasets and evaluation metrics, incorporating discussions on loss functions are also reviewed. This review encompasses recent advancements in single‐task and multi‐task models, highlighting innovations in semi‐supervised, self‐supervised, few‐shot, and zero‐shot learning techniques. Empirical analysis is conducted on both single‐task and multi‐task architectures, predominantly utilizing the U‐Net framework, and is applied across multiple datasets for segmentation and classification tasks. Results demonstrate the effectiveness of these models and provide insights into the strengths and limitations of different approaches. This research contributes to improved detection and diagnosis of lung infections by offering a comprehensive overview of current methodologies and their practical applications.

Abstract Conventional computed tomography (CT) images often suffer from blurred edges and unclear details. Image super‐resolution methods can significantly enhance CT image quality, thereby improving diagnostic accuracy. To better extract detailed features and enhance the cascading effects of different feature levels, we propose a novel medical image super‐resolution algorithm that integrates discrete wavelet transform and multi‐scale adaptive feature selection. Our approach uses both the low‐resolution image and its high‐frequency component from the frequency domain as network inputs, with the high‐frequency component providing learning supervision, which enhances detail fidelity in reconstruction. Additionally, we introduce a multi‐scale adaptive feature selection module to learn from different layers of CT images and their inter‐layer correlations. Finally, the pixel information is efficiently integrated by a coordinate attention mechanism incorporating the concept of squeeze excitation. Experimental results show that our method outperforms state‐of‐the‐art methods, achieving superior reconstruction at scale factors of 2, 4, and 8, especially at scale factor 8, where it surpasses others by 1.12 in PSNR, 0.0145 in SSIM, and 0.0038 in LPIPS. Visually, our method also delivers more accurate details and better perceptual quality.

Abstract Pancreas segmentation has great significance in computer‐aided diagnosis of pancreatic diseases. The small size of the pancreas, high variability in shape, and blurred edges make the task of pancreas segmentation challenging. A new model called SEY‐Net is proposed to solve the above problems, which is a one‐stage model with multi‐inputs. SEY‐Net is composed of three main components. Firstly, the edge information extraction (EIE) module is designed to improve the segmentation accuracy of the pancreas boundary. Then, the SE_ResNet50 is selected as the encoder's backbone to fit the size of the pancreas. Finally, the dual cross‐attention is integrated into the skip connection to better focus on the variable shape of the pancreas. The experimental results shows that the proposed method has better performance and outperforms the other existing state‐of‐the‐art pancreas segmentation methods.

Abstract Fisheye cameras have been widely used in autonomous navigation, visual surveillance, and automatic driving. Due to severe geometric distortion, fisheye images cannot be processed effectively by conventional methods. The existing object detection algorithms cannot better detect the small targets or the objects with large distortion in the fisheye images. The size and scene of available fisheye datasets (such as WoodScape and VOC‐360) cannot satisfy the training of robust network models. Herein, the authors propose Swin‐Fisheye, an end‐to‐end object detection algorithm based on Swin Transformer. A feature pyramid module based on deformable convolution (DFPM) is designed to obtain richer contextual information from the multi‐scale feature maps. In addition, a projection transformation algorithm (PTA) is proposed, which can convert rectilinear images into fisheye images more accurately, and then create a fisheye image dataset (COCO‐Fish). The results of extensive experiments conducted on VOC‐360, WoodScape, and COCO‐Fish demonstrate that the proposed algorithm can achieve satisfactory results compared with state‐of‐the‐art methods.

Abstract Detecting taxi passengers is crucial for assessing taxi driver behavior, which plays a significant role in regulating the taxi industry. Despite the advancements in deep learning, object detection algorithms have not been extensively applied to this domain. In this article, an innovative taxi passenger detection algorithm is introduced based on YOLOv8, a lightweight and highly accurate method designed to automatically monitor driver behavior and regulate the taxi industry. To address the challenge of deploying complex object detection models on mobile devices, the ghost module is incorporated in place of standard convolutions within the C2f module, thereby making the model more lightweight. Furthermore, the model's performance is enhanced by integrating an improved version of Frequency Channel Attention (FCA), termed Parallel Frequency Channel Attention (PFCA), which boosts detection accuracy with minimal additional parameters and computational overhead. Experimental results on a specific taxi passenger dataset demonstrate that the proposed method significantly outperforms the baseline YOLOv8n model. Specifically, the model reduces the number of parameters and floating point operations by 12.96% and 8.18%, respectively, while achieving increases in mAP50 and mAP50‐95 by 0.27 and 0.73 percentage points, respectively.

