Advances in optimization theory have been made systematically by the desire to solve more and more complicated geometric structures that are realised in contemporary applications. This is a rigorous investigation of monotone vector fields and proximal algorithms in the deep geometrical setting of generalized metric spaces (G-metric spaces). Our study fills a general deficiency in the literature by generalizing classical monotonicity principles and proximal point algorithms to support the complex three-point distance structure of G-metric spaces. In this way, by conducting a strict theoretical study, we prove the existence and uniqueness of solutions in the concept of monotone inclusion, are able to develop effective proximal algorithms with guaranteed convergence rates, and illustrate their successful application in different areas of practice. Theoretical contributions that we have made include: (1) the extension of monotonicity theory in all its forms to G-metric spaces with complete characterizations, (2) the construction of strongly convergent proximal point algorithms that are explicit in rate of convergence, and (3) its application to variational inequalities and multi-objective optimization problems in non-standard geometries, where the old metric structures are no longer applicable. Our findings create new opportunities to deal with optimization problems in complex networks, social systems, and the present-day machine learning paradigms.
We study the discrete Cavalieri estimator under systematic sampling from a finite population, which models an object represented by a finite sequence of blocks along a sampling axis. For a fixed population size and a sample size that divides it, we characterize when the estimator has zero variance, namely exactness, through an explicit balance condition that characterizes the zero-variance populations; this turns out to be a simple linear family. We then ask when exactness continues to hold if the sample size is allowed to vary within the even divisors of an even population size. In that case, we prove that exactness across all such even sample sizes necessarily implies the matched-pairs condition that is known to be sufficient at a fixed even sample size. We also derive a variance formula showing that it depends only on how much the sums over certain groups differ from their average. This leads to a concrete partitioning objective for choosing an ordering and helps explain why exact optimization quickly becomes impractical. Guided by this objective and by smooth fractionator practice, we discuss simple heuristics and show that a pairing-based ordering is exact under a simple affine model and remains stable under bounded perturbations.
Accurate malignancy prediction in breast ultrasound imaging is challenged by limited annotated data, high inter-observer variability, and inherent noise in sonographic textures. To address these limitations, we propose a deep learning framework that synergistically integrates multiscale feature fusion and self-supervised learning (SSL) to improve diagnostic performance while minimizing reliance on labeled datasets. The architecture employs a hierarchical convolutional backbone with multiscale feature extractors that capture both coarse contextual semantics and fine-grained morphological cues of lesions. Features across multiple receptive fields are fused via a top-down multiscale fusion strategy using bilinear upsampling and channel concatenation, enhancing the model’s ability to localize and characterize malignant regions. We applied a self-supervised contrastive learning approach tailored for medical ultrasound, incorporating spatial transformation invariance and anatomical context preservation to learn domain-relevant representations from unlabeled data. The pretrained encoder is fine-tuned with a supervised classification head using a limited set of annotated images. Extensive experiments on two publicly available breast ultrasound datasets demonstrate that our model achieves higher performance over state-of-the-art baselines, yielding significant improvements in AUC, F1-score, and sensitivity. Ablation studies confirm the individual and combined efficacy of the multiscale fusion and SSL modules. This work establishes a scalable and label-efficient pipeline for ultrasound-based malignancy prediction, with implications for real-time clinical decision support.
Applying a Wiener-Khintchine type theorem for random point fields, the estimation of the pair correlation function via the frequency domain is presented, which offers certain advantages over conventional estimation, especially for large datasets. The discretization of the point data, i.e., its mapping onto a grid, can be viewed as a digital image, where this mapping includes regularization of the data. Using a fast Fourier transform and its co-transform, the estimation of the pair correlation is consistently embedded in the field of digital image analysis. Finally, building upon this technique, an estimator of the density of the Bartlett spectrum is derived, whose normalization is known in scattering theory as the structure factor. The suitability of the estimators is demonstrated with examples.
