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Quantitative counting of fry is required for multiple reasons, including breeding, transportation, and sales and creating a fish-counting algorithm using image processing technology is proposed as a useful method. The images for fish fry were preprocessed to extract the details of the target fish, using methods including binarization, dilation, and erosion. The thinning and the connected area algorithms were then independently adopted to count the fish fry within the image. The advantages and the disadvantages of the two algorithms under different densities were also compared, revealing that the fish fry pictures with a clear contrast between the foreground and background resulted in a higher accuracy. The main purpose of this research is to solve the problem of fry counting in the case of high density and high overlap. This research provides a reference point for this method based on image technology.

Morphological perceptrons (MPs) can be characterized as feedforward morphological neural networks (MNNs) with applications in classification and regression. The neuronal aggregation functions of current MP versions are drawn from gray-scale mathematical morphology (MM) that can be described in terms of matrix products in a lattice algebra called minimax algebra. Specifically, MPs have components each of which computes a pair-wise infimum of an erosion and an anti-dilation that can be expressed in terms of products of matrices with entries in a complete l-group extension. In this paper, we use the novel concept of an interval descriptor and an n -ary aggregation function on a bounded poset in order to generalize existing gray-scale and fuzzy morphological components (MCs) of morphological and hybrid morphological/linear perceptrons (HMLPs). In addition, we present several other examples of generalized morphological components (GMCs) that can and will be incorporated as computational units into shallow and deep artificial neural networks .

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed in [1], to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples.

How will the rise of China and other illiberal regimes affect the behaviour-shaping power of global liberal norms? The paper uses updated dyadic data on ambassadorial appointments to address this q...

Mineral image segmentation plays a vital role in the realization of machine vision based intelligent ore sorting equipment. However, the existing image segmentation methods still cannot effectively solve the problem of adhesion and overlap between mineral particles, and the segmentation performance of small and irregular particles still needs to be improved. To overcome these bottlenecks, we propose a deep learning based image segmentation method to segment the key areas in mineral images using morphological transformation to process mineral image masks. This investigation explores four aspects of the deep learning-based mineral image segmentation model, including backbone selection, module configuration, loss function construction, and its application in mineral image classification. Specifically, referring to the designs of U-Net, FCN, Seg Net, PSP Net, and DeepLab Net, this experiment uses different backbones as Encoder to building ten mineral image segmentation models with different layers, structures, and sampling methods. Simultaneously, we propose a new loss function suitable for mineral image segmentation and compare CNNs-based segmentation models' training performance under different loss functions. The experiment results show that the proposed mineral image segmentation has excellent segmentation performance, effectively solves adhesion and overlap between adjacent particles without affecting the classification accuracy. By using the Mobile Net as backbone, the PSP Net and DeepLab can achieve a high segmentation performance in mineral image segmentation tasks, and the 15 × 15 is the most suitable size for erosion element structure to process the mask images of the segmentation models.

Universal discrepancy parameters of approximations of discretely specified dependencies by analytical functions and search criteria for optimal values of their coefficients, as well as analysis of features of their application are described. Discrepancy parameters of approximations, which do not depend on the ranges of variation of the values of functions and the number of points of a discretely specified dependence, are proposed. They can be effective for objectively comparing the quality of approximations of any dependencies by any functions. Approximations of a discretely specified dependence of the mathematical expectation of the equivalent electrical resistance of a layer of aluminum granules during spark-erosion dispersion in water on the instantaneous values of the discharge current are carried out. As approximating functions, we chose a power function with an exponent factor –1 and a function based on exponential. Using the criteria of the least approximation error, the optimal values of the coefficients of both approximating functions are founded. It is shown in which cases it is advisable to use the combined search criteria for the optimal values of the coefficients of the approximating functions, and in which are enough simple one-component ones. Ref. 27, fig. 2, tables 2.

Computer‑Aided Systems can improve the performance of breast cancer diagnosis, helping the differentiation and classification of breast benign and malignant lesions. Breast lesions are strongly correlated with their shape, therefore, in this work, firstly, were used quantitative measures based on fractal dimension, which can help characterizing the smoothness or the roughness of mammographic lesion shape, being calculated through the box‑counting method, directly from manually segmented lesions, and after applying a region growing/erosion algorithm. Then, Convolutional neural networks (CNN), which recently have been successfully used in the medical field to detect and classify pathologies in different imaging modalities, were applied in mammographic images. Since the mammographic databases have a restricted number of samples, one way to solve this problem is using a transfer learning approach, in which a CNN, previously pre-trained with a large amount of labelled non-medical data, is subsequently finetuned using a smaller dataset of mammographic images. In this study were applied three different pre-trained networks and were made an evaluation if their performance to classify lesions in mammograms is affected by the use, or not, of normalized images. Was also evaluated the performance of a support vector machine fed with features extracted from the CNN and the combined use of handcrafted features to complement the CNN-extracted features. The obtained results are encouraging and reveal that both use of fractal dimension and CNN can help to improve computer-aided diagnostic of mammographic lesions, with AUC values around 81.3%.

