Shape Descriptors Research Articles

Automatic topology and capacity generation framework for urban drainage systems with deep learning-based land use segmentation and hydrological characterization

This paper proposed a comprehensive and automated framework that integrates the entire urban drainage design process, from refined land use segmentation, to catchment subdivision and characterization, to network topology generation, and finally to hydraulic estimation of pipeline capacity, based on multiple open-source datasets. The method incorporated deep learning-based semantic segmentation, GIS-based hydrological characterization, topology generation and hydraulic calculation algorithms. The performance and applicability of the method were validated through case studies of two cities. The results showed that the deep learning model with prior knowledge could accurately segment urban land use to obtain the detailed shape and boundary description, and achieved higher detection accuracy for water bodies, buildings, and roads. The stormwater drainage topology and conveyance capacity were automatically generated based on subcatchment division and hydrological characterization under a set of topological parameter conditions. In the optimal Critical Success Index (CSI) scenario, only 8% and 21% of the generated pipelines were inconsistent with the expert-designed networks. Compared to the traditional manual design process, the automated approach can save significant time and resources and reduce the reliance on field surveys and empirical/expert work. At the same time, the tool can be employed for system layout and capacity optimization, providing important support for the automation, design, and rehabilitation of stormwater drainage systems.

3D-measurement of particles and particulate assemblies - A review of the paradigm shift in describing anisotropic particles

The goal of seeking advanced solutions to the descriptions of particle shape, packing and tomographic measurement were key areas promoted by Professor Reg Davies. In this paper we review and reflect on the revolution that has taken place over the last 30 years in our ability to describe and measure particle shape going beyond simple shape factors to their real morphologies of complex particles and particulate assemblies. The paper presents a comprehensive review of how shape has been described and some critical analyses in the form of extended tabulations. We show how digital approaches to particle descriptions can be used to predict the properties of particles and assemblies and their use in simulations of particle processing. We note the current status and prospects for the continued development of microtomographic systems to enable the measurement of particle shape in 3D and also the 3D imaging of complex particulate structures to enable property and processing predictions. Examples of these developments and critical appraisal of their utility will be given.

Non-Rigid Registration Via Intelligent Adaptive Feedback Control.

Preserving features or local shape characteristics of a mesh using conventional non-rigid registration methods is always difficult, as the preservation and deformation are competing with each other. The challenge is to find a balance between these two terms in the process of the registration, especially in presence of artefacts in the mesh. We present a non-rigid Iterative Closest Points (ICP) algorithm which addresses the challenge as a control problem. An adaptive feedback control scheme with global asymptotic stability is derived to control the stiffness ratio for maximum feature preservation and minimum mesh quality loss during the registration process. A cost function is formulated with the distance term and the stiffness term where the initial stiffness ratio value is defined by an Adaptive Neuro-Fuzzy Inference System (ANFIS)-based predictor regarding the source mesh and the target mesh topology, and the distance between the correspondences. During the registration process, the stiffness ratio of each vertex is continuously adjusted by the intrinsic information, represented by shape descriptors, of the surrounding surface as well as the steps in the registration process. Besides, the estimated process-dependent stiffness ratios are used as dynamic weights for establishing the correspondences in each step of the registration. Experiments on simple geometric shapes as well as 3D scanning datasets indicated that the proposed approach outperforms current methodologies, especially for the regions where features are not eminent and/or there exist interferences between/among features, due to its ability to embed the inherent properties of the surface in the process of the mesh registration.