Image-based disease diagnosis and treatment have long been used to enhance human health and well-being. Recent advancements in imaging and image processing technologies have spurred significant research in this field, leading to improvement in image modalities that allow better representation of features, ultimately helping healthcare practitioners make more precise diagnoses and treatment plans. Various medical image modalities, including X-rays, Positron Emission Tomography (PET), Computer Tomography (CT), and Magnetic Resonance Imaging (MRI), are widely used. Each modality has its strengths; for instance, MRI provides detailed anatomical information, while PET reveals functional and metabolic data. However, using these modalities separately limits diagnostic potential, as they cannot provide a comprehensive view of both structure and function. The Image Fusion Model (IFM) is designed to overcome this limitation by combining features from both images. Existing IFMs often face challenges such as the loss of high-frequency details, insufficient retention of structural data, and poor preservation of functional information. The proposed model integrates the Fast Discrete Cosine Transform (FDCT), the HSV color model, and a Dual-Channel Pulse-Coupled Neural Network (DC-PCNN) to address these challenges. The model was evaluated using eight MRI and PET image pairs from the Harvard Medical School Image Database, demonstrating competitive performance in terms of spatial frequency (SF), mutual information (MI), image entropy (IE), image quality index (IQI), and margin information retention (MIR). The results show that the proposed model outperforms traditional methods, particularly in preserving high-frequency details while maintaining both structural and functional data integrity.
Histochemical studies of striated muscles are the most widely used tool for examining their functional properties. The fibres that make up these muscles can be identified by revealing the enzymes involved in contraction, which makes it possible to determine whether they perform resistance (aerobic) or strength (anaerobic) functions. These functions are analysed by comparing the physiological cross-sectional areas of the muscles, regardless of the number of fibres that constitute them or their individual diameters. Areas are measured using an estimated stereological point counting technique in which points are associated with surfaces. This work proposes an automatic, computerised measurement method using the histomorphometric programme Metamorph and compares the results obtained through both methods.
Accurate diagnosis of vocal fold disorders is difficult because of subtle variations between pathological conditions. Phonovibrography (PVG), generated from high-speed videoendoscopy (HSV), documents glottal vibration patterns as static images, allowing systemic analysis. In our study, we propose PVGNet, a hybrid deep learning model combining multiscale feature extraction and channel attention, designed specifically for PVG-based classification. We benchmark PVGNet against InceptionResNetV2, VGG19, DenseNet169, and X-ViT across binary, tertiary, and multi-class tasks. PVGNet continuously outperforms baselines in accuracy, F1-score, and AUC, by minimizing false negatives, which is important for reliable diagnosis. These results show PVG’s potential as a diagnostic imaging modality and PVGNet’s effectiveness in automated voice disorder classification.
Immunohistochemistry (IHC) is essential in diagnostic pathology but is often constrained by cost, time, and limited tissue availability. Virtual IHC staining, which predicts IHC stains from standard hematoxylin and eosin (H&E) images, presents a promising alternative. This study introduces a novel Conditional Generative Adversarial Network (cGAN) architecture based on a U-Net with depthwise separable convolutions to enhance the accuracy and efficiency of virtual IHC staining. This architectural refinement improves computational efficiency while preserving high image quality. We trained and evaluated our model using the BCI and MIST datasets and compared its performance against established image-to-image translation techniques, including Pix2Pix, CycleGAN, and a U-Net variant with standard convolutions. Performance was assessed using quantitative metrics such as Peak Signal-to-Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Fréchet Inception Distance (FID). The results showed that our model outperformed these benchmarks, achieving higher PSNR and SSIM scores, lower MAE and RMSE values, and a significantly reduced FID, indicating superior image quality and closer resemblance to ground-truth IHC images. Furthermore, the integration of depthwise separable convolutions led to a notable decrease in inference time and model size, improving its feasibility for clinical applications. These findings highlight the potential of our method as a significant advancement in virtual IHC staining, offering improved accuracy, efficiency, and suitability for broader clinical use.
Quantitative analysis of mast cell (MC) morphology and degranulation states is crucial for assessing inflammatory responses and therapeutic efficacy in biomedical research. This study presents a novel two-stage deep learning framework for the automated quantitative morphological analysis of MC degranulation states in toluidine blue-stained histological sections. We constructed a specialized dataset of 1,054 rat tissue images. In the detection stage, YOLOv11m achieved superior performance with a mean average precision (mAP@0.5) of 84% for locating MCs amidst complex tissue backgrounds. In the classification stage, using the model we previously acquired to extract pure mast cell images, EfficientNetV2-S attained an accuracy of 89.6% ± 2.1% in discriminating degranulation states through fine-grained morphological analysis. Critically, Class Activation Mapping (CAM) visualization demonstrated that the model’s decision logic aligns precisely with pathological features of degranulation—such as membrane rupture and granule dispersal—thereby providing interpretable morphological evidence for automated classification. The proposed framework effectively decouples the tasks of cell localization and state classification, offering a robust, efficient, and morphologically interpretable solution for quantitative image analysis in histopathology. This approach has significant applications in acupuncture mechanism research and can be extended to other fields requiring granular structure analysis.
