Anisotropic Diffusion Research Articles

Enhanced osmosis model with bilateral total variation for effective shadow removal

This research paper presents an innovative technique for shadow images removal. The method involves redefining a contemporary osmosis model by incorporating bilateral total variation (TV) operators. This integration allows to take advantage of robust anisotropic diffusion, resulting in improved image restoration. The paper also outlines new mathematical derivation of the bilateral TV and a combination with nonlinear anisotropic transport term. The experimental results substantiate the effectiveness of the anisotropic osmosis model, showcasing its superior qualitative and quantitative performance when compared to current state-of-the-art techniques.

Manipulating formation of different InGaAs/GaAs nanostructures via tailoring As4 flux

This research provides a flexible approach to manipulate formation of InGaAs nanostructures on the GaAs (100) surface by varying arsenic (As4) beam equivalent pressure (BEP). By selecting the As4/(In+Ga) BEP ratio to be 4, 8, 20, 50 and 100, we were able to obtain different quantum structures from quantum well (QW) to quantum dots (QDs), then to spatially ordered quantum dot chains (QD-chains), and finally to quantum wires (QWRs), respectively. This transformation of nanostructures was explained by anisotropic surface diffusion coupled with the strain relieving Stranski–Krastanov growth mode, while the anisotropy was modulated by increasing As4 flux and subsequently enhanced by multilayer-stacking growth with a suitable spacer thickness. Photoluminescence characteristics show correlation to the nanostructure morphology for each sample. In particular, the formation of QD-chains and QWRs results in anisotropic features that offer potential device applications.

Effects of Anisotropy, Convection, and Relaxation on Nonlinear Reaction-Diffusion Systems

The effects of relaxation, convection, and anisotropy on a two-dimensional, two-equation system of nonlinearly coupled, second-order hyperbolic, advection–reaction–diffusion equations are studied numerically by means of a three-time-level linearized finite difference method. The formulation utilizes a frame-indifferent constitutive equation for the heat and mass diffusion fluxes, taking into account the tensorial character of the thermal diffusivity of heat and mass diffusion. This approach results in a large system of linear algebraic equations at each time level. It is shown that the effects of relaxation are small although they may be noticeable initially if the relaxation times are smaller than the characteristic residence, diffusion, and reaction times. It is also shown that the anisotropy associated with one of the dependent variables does not have an important role in the reaction wave dynamics, whereas the anisotropy of the other dependent variable results in transitions from spiral waves to either large or small curvature reaction fronts. Convection is found to play an important role in the reaction front dynamics depending on the vortex circulation and radius and the anisotropy of the two dependent variables. For clockwise-rotating vortices of large diameter, patterns similar to those observed in planar mixing layers have been found for anisotropic diffusion tensors.

Feature Extraction and Identification of Rheumatoid Nodules Using Advanced Image Processing Techniques

Background/Objectives: Accurate detection and classification of nodules in medical images, particularly rheumatoid nodules, are critical due to the varying nature of these nodules, where their specific type is often unknown before analysis. This study addresses the challenges of multi-class prediction in nodule detection, with a specific focus on rheumatoid nodules, by employing a comprehensive approach to feature extraction and classification. We utilized a diverse dataset of nodules, including rheumatoid nodules sourced from the DermNet dataset and local rheumatologists. Method: This study integrates 62 features, combining traditional image characteristics with advanced graph-based features derived from a superpixel graph constructed through Delaunay triangulation. The key steps include image preprocessing with anisotropic diffusion and Retinex enhancement, superpixel segmentation using SLIC, and graph-based feature extraction. Texture analysis was performed using Gray-Level Co-occurrence Matrix (GLCM) metrics, while shape analysis was conducted with Fourier descriptors. Vascular pattern recognition, crucial for identifying rheumatoid nodules, was enhanced using the Frangi filter. A Hybrid CNN–Transformer model was employed for feature fusion, and feature selection and hyperparameter tuning were optimized using Gray Wolf Optimization (GWO) and Particle Swarm Optimization (PSO). Feature importance was assessed using SHAP values. Results: The proposed methodology achieved an accuracy of 85%, with a precision of 0.85, a recall of 0.89, and an F1 measure of 0.87, demonstrating the effectiveness of the approach in detecting and classifying rheumatoid nodules in both binary and multi-class classification scenarios. Conclusions: This study presents a robust tool for the detection and classification of nodules, particularly rheumatoid nodules, in medical imaging, offering significant potential for improving diagnostic accuracy and aiding in the early identification of rheumatoid conditions.