Formation and coarsening of epitaxially-supported metal nanoclusters

This mini-review describes developments over the last ∼30 years in characterizing the nucleation & growth of epitaxially-supported metal nanoclusters (NCs) or islands during vapor deposition, as well as their post-deposition coarsening. A beyond-mean-field treatment for homogeneous nucleation & growth corrects the deficiencies of traditional treatments in describing, e.g., the island size distribution, but also necessitates consideration of the spatial distribution of islands and their capture zones. We discuss advances in modeling capabilities, including those based upon on an ab-initio level treatment of periphery diffusion kinetics, for description of the non-equilibrium growth shapes of these NCs, focusing on 2D NCs. For post-deposition coarsening of arrays of NCs, there is generally a competition between Ostwald Ripening (OR) and Smoluchowski Ripening (SR). SR is also known as Particle Migration & Coalescence. For 2D NCs in homoepitaxial systems, conventional OR is observed on pristine fcc(111) surfaces, dramatically enhanced OR in the presence of even trace amounts of chalcogens for Cu(111) and Ag(111), and anomalous OR on anisotropic fcc(110) surfaces. The unexpected discovery of SR for fcc(100) homoepitaxial systems prompted extensive analysis of the underlying diffusivities of 2D NCs as a function of size, as well as of NC coalescence dynamics. A comprehensive understanding of these processes is now available. Self-assembly of 3D NCs during deposition, issues related to heterogeneous nucleation, directed assembly, NC growth structure selection, and coarsening are addressed. For SR of 3D epitaxial NCs, recent insights into the size-dependence of diffusivity are described.

Morphometry on the sphere: Cartesian and irreducible Minkowski tensors explained and implemented

Minkowski tensors are comprehensive shape descriptors that robustly capture n-point information in complex random geometries and that have already been extensively applied in the Euclidean plane. Here, we devise a framework for Minkowski tensors on the sphere. We first advance the theory by introducing irreducible Minkowski tensors, which avoid the redundancies of previous representations. We, moreover, generalize Minkowski sky maps to the sphere. These maps are a concept of local anisotropy, which easily adjusts to masked data. We demonstrate the power of our new procedure by applying it to simulations and real data of the Cosmic Microwave Background, finding an anomalous region close to the well-known Cold Spot. The accompanying open-source software, litchi, used to generate these maps from data in the HEALPix-format is made publicly available to facilitate broader integration of Minkowski maps in other fields, such as fluid demixing, porous structures, or geosciences more generally.

Identification Tools of Microplastics from Surface Water Integrating Digital Image Processing and Statistical Techniques.

The primary objective of this study was to demonstrate the potential of digital image analysis as a tool to identify microplastic (MP) particles in surface waters and to facilitate their characterisation in terms of 2D and 3D morphology. Digital image analysis preceded by microscopic analysis was used for an exhaustive quantitative and qualitative evaluation of MPs isolated from the Vistula River. Using image processing procedures, 2D and 3D shape descriptors were determined. Principal Component Analysis was used to interpret the relationships between the parameters studied, characterising MP particle geometry, type and colour. This multivariate analysis of the data allowed three or four main factors to be extracted, explaining approximately 90% of the variation in the data characterising MP morphology. It was found that the first principal component for granules, flakes and films was largely represented by strongly correlated with 2D shape descriptors (area, perimeter, equivalent area diameter) and 3D shape descriptors (Corey Shape Factor, Compactness, Dimensionality). Considering the scraps, principal component PC1 was represented by only five of the above descriptors, and the Compactness variable had the largest contribution to principal component PC2. In addition, for granules, flakes and films, a relationship between 2D shape and the colour of their particles could be observed. For the most numerous MP group identified of multicoloured scraps, no such association was found. The results of our study can be used for further multivariate analysis regarding the presence of microplastic floating on the river surface, with a particular focus on particles of secondary origin. This is of key importance for optimising future efforts in conducting small-scale and multidimensional monitoring of and reducing plastics in the aquatic environment.

Detecting Temporal shape changes with the Euler Characteristic Transform

Abstract Organoids are multi-cellular structures that are cultured in vitro from stem cells to resemble specific organs (e.g., brain, liver) in their three-dimensional composition. Dynamic changes in the shape and composition of these model systems can be used to understand the effect of mutations and treatments in health and disease. In this paper, we propose a new technique in the field of topological data analysis for DEtecting Temporal shape changes with the Euler Characteristic Transform (DETECT). DETECT is a rotationally invariant signature of dynamically changing shapes. We demonstrate our method on a data set of segmented videos of mouse small intestine organoid experiments and show that it outperforms classical shape descriptors. We verify our method on a synthetic organoid data set and illustrate how it generalizes to 3D. We conclude that DETECT offers rigorous quantification of organoids and opens up computationally scalable methods for distinguishing different growth regimes and assessing treatment effects.