Temporomandibular joint (TMJ) is one of the most important, unique and structurally has the highest complex synovial system in the body (1, 2). TMJ, encompassing the temporal bone, mandibular condyle and articular disc, is a diarthrodial joint. As a collective form, Temporomandibular Joint Disorders (TMD) is often with multifactorial etiologies, and these diseases can more commonly affect the soft-tissue components of the TMJ including the articular disc and posterior attachment, the osseous components of the TMJ and also the related muscles (3, 4). The most common cause of the regional orofacial pain of non-dental origin is a result of TMD. Additional symptoms may include TMJ sounds such as clicking, pumping, limited or asymmetric mandibular movement (5). As TMJ is covered by a layer of fibrocartilage, unlike other joints in the human body, the mandibular condyles can be damaged due to cartilage degeneration. In addition, arthritis can also be initiated because of the particular dynamics in the maxillofacial area (6). TMD's are frequently associated with degenerative bone changes which can involve the bone structures of the TMJ such as erosion, flattening, osteophytes, subchondral bone sclerosis and pseudocysts (7). To correctly diagnose the dysfunctions associated with the disease and for adequate treatment planning Knowledge about these bone changes is fundamental (8).

The observation and analyses of cores are the bases of various studies on oil and gas exploration and development. However, the real natural cores suffer from their own instability and constant weathering or erosion as well as experimental damages, leading to the changes of their physical and chemical characteristics. Digital cores can address the above issues by core digitalization and then reusing the original core images or data without damaging the real samples. The 3D reconstruction of pore space actually is an important step for the construction of 3D digital cores. There are two main ways for the reconstruction of pore space including physical experimental methods and numerical reconstruction methods. Physical experimental methods usually are quite time-consuming and expensive while numerical reconstruction methods are relatively inexpensive and more efficient. With the flourishing development of deep learning and its variants, the reconstruction of pore space possibly can benefit from the strong inherent ability of extracting characteristics from training images (TIs) hidden in deep learning. This paper proposes a reconstruction method using a deep residual deconvolution network (DRDN), considered as a variant of deep learning, in which the characteristics of TI are learned by using constant residual convolution in training and then the pore space is reconstructed by adding the previous residual convolution results to each deconvolution layer. Compared to some other typical numerical reconstruction methods, our method shows its efficiency and practicability in the reconstruction of 3D pore space.

In the industrial process, the safety and reliability of the mechanical system determine the quality of the product, and whether small faults can be diagnosed in time is the key to ensuring the safe operation of the system and restraining the deterioration of faults. In recent years, the data-driven fault diagnosis has attracted widespread attention in academia. However, the traditional data-driven fault diagnosis methods rely on the features extracted from expert systems, so that the effect of fault diagnosis is entirely reliant on how well the expert system can extract the features. This paper proposes a new fault diagnosis method based on AlexNet Convolutional neural network (CNN) from a data-driven perspective. Firstly, a new method for converting time-domain vibration signal into RGB image based on erosion operation (EOSTI) is proposed. Initially converted three-dimensional (3-D) images have relatively close structural elements and are difficult to identify. For such defects, the target separated RGB image is generated. Secondly, explore the classification accuracy of AlexNet to make it more suitable for fault classification of different bearing datasets. Finally, the proposed method which is tested on two datasets, including coal washing machine dataset, maintenance fault dataset, has achieved prediction accuracy of 99.43 % and 99.67 %, respectively. The results have been compared with other methods. The comparisons show the effectiveness and accuracy of the proposed approach. The result shows that this method is feasible in engineering practice.

A new fast method for pupil detection and eyetracking real time is being developed based on the study of a boundary-step model of a grayscale image by the Laplacian-Gaussian operator and finding a new proposed descriptor of accumulated differences (point identifier), which displays a measure of the equidistance of each point from the boundaries of some relative monotonous area (for example, the pupil of the eye). The operation of this descriptor is based on the assumption that the pupil in the frame is the most rounded monotonic region with a high brightness difference at the border, the pixels of the region should have an intensity less than a predetermined threshold (but the pupil may not be the darkest region in the image). Taking into account all of the above characteristics of the pupil, the descriptor allows achieving high detection accuracy of its center and size, in contrast to methods based on threshold image segmentation, based on the assumption of the pupil as the darkest area, morphological methods (recursive morphological erosion), correlation or methods that investigate only the boundary image model (Hough transform and its variations with two-dimensional and three-dimensional parameter spaces, the Starburst algorithm, Swirski, RANSAC, ElSe). The possibility of representing the pupil tracking problem as a multidimensional unconstrained optimization problem and its solution by the Hook-Jeeves non-gradient method, where the function expressing the descriptor is used as the objective function, is investigated. In this case, there is no need to calculate the descriptor for each point of the image (compiling a special accumulator function), which significantly speeds up the work of the method. The proposed descriptor and method were analyzed, and a software package was developed in Python 3 (visualization) and C ++ (tracking kernel) in the laboratory of the Physics and Mathematics Faculty of Kamchatka State University of Vitus Bering, which allows illustrating the work of the method and tracking the pupil in real time.

Computer vision algorithms are important for many areas of human activity. In particular, the number of applications related to the need to process images of real-world objects with computerized tools and the subsequent use of descriptive information in a variety of interactive and automated decision-making systems is increased. An important tool for analyzing real-world scenes are approaches to the application of stereo vision algorithms. The important step of many stereo matching algorithms is a disparity map. Depending on the content of the observed scene, part of the values on the disparity map can be immediately attributed to background values on a certain basis, or form a "natural" background, which is characterized by loss of informative data due to unacceptable error of subsequent resultant distance values. The calculated disparity map of any algorithm may contain some shortcomings in the form of discontinuities of continuous information areas caused by the complexity of shooting conditions, the impact of noise of various natures, hardware imperfections, and so on. An approach to mitigating the undesirable influence of negative factors on the resulting disparity is the use of mathematical morphology operations to process disparity maps at the post-processing stage. This paper presents information technology for increasing the content of disparity maps based on the mathematical morphology methods. The technology is based on a combination of morphological operations of erosion and dilation, which eliminates the typical problems of discontinuities of monotone regions and erroneous values on disparity maps. The proposed approach allows reducing the impact of common problems that arise during the operation of stereo matching algorithms, as well as increase the overall informativeness of disparity maps for images of real objects in the absence of partial or complete initial data on the characteristics of the observed scene. The results of testing morphological operations with disparity maps for real objects allow us to conclude about the possibility of partial restoration of areas of disparity maps with gaps in continuous information areas, as well as to reduce the impact of random anomalous values on the overall content of the disparity maps.