19F NMR relaxation of buried tryptophan side chains suggest anisotropic rotational diffusion of the protein RfaH.

The recent application of 19F NMR in the study of biomolecular structure and dynamics has made it a potentially attractive probe to complement traditional 15N/13C labelled probes for backbone and sidechain dynamics, albeit with some complications. The utility of 15N relaxation rates of rigid backbone amide groups to determine the rotational diffusion tensor of proteins is well established. Here we show that the measured 19F relaxation rates of two buried and possibly immobile 19F labelled tryptophan sidechains for the multidomain protein RfaH, in its closed conformation, are in reasonable agreement with the calculated values, only when anisotropic rotational diffusion of the protein is considered. While the sparsity of 19F relaxation data from a limited number of probes precludes the experimental determination of the rotational diffusion tensor here, these results demonstrate the influence of rotational diffusion anisotropy of proteins on 19F NMR relaxation of rigid tryptophan sidechains, while adding to the expanding literature of 19F NMR relaxation data sets in biomolecules.

A unified structure-preserving parametric finite element method for anisotropic surface diffusion

We propose and analyze a unified structure-preserving parametric finite element method (SP-PFEM) for the anisotropic surface diffusion of curves in two dimensions ( d = 2 ) (d=2) and surfaces in three dimensions ( d = 3 ) (d=3) with an arbitrary anisotropic surface energy density γ ( n ) \gamma (\boldsymbol {n}) , where n ∈ S d − 1 \boldsymbol {n}\in \mathbb {S}^{d-1} represents the outward unit vector. By introducing a novel unified surface energy matrix G k ( n ) \boldsymbol {G}_k(\boldsymbol {n}) depending on γ ( n ) \gamma (\boldsymbol {n}) , the Cahn-Hoffman ξ \boldsymbol {\xi } -vector and a stabilizing function k ( n ) : S d − 1 → R k(\boldsymbol {n}):\ \mathbb {S}^{d-1}\to {\mathbb R} , we obtain a unified and conservative variational formulation for the anisotropic surface diffusion via different surface differential operators, including the surface gradient operator, the surface divergence operator and the surface Laplace-Beltrami operator. A SP-PFEM discretization is presented for the variational problem. In order to establish the unconditional energy stability of the proposed SP-PFEM under a very mild condition on γ ( n ) \gamma (\boldsymbol {n}) , we propose a new framework via local energy estimate for proving energy stability/structure-preserving properties of the parametric finite element method for the anisotropic surface diffusion. This framework sheds light on how to prove unconditional energy stability of other numerical methods for geometric partial differential equations. Extensive numerical results are reported to demonstrate the efficiency and accuracy as well as structure-preserving properties of the proposed SP-PFEM for the anisotropic surface diffusion with arbitrary anisotropic surface energy density γ ( n ) \gamma (\boldsymbol {n}) arising from different applications.

Detection and classification on MRI images of brain tumor using YOLO NAS deep learning model