Aspects of Symmetry in Petri Nets

Symmetry is a fundamental mathematical property applicable to the description of various shapes both geometrical and representational. Symmetry is central to understanding the nature of various objects. It can be used as a simplifying principle when structures are created. Petri nets are widely covered formalisms, useful for modeling different types of computer systems or computer configurations. Different forms of Petri nets exist along with several forms of representation. Petri nets are useful for i) deterministic and ii) non-deterministic modeling. The aspect of symmetry in Petri nets requires in-depth treatment that is often overlooked. Symmetry is a fundamental property found in Petri nets. This work tries to briefly touch on these properties and explain them with simple examples. Hopefully, readers will be inspired to carry out more work in this direction.

Comparison of Mammography, Ultrasonography, and both Combined in the Interpretation of Palpable Breast Mass

Background: Breast cancer is the most common female malignancy in worldwide and the second leading cause of female cancer death in the United States (1, 14). On average, every two minutes a woman is diagnosed with breast cancer and one woman will die of breast cancer every thirteen minutes(13) In Libyan breast cancer is most common cancer in female (17 ) Although the majority of palpable lumps are benign, a new palpable breast mass is a common presenting sign of breast cancer. the aim of the study to reveal the role of USS and MG and both in evaluating palpable breast mass because both are available and more accurate in evaluated palpable breast mass depend on the aging and breast density .Materials and methods: prospective study between January 2018 and march 2019 In Department of Radiology in Benghazi medical center (BMC); used the Breast Imaging Reporting and Data System (BI-RADS) classification on fifty palpable breast masses in two models (USS and MG ) and described each masses by selecting a single term from the Bl-RADS lexicon for description mass margin and shape. Kappa values were calculated to assess the agreement between BIRADS assessment category and agreement between descriptions of masses margin and shape .Additionally, another reader used same USS Bl-RADS lexicon for description mass margin to assessed lnter-observer variability. Result :Regarding BIRADS assessment category, agreement between the MG and combined (USS and MG ) interpretations were moderate (K=0.4);agreement between USS and combined (USS and MG ) was very good (k=0.84); agreement between BIRADs category of USS and MG in descriptive shape of palpable breast mass was moderate (k=0.50) while for margin fair agreement (k=0.26).poor lnter-observer variability(k=0.19) in USS Bl-RADS lexicon for description mass margin. Conclusion: USS better than MG in detected palpable breast mass so can be use as diagnostic tool for characterized palpable breast mass.

On the shape description of general solids using Morse theory

The automatic shape description of solids is a problem of interest in manufacturing engineering, amongst other related areas. This description can be either geometrical or topological in nature and can be applied to either surfaces or solids (embedded manifolds). Topological descriptions are specially interesting for the problem of shape comparison and retrieval, where one wants to know if a given shape resembles some other known shape. Some popular topological descriptions use Morse theory to study the topology of manifolds and encode their shape characteristics. A Morse function f is defined on the manifold and the manifold’s shape is indirectly studied by studying the behavior of the critical points of f. This family of methods is well defined for surfaces but does not consider the case of solids. In this paper we address the topological description of solids using Morse theory. Our methodology considers three cases: solids without internal boundaries, solids with internal boundaries and thin-walled solids. We present an algorithm to identify topological changes on these solids using the principle of shape decomposition by Morse handles. The presented algorithm deals with Morse functions that produce parallel planar level sets. Future endeavors should consider other candidate functions.

Advanced Image Processing Techniques for Automated Detection of Healthy and Infected Leaves in Agricultural Systems