Consider a triaxial ellipsoid K of surface area S. Fix an arbitrary point P in the interior of K, that is P ∈ K°, and generate a sectioning plane L32[P] through P, whose normal direction u is uniform random on the unit hemisphere S2+. In the ellipse of section K ∩ L32[P], let M and m denote the lengths of the major and minor principal semiaxes, respectively, and let r denote the distance of P from the ellipse centre. Then Ŝ = 2π(M² + m² + r²) is an unbiased estimator of S. The purpose of this paper is to express Ŝ in terms of the eight parameters involved, namely the lengths of the three principal semiaxes of K, the three Cartesian coordinates of P, and the two spherical polar coordinates (φ, θ) of u. Then Var(Ŝ) is accessible via a double definite integral in (φ, θ), which can be evaluated quickly with available software for any K and any choice of point P ∈ K°.
This paper studies randomized algorithms for unbiased numerical integration of d-dimensional periodic functions using kernel-based quadrature rules, with particular emphasis on rules induced by periodic radial basis function (RBF) kernels. The integration points are either deterministically generated or locally perturbed and then randomly shifted, introducing structured randomness into the scheme. The analysis builds on tools from the theory of reproducing kernel Hilbert spaces (RKHS) and Sobolev interpolation. It is shown that the resulting estimators achieve optimal variance decay rates, effectively capturing the smoothness of the integrand even when the assumed regularity is overestimated. The work is motivated by Cavalieri volume estimation, a classical problem in stereology. The theoretical results generalize this framework to higher dimensions and provide a Fourier-based perspective on smoothness, yielding a flexible and mathematically grounded alternative for randomized quadrature with periodic structure.
Red blood cells (RBCs) exhibit a variety of morphologies that reflect their physiological or pathological state. Accurate classification of these shapes is essential for clinical diagnostics and hematological research. While most current classification methods rely on two-dimensional (2D) imaging, typically obtained through smear preparations that distort the natural three-dimensional (3D) structure of RBCs, these approaches often fail to capture diagnostically relevant 3D shape information and may lead to misclassification. In this work, we propose a novel method for 3D shape classification of RBCs based on two geometric descriptors: the spherical shape factor (F) and the bending energy (E). These descriptors are estimated directly from confocal microscopy image stacks using stereological techniques, thus avoiding the need for full 3D reconstruction. This stereological framework provides efficient, reproducible, and unbiased estimates of morphological features from sets of parallel planar sections. We demonstrate the effectiveness of this approach on a dataset that includes both standard erythrocyte SDE cell types (discocytes, stomatocytes, spherocytes, and echinocytes) and various abnormal morphologies.
In this paper, we present recurrence relations for the Jacobi weighted orthogonal polynomials P-n,r((alpha,beta ,gamma)) (u, v, w) with r = 0,1, ... ,n, where n >= 0, defined on the triangular domain T = {(u, v, w) : u, v, w >= 0, u + v + w = 1} for values of alpha, beta, gamma > -1. In particular, we construct univariate recurrence relations for Jacobi polynomials when w = 0, considering three specific cases. These recurrence relations provide an efficient and straightforward alternative for computing Jacobi polynomials, offering a simpler approach compared to traditional methods.
Effective classification of medical images is vital for accurate diagnosis and treatment, but noisy datasets remain a significant challenge, obscuring critical features and leading to unreliable predictions. To address this, we propose RobustDeiT, a noise-robust architecture based on the Data-efficient Image Transformer (DeiT), tailored for medical image classification in noisy environments. By integrating a multi-stage preprocessing pipeline, our approach systematically reduces noise, enhances contrast, and highlights fine details, ensuring the preservation of essential features. Advanced denoising methods, contrast enhancement with Contrast Limited Adaptive Histogram Equalization, and sharpening via unsharp masking collectively improve image quality, enabling the model to extract meaningful patterns. Extensive evaluations demonstrate that RobustDeiT achieves superior performance across diverse metrics, establishing its effectiveness in handling noisy medical imaging datasets and paving the way for reliable and accurate classification in real-world scenarios.