If a brain tumor is not properly diagnosed, it might result in fatal consequences and major health issues. As a result, a key component of diagnosis is the early identification of brain tumors and the precise categorization of brain tumor types. This research work focusses on detection and classification such as pituitary, meningioma, glioma, and non-tumorous tumors from brain tumor MRI image using YOLO NAS model. Advances in deep learning have led to an increasing awareness of computer-aided diagnosis technology. To improve classification performance, the input data set is acquired from the REMBRANDT repository using the Digital Database of Brain Tumor Magnetic Resonance Images. The primary phases of this task include segmentation, classification, and pre-processing. The researcher preprocessed the RGB image to exclude any undesired spots before locating the ROI. For each brain tumor image, we used the hybrid anisotropic diffusion filtering (HADF) technique to remove noise. The Encoder-Decoder Network (En–DeNet), which uses a deep neural network based on U-Net as the encoder and a pre-trained EfficientNet as the decoder, is then used to segment the MRI images. A proposed model was developed using a deep learning-based YOLO NAS technique to identify brain cancers from MRI images such as meningioma tumors, non-tumor, glioma tumors, and pituitary tumors. The suggested model's classification performance is weighed based on parameters such as precision, F1-score, sensitivity, accuracy, and specificity. The proposed fusion method YOLO NAS has improved classification results of accuracy (AC = 0.997%), specificity (SP = 0.985%), precision (PR = 0.982%), F1-score (F1 = 0.992%), and sensitivity (SE = 0.985%) using 2570 MRI data for training and 630 data for testing and validation of brain tumor cases. The results show that the brain tumor type classification system based on the proposed YOLO NAS technique works better than the DNN, PDCNN, DenseNet-161, and DCNN-SGD model classifiers.

Modelling and Analysis of Advanced Dynamic Learning Techniques and Anisotropic Diffusion Filtering for Automated Crack Detection in Civil Structures

This study introduces a cutting-edge automated system that leverages dynamic learning methods for detecting cracks in civil structures. By combining pioneering preprocessing techniques with leading-edge machine learning algorithms, the proposed system aims to surpass the constraints of conventional manual inspection approaches. The methodology incorporates Anisotropic Diffusion Non-Local Mean Filtering (ADNLMF) for noise reduction and YOLO v3 for precise object detection. The system's effectiveness is substantiated using an extensive dataset, displaying substantial enhancements in both accuracy and efficiency.

Simulated hydrogen diffusion in diamond grain boundaries

To evaluate hydrogen diffusion within diamond, a series of molecular dynamics simulations have been carried out in which diffusion coefficients and activation energies were determined. Diamond grown via chemical vapour deposition (CVD) contains a high hydrogen concentration within grain boundaries, because of this, common tilt grain boundaries were recreated from transmission electron microscopy images taken from literature. Diffusion coefficients of hydrogen placed within the grain boundary were estimated and compared to the bulk diffusion. Unlike many crystalline structures, some grain boundaries presented limited diffusion when compared to the bulk. Diffusion characteristics of grain boundaries are thought to be a result of channelling effects combined with the formation of sp3C-H bonds with sp2 carbon present within some grain boundaries - increasing and decreasing diffusion rates respectively. Potential wells were observed across some but not all the grain boundaries resulting in hydrogen trapping and anisotropic diffusion.

Analysis of methods and algorithms for image filtering and quality enhancement

This paper addresses the prevalent issue of image noise and presents methods for its mitigation. The paper describes, analyses and tests a variety of image filtering techniques, with specific reference to their use in different contexts. The filtering methods can be classified into two principal categories: linear filters, which include the Gaussian and mean filters, and non-linear filters, which comprise the median filter, the Fast Fourier Transform (FFT), the Non-Local Means (NLM) filter, and the anisotropic diffusion filter. The efficacy of each filter is mathematically described and evaluated on RGB images using the Python programming language. The study delineates the evaluation metrics and their respective advantages and disadvantages. The Root Mean Square Error (RMSE) and Peak Signal-to-Noise Ratio (PSNR) are employed as criteria for the analysis of algorithm efficiency. Furthermore, the mean execution time for each algorithm is also monitored. The experimental data suggests that linear filters are relatively fast but produce inferior results and are best employed as preparatory measures. Non-linear filters have been demonstrated to be more robust and applicable to a variety of noise types, although it has been established that they require parameter fine-tuning. The study demonstrates that anisotropic diffusion is suitable for both manual image processing and real-time applications, offering an optimal balance between processing speed and denoised image quality. NLM is optimal for high-quality single image processing due to its superior results, despite a slower processing speed. FFT is noted for its efficiency in eliminating periodic noise. Further research will be conducted on advancing filtering techniques for different real-world scenarios and autonomous systems.