The sequential application of erosion–abrasion is an innovative technique for shaping of electrically conductive objects but the integrated effect of erosion–abrasion in shaping makes the process c...

Recent trends in automation industries focus on the recognition and classification of various patterns of part families. In this context, It is proposed to design and develop a “Reference Based Dimension Prediction (RDP) System” for recognition and classification of part families in various industrial components along with determination of dimensions effectively. RDP system works in sequential phases namely; a). Capturing the image of component b). Converting the image into gray scale followed by smoothing of image by using Gaussian filter c). Transforming the blurred gray image into ‘Canny’ image d). Noise removal of ‘Canny’ image by applying threshold to it e). Dilation and erosion operation on resultant image f). Resultant image act as input to RDP system and g). Creation of reference Object. Further, Dimensions are predicted by RDP system by facilitating Euclidean Distance and Manhattan Distance Method along with Reference object which included as a part of input image. Reference Based Dimension Prediction System employs methodology related to dimensions of design and manufacturing attributes which predicts in referencing the dimensions of other reference object. In this framework, the pixel density of the reference object is used to compute prediction for determining the dimensions of unknown object. The experimental results obtained using proposed referencing dimension prediction model achieves 99% precision in predicting dimensions which is further used to identify and classify the part family.

Convolutional neural networks (CNNs) have becomequite popular for solving many different tasks in remote sensingdata processing. The convolution is a linear operation whichextracts features from the input data. However, nonlinear operationsare able to better characterize the internal relationshipsand hidden patterns within complex remote sensing data, suchas hyperspectral images (HSIs). Morphological operations arepowerful nonlinear transformations for feature extraction thatpreserve the essential characteristics of the image, such asborders, shape and structural information. In this paper, anew end-to-end morphological deep learning framework (calledMorphConvHyperNet) is introduced. The proposed approachefficiently models nonlinear information during the trainingprocess of HSI classification. Specifically our method includesspectral and spatial morphological blocks to extract relevantfeatures from the HSI input data. These morphological blocksconsist of two basic 2D morphological operators (erosion anddilation) in the respective layers, followed by a weighted combinationof the feature maps. Both layers can successfully encodethe nonlinear information related to shape and size, playing animportant role in classification performance. Our experimentalresults, obtained on five widely used HSIs, reveal that our newlyproposed MorphConvHyperNet offers comparable (and evensuperior) performance when compared to traditional 2D and 3DCNNs for HSI classification.

We propose a new type of curvature flow for curves in 2D and surfaces in 3D. The flow is inspired by the mathematical morphology opening and closing operations. These operations are classically defined by composition of dilation and erosion operations. In practice, existing methods implemented this way will result in re-discretizing the entire shape, even if some parts of the surface do not change. Instead, our surface-only curvature-based flow moves the surface selectively in areas that should be repositioned. In our triangle mesh discretization, vertices in regions unaffected by the opening or closing will remain exactly in place and do not affect our method's complexity, which is output-sensitive.

One of the challenges in materials science is to design functional, synthetic polymers that match the desired properties of a specific application. Achieving high stiffness and strength under physi...

Elbow erosion monitoring is of great significance to the safety of pipeline systems and maintenance personnel. This paper proposes a new elbow erosion monitoring method, which combines the PZT (lead zirconate titanate) enabled active sensing with the fractional Fourier transform (FrRT), and takes the fractional-order energy peak of the stress wave signal as the damage index. Three 90°-elbows and three 90°-elbow assemblies were used in the experimental studies. Under different erosion degrees, the mass reduction of the three separate elbows was measured by high-precision electronic scale and the residual thickness of the three elbow assemblies was detected by ultrasonic thickness gauge. Two pieces of PZT patches were respectively used to excite and receive the signals in the active sensing. FrFT was used to distinguish the linear sweep signal components of stress wave signals from the energy of other interference or noise signals, and the fractional-order energy peak was used as the damage index. The results show that there is a one-to-one relationship between mass of erosion loss and damage index. Compared with the traditional time domain signal energy method, the new method has the advantage of eliminating the saturation phenomenon. The proposed method and damage index proposed in this paper will be a promising tool for real-time monitoring of elbow erosion.

We consider the periodic boundary value problem for the nonlocal erosion equation with two spatial variables and obtain sufficient conditions for the existence and stability of spatially inhomogeneous cycles. We analyze the boundary value problem in the case where the length of the domain is essentially greater than the width and obtain conditions for the existence of sufficiently many spatially inhomogeneous cycles depending on both spatial variables. For narrow domains the problem is reduced to analyzing an auxiliary boundary value problem for the Ginzburg–Landau equation.