Advances in computer vision and machine learning have transformed leaf disease detection by enabling efficient and accurate identification of subtle disease signs in leaves. Leveraging high-resolution imaging, pattern recognition algorithms, and deep learning models, researchers and farmers can now conduct automated detection across various plant species. The development focuses on sophisticated image processing techniques applied to diverse datasets captured under controlled conditions, ensuring comprehensive coverage of lighting, time, and weather variations. Expert annotation of infection stages and types enhances dataset reliability, while pre-processing stages such as resizing and normalization optimize image consistency for robust model training. Data augmentation techniques enrich dataset diversity, complemented by feature extraction methods like RGB color analysis, GLCM texture analysis, and shape descriptors to discern healthy and infected leaves with precision Validation through K-fold cross-validation ensures model reliability across diverse datasets, culminating in a deployable application for real-time leaf health monitoring. Results demonstrate significant advancements, with the proposed model achieving 92% accuracy, surpassing Logistic Regression (87%), Decision Tree (82%), and Support Vector Machine (79%). Over 10 epochs, the model achieves steady improvements to 95% training accuracy and 85% validation accuracy, underscoring its effectiveness. Implementing data augmentation boosts accuracy from 85% to 89%, while analysis of prediction errors refines model performance for enhanced automated plant health monitoring and precision agriculture applications. These advancements highlight the transformative impact of technology in safeguarding crop resilience and optimizing agricultural practices.

Characterizing Cellular Physiological States with Three-Dimensional Shape Descriptors for Cell Membranes.

The shape of a cell as defined by its membrane can be closely associated with its physiological state. For example, the irregular shapes of cancerous cells and elongated shapes of neuron cells often reflect specific functions, such as cell motility and cell communication. However, it remains unclear whether and which cell shape descriptors can characterize different cellular physiological states. In this study, 12 geometric shape descriptors for a three-dimensional (3D) object were collected from the previous literature and tested with a public dataset of ~400,000 independent 3D cell regions segmented based on fluorescent labeling of the cell membranes in Caenorhabditis elegans embryos. It is revealed that those shape descriptors can faithfully characterize cellular physiological states, including (1) cell division (cytokinesis), along with an abrupt increase in the elongation ratio; (2) a negative correlation of cell migration speed with cell sphericity; (3) cell lineage specification with symmetrically patterned cell shape changes; and (4) cell fate specification with differential gene expression and differential cell shapes. The descriptors established may be used to identify and predict the diverse physiological states in numerous cells, which could be used for not only studying developmental morphogenesis but also diagnosing human disease (e.g., the rapid detection of abnormal cells).

Leveraging Descriptor Learning and Functional Map-based Shape Matching for Automatic Landmark Acquisition.

Geometric morphometrics is widely employed across the biological sciences for the quantification of morphological traits. However, the scalability of these methods to large datasets is hampered by the requisite placement of landmarks, which can be laborious and time consuming if done manually. Additionally, the selected landmarks embody a particular hypothesis regarding the critical geometry pertinent to the biological inquiry at hand. Modifying this hypothesis lacks flexibility, necessitating the acquisition of an entirely new set of landmarks on the entire dataset to reflect any theoretical adjustments. In our research, we investigate the precision and accuracy of landmarks derived from the comprehensive set of functional correspondences acquired through the functional map framework of geometry processing. We use a deep functional map network to learn shape descriptors that effectively yield functional map-based and point-to-point correspondences between the specimens in our dataset. We then interrogate these maps to identify corresponding landmarks given manually placed landmarks from the entire dataset. We assess our method by automating the landmarking process on a dataset comprising mandibles from various rodent species, comparing its efficacy against MALPACA, a cutting-edge technique for automatic landmark placement. Compared to MALPACA, our model is notably faster and maintains competitive accuracy. The Root Mean Square Error (RMSE) analysis reveals that while MALPACA generally exhibits the lowest RMSE, our models perform comparably, especially with smaller training datasets, suggesting strong generalizability. Visual evaluations confirm the precision of our landmark placements, with deviations remaining within an acceptable range. These findings underscore the potential of unsupervised learning models in anatomical landmark placement, providing a viable and efficient alternative to traditional methods.

3D Tortuosity computation as a shape descriptor and its application to brain structure analysis

In this study, we propose a novel method for quantifying tortuosity in 3D voxelized objects. As a shape characteristic, tortuosity has been widely recognized as a valuable feature in image analysis, particularly in the field of medical imaging. Our proposed method extends the two-dimensional approach of the Slope Chain Code (SCC) which creates a one-dimensional representation of curves. The utility of 3D tortuosity (τ3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{3D}$$\\end{document}) as a shape descriptor was investigated by characterizing brain structures. The results of the τ3D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au _{3D}$$\\end{document} computation on the central sulcus and the main lobes revealed significant differences between Alzheimer’s disease (AD) patients and control subjects, suggesting its potential as a biomarker for AD. We found a p<0.05\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p<0.05$$\\end{document} for the left central sulcus and the four brain lobes.