Analysis of an iterative reconstruction method in comparison of the standard reconstruction method

ABSTRACT We present a detailed analysis of a new iterative density reconstruction algorithm. This algorithm uses a decreasing smoothing scale to better reconstruct the density field in Lagrangian space. We implement this algorithm to run on the quijote simulations, and extend it to (a) include a smoothing kernel that smoothly goes from anisotropic to isotropic, and (b) a variant that does not correct for redshift space distortions. We compare the performance of this algorithm with the standard reconstruction method. Our examinations of the methods include cross-correlation of the reconstructed density field with the linear density field, reconstructed two-point functions, and BAO parameter fitting. We also examine the impact of various parameters, such as smoothing scale, anisotropic smoothing, tracer type/bias, and the inclusion of second order perturbation theory. We find that the two reconstruction algorithms are comparable in most of the areas we examine. In particular, both algorithms give consistent fittings of BAO parameters. The fits are robust over a range of smoothing scales. We find the iterative algorithm is significantly better at removing redshift space distortions. The new algorithm will be a promising method to be employed in the ongoing and future large-scale structure surveys.

Evaluating the Impact of Filtering Techniques on Deep Learning-Based Brain Tumour Segmentation

Gliomas are a common and aggressive kind of brain tumour that is difficult to diagnose due to their infiltrative development, variable clinical presentation, and complex behaviour, making them an important focus in neuro-oncology. Segmentation of brain tumour images is critical for improving diagnosis, prognosis, and treatment options. Manually segmenting brain tumours is time-consuming and challenging. Automatic segmentation algorithms can significantly improve the accuracy and efficiency of tumour identification, thus improving treatment planning and outcomes. Deep learning-based segmentation tumours have shown significant advances in the last few years. This study evaluates the impact of four denoising filters, namely median, Gaussian, anisotropic diffusion, and bilateral, on tumour detection and segmentation. The U-Net architecture is applied for the segmentation of 3064 contrast-enhanced magnetic resonance images from 233 patients diagnosed with meningiomas, gliomas, and pituitary tumours. The results of this work demonstrate that bilateral filtering yields superior outcomes, proving to be a robust and computationally efficient approach in brain tumour segmentation. This method reduces the processing time by 12 epochs, which in turn contributes to lowering greenhouse gas emissions by optimizing computational resources and minimizing energy consumption.

Electrochemical-mechanical coupled interfacial degradation model of Ternary polymer composite cathodes in all-solid-state batteries

Despite significant attention focused on the composite cathode composed of active particles, which is considered to increase the interfacial areas and satisfy high areal load, suffers from interfacial issues. In this article, we formulate an electrochemical-mechanical model of LiNixMnyCozO2 (NMC) composite cathode coupling the relations between interfacial degradation, charge transformation, diffusion transport, and mechanical deformation under cyclic loads. Based on the transition state theory, we regard the interfacial degradation as an energy barrier dependent on the interfacial debonding state. Physical mismatch due to chemical expansion results in interfacial current distinction, anisotropic Li diffusion and excessive local stress. Compared to single-crystal NMC particles, the effect of interfacial separation and internal cracks triggers an extremely nonuniformity of Li distribution within random orientation polycrystalline-type particles. The external pressure in the range of operation can cause mechanical deformation to fill in the interface vacancies, which effectively alleviates the rapid growth of damage and provides a better cyclic performance. Moreover, soft polymer-based solid electrolytes take advantage of their flexible property to deal with solid-solid contact, providing considerable maintenance of interface stability. This present framework reveals the failure mechanism with electrochemical-mechanical coupled relations for composite cathode materials and broadens the design guidance toward improving interfacial integrity.

Compactness results for a Dirichlet energy of nonlocal gradient with applications

AbstractWe prove two compactness results for function spaces with finite Dirichlet energy of half‐space nonlocal gradients. In each of these results, we provide sufficient conditions on a sequence of kernel functions that guarantee the asymptotic compact embedding of the associated nonlocal function spaces into the class of square‐integrable functions. Moreover, we will demonstrate that the sequence of nonlocal function spaces converges in an appropriate sense to a limiting function space. As an application, we prove uniform Poincaré‐type inequalities for sequence of half‐space gradient operators. We also apply the compactness result to demonstrate the convergence of appropriately parameterized nonlocal heterogeneous anisotropic diffusion problems. We will construct asymptotically compatible schemes for these type of problems. Another application concerns the convergence and robust discretization of a nonlocal optimal control problem.