Abstract Unmanned aerial vehicle insulator detection that aims to recognize defective insulators from transmission lines has made significant progress in recent years. However, it still faces challenges, such as the complex background of aerial images and the small memory of unmanned aerial vehicles. This paper proposes a refined insulator detection algorithm that integrates the attention mechanism in YOLOv8 to improve the feature extraction ability. Specifically, this paper introduces a fast vision transformers structure in the you only look once (YOLO) v8 backbone section to enhance feature extraction by capturing local and global features. Additionally, the global attention mechanism is incorporated in the neck for additional feature extraction by merging comprehensive spatial and channel information into the output. Furthermore, we amalgamate depth‐wise convolution, graph convolution, and residual operation in the global attention mechanism module. This design can mitigate the issues of gradient vanishing or exploding and meanwhile enhance the distinction between spatial attention and channel attention. The proposed model is then applied to a public dataset and a set of real images from a specific power station, and the detection results show that it outperforms many competitors in terms of accuracy, efficiency, and memory size.

Abstract Detecting small targets in infrared images is crucial for ground surveillance and air traffic control. However, distinguishing small infrared targets from similar backgrounds is challenging due to their lack of structural and textural characteristics. To address these challenges, this study proposes a novel global information‐aware network with global interaction graph attention (GIGA) for infrared small target detection. The GIGA consists of a global interaction layer (GILayer), graph attention weights (GAW), and a global relational learning (GRL) module. Specifically, the GILayer dynamically learns global inter‐pixel relationships of small target images by enhancing the dependencies between feature dimensions. The GAW component calculates pixel‐by‐pixel similarity across the entire feature map using graph attention mechanisms, while the GRL module retains critical similarity features in the feature extraction network, thereby facilitating small target detection. Additionally, the multi‐scale context fusion module utilises self‐attention and dilation convolution to complement richer feature details at different scales. Experimental results on both natural and synthetic datasets demonstrate the proposed method's superiority over other state‐of‐the‐art conventional and deep learning approaches in infrared small target detection.

Abstract In recent years, deep learning models have dramatically influenced image inpainting. However, many existing studies still suffer from over‐smoothed or blurred textures when missing regions are large or contain rich visual details. To restore textures at a fine‐grained level, a multi‐stage inpainting approach is proposed, which applies a series of partial inpainting modules as well as a progressive inpainting module to inpaint missing areas from their boundaries to the centre successively. Some improvements are made on the partial convolutions to reduce artifacts like blurriness, which require a convolution kernel to contain known pixels more than a certain proportion. Towards photorealistic inpainting results, the intermediate outputs from each stage are used to compute the loss. Finally, to facilitate the training process, a multi‐step training is designed that progressively adds inpainting modules to optimize the model. Experiments show that this method outperforms the current excellent techniques on the publicly available datasets: CelebA, Places2 and Paris StreetView.

Abstract Target detection in autonomous driving tasks presents a complex and critical challenge due to the diversity of targets and the intricacy of the environment. To address this issue, this paper proposes an enhanced YOLOv8 model. Firstly, the original large target detection head is removed and replaced with a detection head tailored for small targets and high‐level semantic details. Secondly, an adaptive feature fusion method is proposed, where input feature maps are processed using dilated convolutions with different dilation rates, followed by adaptive feature fusion to generate adaptive weights. Finally, an improved attention mechanism is incorporated to enhance the model's focus on target regions. Additionally, the impact of Group Shuffle Convolution (GSConv) on the model's detection speed is investigated. Validated on two public datasets, the model achieves a mean Average Precision (mAP) of 53.7% and 53.5%. Although introducing GSConv results in a slight decrease in mAP, it significantly improves frames per second. These findings underscore the effectiveness of the proposed model in autonomous driving tasks.

Abstract Semantic segmentation is a fundamental computer vision task, and deep learning methods have been successfully applied to this field. However, target morphology continues to exhibit the incomplete prediction problem, which is attributable to the low feature utilisation and the insufficiency of spatial location information. This paper proposes a novel cross fusion network with unit attention mechanism (CF‐Net) for semantic segmentation. The two hallmarks of the framework are the usage of a multi‐scale fusion module and the unit attention mechanism. Multi‐scale fusion module can integrate multi‐branch outputs with different receptive fields, which obtain fine‐grained target details and visual contextual information. The cross fusion network is optimised with a unit attention mechanism to fuse intermediate features, which enables the acquisition of more accurate and effective spatial location information while maintaining consistency in feature space. The experimental results demonstrate that the proposed CF‐Net outperforms favourably comparable with other existing methods on the CamVid, Cityscapes, and PASCAL VOC 2012 databases, which also verifies the Effectiveness and reliability of our method.