Analysis of Manifold and its Application

Manifold learning is a field of study in machine learning and statistics that is closely associated with dimensionality reduction algorithmic techniques is gaining popularity these days. There are two types of manifold learning approaches: linear and nonlinear. Principal component analysis (PCA) and multidimensional scaling (MDS) are two examples of linear techniques that have long been staples in the statistician's arsenal for evaluating multivariate data. Nonlinear manifold learning, which encompasses diffusion maps, Laplacian Eigenmaps, Hessian Eigenmaps, Isomap, and local linear embedding, has seen a surge in research effort recently. A few of these methods are nonlinear extensions of linear approaches. A nearest search, the definition of distances or affinities between points (a crucial component of these methods' effectiveness), and an Eigen problem for embedding high-dimensional points into a lower dimensional space make up the algorithmic process of the majority of these techniques. The strengths and weaknesses of the new method are briefly reviewed in this article. In the field of computer graphics, we utilize a particular manifold learning method was first presented in statistics and machine learning to create a global, Spectral-based shape descriptor.

A Road Behavior Pattern-Detection Model in Querétaro City Streets by the Use of Shape Descriptors

In this research, a proposed model aims to automatically identify patterns of spatial and temporal behavior of moving objects in video sequences. The moving objects are analyzed and characterized based on their shape and observable attributes in displacement. To quantify the moving objects over time and form a homogeneous database, a set of shape descriptors is introduced. Geometric measurements of shape, contrast, and connectedness are used to represent each moving object. The proposal uses Granger’s theory to find causal relationships from the history of each moving object stored in a database. The model is tested in two scenarios; the first is a public database, and the second scenario uses a proprietary database from a real scenario. The results show an average accuracy value of 78% in the detection of atypical behaviors in positive and negative dependence relationships.

Machine learning regression algorithms for predicting muscle, bone, carcass fat and commercial cuts in hairless lambs

The growth in demand and demand for quality in the sheep chain has generated the need for automation techniques in the meat industry and the need to obtain responses with greater speed and standardization. The research aimed to predict tissue characteristics of the carcass and commercial cuts based on measurements obtained by VIA – see oimage analysis, carried out on cold carcasses of hairless lambs, using machine learning employing regressive techniques for variable selection. Information from 72 carcasses of castrated male lambs, aged between 8 and 11 months, with an average cold carcass weight of 16.13 ± 3.98 kg, was used. Images of the right side of the carcasses were captured from the dorsal and lateral views using a digital camera. From the ImageJ2 software, VIA data, measurements and shape descriptors (areas, perimeters, widths, lengths, convexities, solidities) were obtained, combined with cold carcass weight and used to generate four sets of data, called descriptor sets (DSs). Obtaining DS1, DS1’, DS2, DS2’, DS3, DS3’, DS4 AND DS4’. To generate these sets, a database was formed and divided into a training bank (with 70% of the observations) and a test bank (30% of the observations). Multiple linear regression models were developed using Stepwise, LASSO, and Elastic Net regression methods, combined with k-fold cross-validation, to evaluate the performance of the models. The accuracy of the estimates was based on RMSE, R2, Pearson correlation and bias metrics. For the variables tested in this study, the proposed shape descriptors were mostly efficient in predicting tissue and weight variables. DS1' with the LASSO technique presented the best adjustments for variables total muscle and fat followed by shoulder, loin and rib cuts. The descriptors tested by this study were able to predict with quality the vast majority of the characteristics tested, the variable cold carcass weight (CCW), introduced as additional predictor, promoted a consistent improvement in the fits of all models. DS1 presented greater constancy for the twenty-three predicted characteristics and Stepwise presented the worst predictive performance, in relation to LASSO and Elastic Net. Despite close adjustments between the generated models, in general, Elastic Net presented lower performance than LASSO.