Land Cover (LC) plays a key role in many disciplines and its classification from optical imagery is one of the prevalent applications of remote sensing. Besides years of researches and innovation on LC, the classification of some areas of the World is still challenging due to environmental and climatic constraints, such as the one of the mountainous chains. In this contribution, we propose a specific methodology for the classification of the Land Cover in mountainous areas using Sentinel 2, 1C-level imagery. The classification considers some specific high-altitude mountainous classes: clustered bare soils that are particularly prone to erosion, glaciers, and solid-rocky areas. It consists of a pixel-based multi-epochs classification using random forest algorithm performed in Google Earth Engine (GEE). The study area is located in the western Alps between Italy and France and the analyzed dataset refers to 2017–2019 imagery captured in the summertime only. The dataset was pre-processed, enriched of derivative features (radiometric, histogram-based and textural). A workflow for the reduction of the computational effort for the classification, which includes correlation and importance analysis of input features, was developed. Each image of the dataset was separately classified using random forest classification algorithm and then aggregated each other by the most frequent pixel value. The results show the high impact of textural features in the separation of the mountainous-specific classes the overall accuracy of the final classification achieves 0.945.

Benggang are characterized by deep-cut slopes with various shapes and depressions on the vast weathered crust slopes in southern China. The gully heads have been continuously collapsed and eroded to form a chair-like erosion landforms. It develops rapidly, and leads to large amounts of erosion, with the hazards of damaging land resources, destroying basic farmland, and deteriorating ecological environment. To study and manage Benggang, the primary task is to discover it. Traditional methods based on local in-situ investigations, which are not only labour-consuming but also inefficient. These methods are difficult to meet the needs of large-scale investigations of Benggang. This paper proposes a method for automatic Benggang recognition based on Ultra-High Resolution (UHR) DOM (Digital Orthophoto Map) and DSM (Digital Surface Model) obtained from UAV (Unmanned Aerial Vehicle) survey. This method adopts a Bag of Visual-Topographical Words (BoV-TW) model. The local features extracted from DOM and DSM are represented based on BoV-TW, and fused by Latent Dirichlet Allocation (LDA). Finally Support Vector Machine (SVM) is adopted as a supervised classifier to achieve high-precision automatic Benggang recognition. Experimental results prove that the total accuracy of our method can be maintained at about 95%, with recall and precision above 80% (the highest are 97.22% and 94.44%, respectively), which are significantly higher than the methods of using only DOM local features and using only BoV-TW.

Tooth-erosion is the surface loss of dental hard tissue mostly associated with an acid attack. The aim was to compare dentin and enamel erosion depth measurements using micro-computed tomography (microCT) and light microscopy (LM). Enamel/dentin blocks were prepared from caries-free human molar-teeth (N = 12). Teeth were sectioned to a rectangular shape of 4 × 4 × 6 mm. Specimens were treated with water (NC) or 1.0% citric-acid solution (PC). After treatment, specimens were scanned with micro-computed tomography. On completion, specimens were sectioned and observed under a light-microscope. Lesion depth was observed with 10× magnification and images transferred to Simpleware software. Vertical distance from lesion surface to bottom was measured. Pearson correlation test was used to evaluate correlation and Wilcoxon Signed Rank test to evaluate differences in the two-analysis methods. Mean enamel erosion depth was 0.63 and 38.38 μm (microCT) and 0.54 and 39.43 μm (LM) for NC and PC, respectively. Dentin erosion depth was 0.72 and 48.05 μm (microCT) and 0.56 and 49.92 μm (LM) for NC and PC, respectively. There was a significant correlation between the two-analysis methods (r = 0.998; p < .001). No statistically significant difference in results were obtained when microCT and LM were compared (p = .584). This results obtained from the current study suggested that erosion depth measurements made using microCT and LM yielded comparable results. The microCT method is preferred if the conservation of specimens is desired.

This study employed a digital evaluation approach for determining the nodule size of a no heat-treatment pearlite structure, as well as the grain size of the ferrite phase via an image morphology process methodology. The grain size of steel has great influence on the mechanical properties of manufactured materials, making it a necessary metallographic inspection item for materials. The properties affected by grain size include hardness, failure life, ultimate stress, electric characteristics, and heat expansion rate. In general, grain size inspection has two approaches: manual comparison and digital computation. In manual comparison, the comparison of standard graphics or the observation of an eyepiece inserted on a microscope can be progressed. For digital computation, planimetric and intercept procedures are applied according to international standards. This study thus applied an image processing algorithm to identify the observed image after undergoing seven times of erosion and dilation operations.

Exposed aggregate is a typical feature of the abrasion erosion in stilling basin slabs concrete surface. Although a variety of underwater robots are designed for inspection, the exposed aggregate detection for identifying abrasion is often done by manual work. The scarcity of image samples, large differences in aggregate size, color and shape are the main difficulties in automatic detection. To address this problem, an improved Attention U-Net deep fully convolutional network-based detection method was proposed. To realize this method, underwater images in site were captured via a self-developed operated underwater robot. Through randomly separating and the cropping of the 128 underwater images, the 512×512 pixels images dataset was built according to the ratio of 8:1:1, including 408 training images, 52 validation images and 52 test images. After the data augmentation, loss function and the optimizer were carefully designed and selected, the proposed Attention U-Net architecture was evaluated on this dataset. For comparative research, the full convolution network (FCN) and U-Net network were trained with the same training and validation dataset. The performance comparison on the test dataset showed that the Attention U-Net architecture has better detection accuracy.