Enhancing photoacoustic imaging for lung diagnostics and BCI communication: simulation of cavity structures artifact generation and evaluation of noise reduction techniques.

Pandemics like COVID-19 have highlighted the potential of Photoacoustic imaging (PAI) for Brain-Computer Interface (BCI) communication and lung diagnostics. However, PAI struggles with the clear imaging of blood vessels in areas like the lungs and brain due to their cavity structures. This paper presents a simulation model to analyze the generation and propagation mechanism within phantom tissues of PAI artifacts, focusing on the evaluation of both Anisotropic diffusion filtering (ADF) and Non-local mean (NLM) filtering, which significantly reduce noise and eliminate artifacts and signify a pivotal point for selecting artifact-removal algorithms under varying conditions of light distribution. Experimental validation demonstrated the efficacy of our technique, elucidating the effect of light source uniformity on artifact-removal performance. The NLM filtering simulation and ADF experimental validation increased the peak signal-to-noise ratio by 11.33% and 18.1%, respectively. The proposed technique adds a promising dimension for BCI and is an accurate imaging solution for diagnosing lung diseases.

How the zebra got its stripes: Curvature-dependent diffusion orients Turing patterns on three-dimensional surfaces.

Many animals have patterned fur, feathers, or scales, such as the stripes of a zebra. Turing models, or reaction-diffusion systems, are a class of mathematical models of interacting species that have been successfully used to generate animal-like patterns for many species. When diffusion of the inhibitor is high enough relative to the activator, a diffusion-driven instability can spontaneously form patterns. However, it is not just the type of pattern but also the orientation that matters, and it remains unclear how patterns are oriented in practice. Here, we propose a mechanism by which the curvature of the surface influences the rate of diffusion, and can recapture the correct orientation of stripes on models of a zebra and of a cat in numerical simulations. Previous work has shown how anisotropic diffusion can give stripe forming reaction-diffusion systems a bias in orientation. From the observation that zebra stripes run around the direction of highest curvature, that is around the torso and legs, we apply this result by modifying the anisotropic diffusion rates based on the local curvature. These results show how local geometry can influence the reaction dynamics to give robust, global-scale patterns. Overall, this model proposes a coupling between the system geometry and reaction-diffusion dynamics that can give global control over the patterning by using only local curvature information. Such a model can give shape and positioning information in animal development without the need for spatially dependent morphogen gradients.

A Study on Resolving Dynamic analysis using deep learning Framework Logical Methods

Deep learning technologies have gained a great deal of interest in recent months for demonstrating material removal capabilities in a variety of separation, categorization, as well as other machine vision activities. The majority of these deep networks are built employing convolution or completely convolution structures. Our suggested Dynamic and Static gestures System guided by a hand gesture high dimensional data methodology We use a snapshot of a human's thoracic spine to determine the person's depth and the size of the space around his or her hands. In this research, we provide a novel object-based deep-learning framework for semantic segmentation of extremely high-resolution satellite data. In specifically, we leverage object-based prior record by augmenting a fully convolutional neural network's training strategy with an anisotropic diffusion data pre-processing phase and an additional loss term. The goal of this restricted framework is to ensure that similar visual data is assigned to the same semantic class. Here, we employ intermediate steps based on traditional image processing techniques to aid in the resolution of the subsequent problem of classification, detection, or segmentation. Research shows that adding pre- and post-processing steps to a deep learning pipeline can boost model performance over using only the network. Recent advances in UQ algorithms used for deep learning are analysed, and their potential for use in relevance feedback is addressed. It also emphasizes basic research difficulties and directions linked with UQ. Quantifiably, man-made classes with more precise geometry, such as buildings, benefited the most from our strategy, particularly along object borders, indicating the developed approach's enormous potential. The purpose of this paper is to offer an overview of the approaches used inside deep learning frameworks to either appropriately prepare the input (pre-processing) or enhance the outcomes of the network output (post-processing), with an emphasis on digital pathology image analysis.