Crater Triangle Matching Algorithm Based on Fused Geometric and Regional Features

Craters are regarded as significant navigation landmarks during the descent and landing process in small body exploration missions for their universality. Recognizing and matching craters is a crucial prerequisite for visual and LIDAR-based navigation tasks. Compared to traditional algorithms, deep learning-based crater detection algorithms can achieve a higher recognition rate. However, matching crater detection results under various image transformations still poses challenges. To address the problem, a composite feature-matching algorithm that combines geometric descriptors and region descriptors (extracting normalized region pixel gradient features as feature vectors) is proposed. First, the geometric configuration map is constructed based on the crater detection results. Then, geometric descriptors and region descriptors are established within each feature primitive of the map. Subsequently, taking the salience of geometric features into consideration, composite feature descriptors with scale, rotation, and illumination invariance are generated through fusion geometric and region descriptors. Finally, descriptor matching is accomplished by computing the relative distances between descriptors and adhering to the nearest neighbor principle. Experimental results show that the composite feature descriptor proposed in this paper has better matching performance than only using shape descriptors or region descriptors, and can achieve a more than 90% correct matching rate, which can provide technical support for the small body visual navigation task.

Segmentation of Renal Thyroid Follicle Colloid in Common Carp: Insights into Perfluorooctanoic Acid-Induced Morphometric Alterations.

Perfluorooctanoic acid (PFOA) is a globally prevalent contaminant of concern recognised for its persistence and detrimental effects on both wildlife and humans. While PFOA has been established as a disruptor of thyroid function, limited data exist regarding its impact on thyroid morphology. The kidney of the common carp (Cyprinus carpio) harbours numerous thyroid follicles, rendering it a valuable biomarker organ for investigating PFOA-induced thyroid alterations. Renal tissue slides, stained with the Alcian blue/PAS method, were examined from carp in three experimental groups: unexposed, exposed to 200 ng L-1, and exposed to 2 mg L-1 of PFOA over 56 days. Thyroid follicle colloids were segmented, and related morphometric parameters, including perimeter, area, and shape descriptors, were obtained. Statistical analyses revealed significant reductions in thyroid follicle colloid perimeter and area in the 200 ng L-1 PFOA group compared to the unexposed and 2 mg L-1 PFOA groups. Additionally, the fish exposed to PFOA exhibited a significantly higher follicle count compared to the unexposed fish. These findings collectively suggest that PFOA induces thyroid folliculogenesis, emphasising its impact on thyroid morphology even at an environmentally relevant concentration (200 ng L-1).

The spatiotemporal richness of hummingbird wing deformations.

Animals exhibit an abundant diversity of forms, and this diversity is even more evident when considering animals that can change shape on demand. The evolution of flexibility contributes to aspects of performance from propulsive efficiency to environmental navigation. It is, however, challenging to quantify and compare body parts that, by their nature, dynamically vary in shape over many time scales. Commonly, body configurations are tracked by labelled markers and quantified parametrically through conventional measures of size and shape (descriptor approach) or non-parametrically through data-driven analyses that broadly capture spatiotemporal deformation patterns (shape variable approach). We developed a weightless marker tracking technique and combined these analytic approaches to study wing morphological flexibility in hoverfeeding Anna's hummingbirds (Calypte anna). Four shape variables explained >95% of typical stroke cycle wing shape variation and were broadly correlated with specific conventional descriptors such as wing twist and area. Moreover, shape variables decomposed wing deformations into pairs of in-plane and out-of-plane components at integer multiples of the stroke frequency. This property allowed us to identify spatiotemporal deformation profiles characteristic of hoverfeeding with experimentally imposed kinematic constraints, including through shape variables explaining <10% of typical shape variation. Hoverfeeding in front of a visual barrier restricted stroke amplitude and elicited increased stroke frequencies together with in-plane and out-of-plane deformations throughout the stroke cycle. Lifting submaximal loads increased stroke amplitudes at similar stroke frequencies together with prominent in-plane deformations during the upstroke and pronation. Our study highlights how spatially and temporally distinct changes in wing shape can contribute to agile fluidic locomotion.