The persistence diagram of Cohen-Steiner, Edelsbrunner, and Harer was recently generalized by Patel to the case of constructible persistence modules with values in a symmetric monoidal category with images. Patel also introduced a distance for persistence diagrams, the erosion distance. Motivated by this work, we extend the erosion distance to a distance of rank invariants of generalized persistence modules by using the generalization of the interleaving distance of Bubenik, de Silva, and Scott as a guideline. This extension of the erosion distance also gives, as a special case, a distance for multidimensional persistent homology groups with torsion introduced by Frosini. We show that the erosion distance is stable with respect to the interleaving distance, and that it gives a lower bound for the natural pseudo-distance in the case of sublevel set persistent homology of continuous functions., 23 pages

This part of the paper presents the relation between the working conditions, nozzle geometry, nozzle diameter, and jet behavior. Experimental work has been made by impinging the submerged jets on the copper specimen as a target for a period of time. The mass loss and erosion rate at various conditions were measured, calculated and analyzed. For the visualization, a high-speed camera was used and the obtained data were processed to measure parameters which are used to characterize the clouds. Correlations among the jet dynamic power, the cavity length, erosion rate, and the pertinent experimental parameters are apparent. In addition, formulas are proposed to conveniently compare the efficiency of jetting systems based on working conditions. Based on the mathematical analyses of the obtained results a new form for cavitation number calculation is proposed.

Purpose AccuBoost is a complex non-invasive brachytherapy procedure for breast treatment. This technique requires a radiation oncologist to manually select applicator grid position and size by overlaying transparencies over a mammographic image to encompass surgical clips and resected tumor bed. An algorithm was developed in MATLAB™ to automate the selection of round applicators based on surgical clip position. Material and methods A total of 42 mammograms belonging to 10 patients were retrospectively analyzed. Images were pre-processed by masking imprinted localization grid and regions around the grid. A threshold was applied to isolate high-intensity pixels and generate a binary image. A set of morphological operations including region dilation, filling, clearing border structures, and erosion were performed to segment the different regions. A support vector machine classification model was trained to categorize segmented regions as either surgical clips or miscellaneous objects based on different region properties (area, perimeter, eccentricity, circularity, minor axis length, and intensity-derived quantities). Applicator center position was determined by calculating the centroid of detected clips. Size of the applicator was determined with the smallest circle that encompassed all clips with an isotropic 1.0 cm margin. Results The clip identification model classified 946 regions, with a sensitivity of 96.6% and a specificity of 98.2%. Applicator position was correctly predicted for 20 of 42 fractions and was within 0.5 cm of physician-selected position for 33 of 42 fractions. Applicator size was correctly predicted for 25 out of 42 fractions. Conclusions The proposed algorithm provided a method to quantitatively determine applicator position and size for AccuBoost treatments, and may serve as a tool for independent verifications. The discrepancy between physician-selected and algorithm-predicted determinations of applicator position and size suggests that the methodology may be further improved by considering radiomic features of breast tissue in addition to clip position.

This study proposed a new automatic measurement method of spinal curvature on ultrasound coronal images in adolescent idiopathic scoliosis (AIS). After preprocessing of Gaussian enhancement, the symmetric information of the image was extracted using the phase congruency. Then bony features were segmented from the soft tissues and background using the greyscale polarity. The morphological methods of image erosion and top-bottom-hat transformation, and geometric moment were utilized to identify the spinous column profile from the transverse processes. Finally, the spine deformity curve was obtained using robust regression. In-vivo experiments based on AIS patients were performed to evaluate the performance of the developed method. The comparison results revealed there was a significant correlation (y = 0.81x, r = 0.86) and good agreement between the new automatic method and the manual measurement method. It can be expected that this novel method may help to provide effective and objective deformity assessment method during the ultrasound scanning for AIS patients.

ObjectivesTo determine if superimposition of sequential scans can discriminate between different fluorides at step heights less than 5 μm on natural human enamel surfaces.Materials and methodsNatural, unpolished, human enamel specimens (n = 60) were randomly assigned to one of three pre-treatment toothpaste slurries with a calcium silicate/fluoride, fluoride-only and a control. Baseline and post treatment scans, from a non-contacting profilometer with a 0.01 μm z-axis and ResultsConfidence and resolution of superimposition and subtraction of repeated profiles from unpolished enamel revealed accuracy within 1–2 μm. The technique was able to discriminate between the fluorides demonstrating statistical differences in mean (SD) 3D step height (μm) of 1.96 (0.40) and 2.75 (0.49) (p = 0.0024). There was a statistically significant increase in surface roughness for all groups after 15 min erosion compared to baseline. But no statistically significant difference between the interventions after 15 min erosion but there was compared to no fluoride (p = 0.006).ConclusionSuperimposition and subtraction of profiles could discriminate between fluoride interventions, which showed statistical differences in enamel loss differences less than 3 μm.Clinical significanceThis erosion model and data analysis workflow was able to distinguish differences between scans of 3 μm on unpolished enamel following the interaction with fluoride.

The aim of this study is geomorphometric relief classification of a temperate latitude upland area in Central Europe. The Silesian Upland represents diversified structural relief which contains a fan-shaped configuration of long thresholds and wide erosion depressions. A 20 m × 20 m digital elevation model (DEM) provided input data for the analysis. The k-median method was applied to examine morphometric variables of the relief. The aim of these activities was to identify clusters with objects of similar mathematical characteristics. These clusters were the basis of landform classification. Smaller numbers of clusters 4 transparently show hypsometric relationships. Key elements of the morphology of the area were clearly visible. The division into 6 clusters gives the best results—a detailed but clear image of the morphological diversity by distinguishing characteristic landform elements. The results for 8 clusters show significant background noise and are ambiguous, which makes them difficult to identify. Our research has confirmed that the k-median method is a useful tool for landform classifications. We determined optimal parameters of this method (filtering window size, DEM resolution, number of clusters, aspect influence).