Skin damage is one of the most frequent side effects during radiotherapy in patients with cancer diseases. In this study, the stereological method was used to assess the level of CD31 and CD34 expression on the skin microvascular endothelial cells after radiotherapy. We collected thirty radiation-ulcer skin samples, each of which has three studied regions: area of ulcer, adjacent area and unwounded area. We found that the surface density (Sv) and length density (Lv) of blood vessel with CD31 and CD34 positive decreased significantly from center to outside of the ulcer. We conclude that stereological method could be used to evaluate the results of CD31 and CD34 expression on skin microvascular endothelial cells after radiotherapy. Moreover, the success of our study may permit to following application of this morphological quantitative method for analysis of further immunohistochemistry studies.
Johan Debayle, professor at the Institut Mines-T´el´ecom (IMT), deputy director of the Georges Friedel Laboratory and the Center for the Science of Industrial and Natural Processes (SPIN) at Mines Saint-Étienne, passed away on Thursday, September 5, 2024. He was also an adjunct professor at Gadjah Mada University (UGM) in Indonesia.
The tomato salad problem describes a stereological bias in the microscopic characterization of particulate systems, particularly in transmission electron microscopy (TEM). When a thin section is prepared from a material containing dispersed particles, the observed particle size distribution in micrographs may differ from the true distribution due to truncation effects and sampling bias. Depending on the initial size distribution, the observed mean particle size may appear smaller or larger than the actual mean. This work presents a Monte Carlo simulation of the tomato salad problem, implemented in R, to study the effects of foil thickness and particle size distribution on observed size measurements. Simulated results are compared with analytical predictions, showing good agreement. The study also highlights the impact of stochastic sampling errors, which can exceed the bias introduced by the tomato salad problem, emphasizing the need for sufficient sampling in microscopic analysis. The developed simulation may serve as an educational tool and could be extended in future work to analyze non-spherical particles and sample preparation artifacts.
Image mosaic is of significance in various areas such as object tracking and drone reconnaissance. Aiming at the problems of poor performance and high rate of false match in foggy images, an improved stitching method based on local guided KAZE and dark channel prior is proposed. First of all, the KAZE algorithm is utilized for rough feature matching. Secondly, a local fixed point asymptotic method is introduced to optimize the global objective and eliminate mismatched point pairs. Then, the warp images are obtained by the estimated transformation matrix. Thirdly, the compensation of color and luminance difference of the overlap is applied to the overall image, which improves the inhomogeneity of stitching image. Eventually, the final result is obtained by enhancing algorithm based on dark channel prior. The proposed algorithm is assessed through intuitive renderings and quantitative values. Furthermore, the proposed method is compared with other common stitching methods. The results reveal that the method proposed in this paper gives the best performance in terms of the magnitude of feature matching pairs, the mean absolute error (MAE), the root mean square error (RMSE) and the processing time.
In this paper, we propose a novel method for palmprint classification. We extract the central region from the palmprint image, calculate eight filter faces (FF) from the region based on eight pairs of filters, compute the Fourier features from each FF, classify each of them to one known class, and then perform majority voting to determine the final class label of the unknown palmprint image. By examining the structures of the selected filters, we can see that our new method can suppress random noise and at the same time it can extract directional features from the palmprint images. This is the main reason why FF-based methods are better than non-FF-based methods for palmprint classification. In addition, the majority winning policy (voting) based on eight FFs improves classification accuracies significantly. Experimental results demonstrate that our new method outperforms several existing methods for palmprint classification.
With the advancement of target detection technology, the need for accurate detection of complex scenes is becoming increasingly important in various industries. This can not only improve productivity, but also ensure public safety. However, the current mainstream target detection algorithms have some problems in dealing with complex scenes, for example, some detection models are not able to detect in real time, and the accuracy of the model is degraded when facing disturbing factors such as target occlusion, and low-contrast scenes. In order for these problems to be mitigated, this paper proposes a lightweight convolution LDGConv (LightweightDepthGhost Convolution), which is utilized to improve the YOLOv8 network model by replacing part of the traditional convolution of the Neck network with this convolution, and improving the bottleneck module in a lightweight way. In addition, we add the Coordinate Attention mechanism to the Neck part. Our proposed model improves mAP50 on the VOC dataset by 1.3% while reducing computation and parameters by 9.8% and 15.3%, respectively, compared to the original model. In the experiments on the steel surface defects dataset NEU-DET, our model overall outperforms the current mainstream detection models. The model is capable of high-precision and low-computational-cost target detection, thus saving labor costs and improving public health and safety and productivity.