Image Enhancement Using Bidimensional Empirical Mode Decomposition and Morphological Operations for Brain Tumor Detection and Classification.

The three steps of brain image processing – preprocessing, segmentation, and classification are becoming increasingly important in patient care. The aim of this article is to present a proposed method in the mentioned three-steps, with emphasis on the preprocessing step, which includes noise removal and contrast enhancement. The fast and adaptive bidimensional empirical mode decomposition and the anisotropic diffusion equation as well as the modified combination of top-hat and bottom-hat transforms are used for noise reduction and contrast enhancement. Fast C-means clustering with enhanced image is used to detect tumors and the tumor cluster corresponds to the maximum centroid. Finally, Ensemble learning is used for classification. The Figshare brain tumor dataset contains magnetic resonance images used for data selection. The optimal parameters for both noise reduction and contrast enhancement are investigated using a tumor contaminated with Gaussian noise. The results are evaluated against state-of-the-art results and qualitative performance metrics to demonstrate the dominance of the proposed approach. The fast C-means algorithm is applied to detect tumors using twelve enhanced images. The detected tumors were compared to the ground truth and showed an accuracy and specificity of 99% each, and a sensitivity and precision of 90% each. Six statistical features are retrieved from 150 enhanced images using wavelet packet coefficients at level 4 of the Daubechies 4 wavelet function. These features are used to develop the classifier model using ensemble learning to create a model with training and testing accuracy of 96.7% and 76.7%, respectively. When this model is applied to classify twelve detected tumor images, the accuracy is 75%; there are three misclassified images, all of which belong to the pituitary disease group. Based on the research, it appears that the proposed approach could lead to the development of computer-aided diagnosis (CADx) software that physicians can use as a reference for the treatment of rain tumor.

Perona-Malik Diffusion-Driven Regularization for Image Resolution Enhancement in Electrical Capacitance Tomography

Electrical Capacitance Tomography (ECT) is a non-invasive promising method for monitoring industrial processes, such as oil-gas flow in pipelines and solid-gas flow in pneumatic systems. Despite its potential benefits, ECT generates poor-quality images, often used only for qualitative analysis. A non-linear relationship between measured capacitances and permittivity distribution and the ill-posedness of the sensitivity matrix elements causes this limitation. This hinders the applicability of ECT in monitoring online industrial process applications. This work proposes a reconstruction method based on a nonlinear diffusion function to generate high-quality images from the measured capacitance data from the ECT system. The diffusion regularization functional helps to remove noise and preserve semantic features. Experimental results reveal that the proposed method generates high-quality and visually appealing images with a 15% reduction in distribution error and a 10% increase in correlation coefficient compared to state-of-the-art methods such as linear back projection and projected landweber. This allows further investigation into how nonlinear anisotropic diffusion can improve the applicability of ECT systems in industrial control and monitoring.

Detection of Encroachment in Civil Structure Using Dynamic Learning Techniques

Identifying cracks through visual inspection and automated surveys are both effective methods. While both approaches yield satisfactory distress analysis results, automated crack recognition technology stands out for its speed and cost-effectiveness compared to traditional human visual detection methods. This study introduces an innovative approach, namely "crack encroachment in concrete structures classified using DCNN" which employs a Deep Convolutional Neural Network. To enhance the precision of crack detection, the input image undergoes denoising through ADNLMF (Anisotropic Diffusion Non-Local Mean Filtering), preserving edges, textures, and features. Crack discrimination between crack and non-crack images was achieved using Yolo v3, and a deep convolutional neural network classifier was employed to identify specific crack types based on their widths, utilizing crack width transform. This method not only enhances accuracy but also reduces network complexity and processing time. A comprehensive performance comparison with existing crack identification techniques indicates that our proposed methodology for concrete structure crack recognition produces superior results.