We present an approach for segmenting an indoor unstructured point cloud into multiple rooms without additional information. Our proposed approach starts by applying a cloth simulation filter (CSF) to the raw dataset to detect point cloud-related ceiling patches without inverting the point cloud. Next, a grid map analysis is conducted for initial room segmentation. It is updated using a morphological erosion process and a neighborhood filter with an adaptive threshold. Finally, boundary recovery is utilized to correct for any incomplete room boundaries obtained from the previous steps. The capabilities and accuracy of our approach were evaluated on different point cloud datasets, and the average recall and precision were 97.13% and 96.60%, respectively. Further validation with the datasets of different levels of noise and registration errors show that this approach achieves an average recall and precision of 99.24% and 99.90%, respectively.

This paper presents a finite element model for the simulation of ice–structure interaction problems, which are dominated by crushing. The failure mode of ice depends significantly on the strain rate. At low strain rates, the ice behaves ductile, whereas at high strain rates it reacts in brittle mode. This paper focuses on the brittle mode, which is the dominating mode for ship–ice interactions. A multitude of numerical approaches for the simulation of ice can be found in the literature. Nevertheless, the literature approaches do not seem suitable for the simulation of continuous ice–structure interaction processes at low and high confinement ratios in brittle mode. Therefore, this paper seeks to simulate the ice–structure interaction with the finite element method (FEM). The objective of the here introduced Mohr-Coulomb Nodal Split (MCNS) model is to represent the essential material behavior of ice in an efficient formulation. To preserve mass and energy as much as possible, the node splitting technique is applied, instead of the frequently used element erosion technique. The intention of the presented model is not to reproduce individual cracks with high accuracy, because this is not possible with a reasonable element size, due to the large number of crack fronts forming during the ice–structure interaction process. To validate the findings of the model, the simulated maximum ice forces and contact pressures are compared with ice extrusion and double pendulum tests. During validation, the MCNS model shows a very good agreement with these experimental values.

In this paper, morphological operations on hexagonal lattices and regular hexagonal regions are applied to 2D parallel beam computerized tomography (CT) image denoising. To show some denoising effects of the morphological operations, for an input image, we add certain amount of noise to get the noised image; and perform Radon transform and inverse Radon transform on the noised image to obtain a CT image. To compare hexagonal lattices with square lattices fairly, the CT image is resampled to an image defined on a certain randomized grid, which is in turn resampled to an image defined on a hexagonal lattice and an image defined on the corresponding square lattice (with the same sampling rate), respectively. For the morphological operations, we use a structuring element defined on a hexagonal lattice and a structuring element defined on a square lattice such that those two structuring elements have the same number of ones. Each of those two images performs an erosion with the corresponding structuring element. Then use those two images as masks and use the two corresponding eroded images as makers to perform morphological image reconstructions to obtain the two reconstructed images. Finally, both usual and Phantom images are used as test images. For many different tested noise levels, the output data show that the image reconstructed on the hexagonal lattice is usually more similar to the input image than the one reconstructed on the square lattice.

The Finite Element Method has been widely employed in engineering and physical sciences due to its huge applicability that resulted in commercial software used for both industries and academic researches. Recently, those software were improved to simulate moving boundary problems, like phase change and mechanical erosion, which is a common physical process in ablation problems. The ABAQUS software affords a subroutine called UMESHMOTION, which is combined with Arbitrary Lagrangian–Eulerian Mesh to allow modeling heat-transfer with ablation. However, the subroutine must be adapted to the particular modeling for this problem. In the present work, a subroutine code was developed to investigate ablation of a material; the results were compared with results obtained from a different numerical approach, and the physical model is validated with data extracted from an experimental test case. The results obtained were physically coherent with the proposed model, and the methodology developed allows it to be used in future ablation engineering problems including nozzle thermo-structural analysis.

OBJECTIVE This article describes a digital workflow using virtual enamel evaluation and a stereolithographic template for accurate tooth preparation for a complex exogenous dental erosion. CLINICAL CONSIDERATIONS A 22-year-old man with different degrees of defects on the labial surface in esthetic area was diagnosed as exogenous dental erosion. The residual undamaged enamel area and depth of defect were measured and analyzed accurately by creating a digital virtual patient based on the pretreatment data. According to the different conditions of residual enamel and tooth defect, the treatment plans of porcelain veneer, crown and composite resin were chosen for corresponding involved teeth. Based on the virtual wax-up and the suggested material thickness, a template for tooth preparation was designed and three-dimensional printed. This template together with a special bur indicating the reduction depth accurately guided the teeth preparation and achieved a long-term effect. CONCLUSIONS The virtual enamel evaluation contributes to obtaining the appropriate corresponding treatment plan objectively. The stereolithographic template effectively meets the accuracy of tooth preparation, preserving the tooth hard tissue to the greatest extent. CLINICAL SIGNIFICANCE The digital workflow described here may provide a quantifiable evaluation method and an accurate tooth preparation method for exogenous dental erosion.

Background To estimate median liver iron concentration (LIC) calculated from magnetic resonance imaging, excluded vessels of the liver parenchyma region were defined manually. Previous works proposed the automated method for excluding vessels from the liver region. However, only user-defined liver region remained a manual process. Therefore, this work aimed to develop an automated liver region segmentation technique to automate the whole process of median LIC calculation. Methods 553 MR examinations from 471 thalassemia major patients were used in this study. LIC maps (in mg/g dry weight) were calculated and used as the input of segmentation procedures. Anatomical landmark data were detected and used to restrict ROI. After that, the liver region was segmented using fuzzy c-means clustering and reduced segmentation errors by morphological processes. According to the clinical application, erosion with a suitable size of the structuring element was applied to reduce the segmented liver region to avoid uncertainty around the edge of the liver. The segmentation results were evaluated by comparing with manual segmentation performed by a board-certified radiologist. Results The proposed method was able to produce a good grade output in approximately 81% of all data. Approximately 11% of all data required an easy modification step. The rest of the output, approximately 8%, was an unsuccessful grade and required manual intervention by a user. For the evaluation matrices, percent dice similarity coefficient (%DSC) was in the range 86–92, percent Jaccard index (%JC) was 78–86, and Hausdorff distance (H) was 14–28 mm, respectively. In this study, percent false positive (%FP) and percent false negative (%FN) were applied to evaluate under- and over-segmentation that other evaluation matrices could not handle. The average of operation times could be reduced from 10 s per case using traditional method, to 1.5 s per case using our proposed method. Conclusion The experimental results showed that the proposed method provided an effective automated liver segmentation technique, which can be applied clinically for automated median LIC calculation in thalassemia major patients.

The detection of building edges from very high resolution (VHR) remote sensing imagery is essential to various geo-related applications, including surveying and mapping, urban management, etc. Recently, the rapid development of deep convolutional neural networks (DCNNs) has achieved remarkable progress in edge detection; however, there has always been the problem of edge thickness due to the large receptive field of DCNNs. In this paper, we proposed a multi-scale erosion network (ME-Net) for building edge detection to crisp the building edge through two innovative approaches: (1) embedding an erosion module (EM) in the network to crisp the edge and (2) adding the Dice coefficient and local cross entropy of edge neighbors into the loss function to increase its sensitivity to the receptive field. In addition, a new metric, Ene, to measure the crispness of the predicted building edge was proposed. The experiment results show that ME-Net not only detects the clearest and crispest building edges, but also achieves the best OA of 98.75%, 95.00% and 95.51% on three building edge datasets, and exceeds other edge detection networks 3.17% and 0.44% at least in strict F1-score and Ene. In a word, the proposed ME-Net is an effective and practical approach for detecting crisp building edges from VHR remote sensing imagery.

Text Summarization has been an area of interest for many years. It refers to creating a concise text of a document without any lose of information. Researchers in the area of natural language processing have developed many abstractive and extractive methods for creating summary. Abstractive summaries modifies the sentences and creates a modified concise form, while extractive summaries pick relevant sentences. The extractive method used in this work is a novel one which models the document as an Intuitionistic Fuzzy Hypergraph (IFHG). The main objectives of the work are to convert a document in to an IFHG, apply morphological operations to it and to create a summary filter. This is the premier work which applies morphological operations on IFHG that is modeled on a text. The method has generated summary which is almost similar to a human generated summary and showed more accuracy when compared with other machine generated summaries. An attempt to apply skelton operation on text hypergraph is also made.

A widely used skeletonization technique is thinning, which is an iterative layer-by-layer erosion in a topology preserving way. In the conventional implementation of thinning algorithms, the deletability of all border pixels in the actual picture is to be investigated. That is why we introduced the concept of 1-attempt thinning. In the case of a 1-attempt algorithm, if a border pixel is not deletable in an iteration step, it cannot be deleted in the remaining thinning phases. This paper presents a computationally efficient implementation scheme for 1-attempt 2-subfield parallel thinning; proves that a 2-subfield parallel thinning algorithm (acting on the conventional 2D square grid) is 1-attempt; shows that 1-attempt property is useful and algorithms fulfilling this property can be implemented with a remarkable speed up.

INTRODUCTION AND OBJECTIVE:Inferior Vena Cava (IVC) filters are a common preventative tool for pulmonary embolism in high-risk patients. Erosion of a filter limb is a known entity, yet usually beni...

Fuzzy image processing involves various fuzzy approaches. These fuzzy approaches help in understanding and processing of images as fuzzy sets. Mathematical morphology is used for analysing the shapes and forms of the objects in images. In morphological methods structuring elements are applied to an input image which creates an output image of the same size. The size and shape of the neighbourhood is chosen in such a way that a morphological operation relating to different shapes in the input image is constructed. In this paper the pixel values of an image are converted to fuzzy near membership values and the corresponding image is found. Using the fuzzy near membership image, gray and binary images are formed using MATLAB. Mathematical morphology operations dilation, erosion, opening and closing for different structuring elements such as line, square, diamond, sphere, disk, cube, neighbourhood, octagon and rectangle are performed for fuzzy membership and binary images. Taking dilation and opening as upper approximations, erosion and closing as lower approximations, the exact measures are calculated for different structuring elements and the corresponding images formed. It is found that the exact measure for the structuring element neighbourhood of fuzzy near membership and binary images are exactly equal. The corresponding images are also exactly similar.

This paper first introduces the basic operations of mathematical morphology, such as erosion, expansion, opening and closing, and then introduces the hit miss transformation. Then it briefly describes the Chinese Guqin art and the music score collection of “Zheyin shiziqinpu”. Finally, the image processing of Guqin music score is carried out by using the method of mathematical morphology, Mathematical morphology has a good effect on Guqin score processing.

In this paper, we propose a 3D fully automatic joint erosion algorithms for hand HR-pQCT, and its performance can reach consensus with human specialist.

Morphological operators are nonlinear transformations commonly used in image processing. Their theoretical foundation is based on lattice theory, and it is a well-known result that a large class of image operators can be expressed in terms of two basic ones, the erosions and the dilations. In practice, useful operators can be built by combining these two operators, and the new operators can be further combined to implement more complex transformations. The possibility of implementing a compact combination that performs a complex transformation of images is particularly appealing in resource-constrained hardware scenarios. However, finding a proper combination may require a considerable trial-and-error effort. This difficulty has motivated the development of machine-learning-based approaches for designing morphological image operators. In this work, we present an overview of this topic, divided in three parts. First, we review and discuss the representation structure of morphological image operators. Then we address the problem of learning morphological image operators from data, and how representation manifests in the formulation of this problem as well as in the learned operators. In the last part we focus on recent morphological image operator learning methods that take advantage of deep-learning frameworks. We close with discussions and a list of prospective future research directions.

Code summarization aims to summarize code functionality as high-level nature language descriptions to assist in code comprehension. Recent approaches in this field mainly focus on generating summaries for code with precise identifier names, in which meaningful words can be found indicating code functionality. When faced with lexically confusing code, current approaches are likely to fail since the correlation between code lexical tokens and summaries is scarce. To tackle this problem, we propose a novel summarization framework named VECOS. VECOS introduces an erosion mechanism to conquer the model's reliance on precisely defined lexical information. To facilitate learning the eroded code's functionality, we force the representation of the eroded code to align with the representation of its original counterpart via variational inference. Experimental results show that our approach outperforms the state-of-the-art approaches to generate coherent and reliable summaries for various lexically confusing code.

The rate of erosion of a geomorphic surface depends on its local gradient and on the material fluxes over it. Since both quantities are functions of the shape of the catchment surface, this dependence constitutes a mathematical straitjacket, in the sense that – subject to simplifying assumptions about the erosion process, and absent variations in external forcing and erodibility – the rate of change of surface geometry is solely a function of surface geometry. Here we demonstrate how to use this geometric self-constraint to convert an erosion model into its equivalent Hamiltonian, and explore the implications of having a Hamiltonian description of the erosion process. To achieve this conversion, we recognize that the rate of erosion defines the velocity of surface motion in its orthogonal direction, and we express this rate in its reciprocal form as the surface-normal slowness. By rewriting surface tilt in terms of normal slowness components, and by deploying a substitution developed in geometric mechanics, we extract what is known as the fundamental metric function of the model phase space; its square is the Hamiltonian. Such a Hamiltonian provides several new ways of solving for the evolution of an erosion surface: here we use it to derive Hamilton's ray tracing equations, which describe both the velocity of a surface point and the rate of change of the surface-normal slowness at that point. In this context, erosion involves two distinct directions: (i) the surface-normal direction, which points subvertically downwards, and (ii) the erosion ray direction, which points upstream at a generally small angle to horizontal with a sign controlled by the scaling of erosion with slope. If the model erosion rate scales faster than linearly with gradient, the rays point obliquely upwards; but if erosion scales sublinearly with gradient, the rays point obliquely downwards. Analysis of the Hamiltonian shows that these rays carry boundary-condition information upstream, and that they are geodesics, meaning that erosion takes the path of least erosion time. This constitutes a definition of the variational principle governing landscape evolution. In contrast with previous studies of network self-organization, neither energy nor energy dissipation is invoked in this variational principle, only geometry.

Wood knots are scaring formed by the death of branches in the trunk, which has a great influence on the quality of logs. To accurately detect the shape and area of wood knots is of great significance to the production and processing of wood. Wood images with live knots, dead knots, rotten knots and multiple knots are processed with the gray level transformation, Gaussian filtering which are carried out successively. Otsu algorithm is used for image thresholding, followed by erosion and dilation, remove connected domains, edge markers, number of knots, roundness detection, the ratio of the areas of the knots and whole image. The results show that the contour of knots can be detected accurately after processing. The number of knots, the roundness and area of knots are determined. The algorithms mentioned above are embedded into a Graphical User Interface(GUI) by using Matlab callback functions.

Mathematical morphology has been explored in deep learning architectures, as a substitute to convolution, for problems like pattern recognition and object detection. One major advantage of using morphology in deep learning is the utility of morphological erosion and dilation. Specifically, these operations naturally embody interpretability due to their underlying connections to the analysis of geometric structures. While the use of these operations results in explainable learned filters, morphological deep learning lacks attribution modeling, i.e., a paradigm to specify what areas of the original observed image are important. Furthermore, convolution-based deep learning has achieved attribution modeling through a variety of neural eXplainable Artificial Intelligence (XAI) paradigms (e.g., saliency maps, integrated gradients, guided backpropagation, and gradient class activation mapping). Thus, a problem for morphology-based deep learning is that these XAI methods do not have a morphological interpretation due to the differences in the underlying mathematics. Herein, we extend the neural XAI paradigm of saliency maps to morphological deep learning, and by doing, so provide an example of morphological attribution modeling. Furthermore, our qualitative results highlight some advantages of using morphological attribution modeling.

This study proposes the exploitation of deep learning for quantitative assessment of visual detectability of different types of in-service damage in laminated composite structures such as aircraft and wind turbine blades. A comprehensive image-based data set is collected from the literature containing common microscale damage mechanisms (matrix cracking and fibre breakage) and macroscale damage mechanisms (impact and erosion). Then, automated classification of the damage type and severity was done by pre-trained version of AlexNet that is a stable convolutional neural network for image processing . Pre-trained ResNet-50 and 5 other user-defined convolutional neural networks were also used to evaluate the performance of AlexNet. The results demonstrated that employing AlexNet network, using the relatively small image dataset, provided the highest accuracy level (87%–96%) for identifying the damage severity and types in a reasonable computational time. The generated knowledge and the collected image data in this paper will facilitate further research and development in the field of autonomous visual inspection of composite structures with the potential to significantly reduce the costs, health & safety risks and downtime associated with integrity assessment.