Concave Hulls Research Articles

Deephullnet: a deep learning approach for solving the convex hull and concave hull problems with transformer

ABSTRACT Convex and concave hulls originating from computational geometry are widely applied in practice. For instance, to determine the boundaries of a geographical area within a group of cities, convex hulls can represent the approximate boundaries of the areas. Concave hulls can accurately describe the shape of the area. The traditional methods for solving two-dimensional convex hull problems include the Jarvis March algorithm and the Graham scanning algorithm. The K-nearest neighbours and alpha-shape methods are designed for solving the concave hull problem. Other than traditional algorithms, we consider using deep neural networks to handle the convex and concave hull problems. General neural networks cannot deal with the problem whose output is a variable-length sequence. Our study provides a machine-learning approach for solving the convex hull and concave hull problems. We combine the Pointer network (Ptr-Net) with the Transformer model and propose the DeepHullNet. The trained DeepHullNet can provide a feasible solution in the majority of cases. The experimental results show that DeepHullNet outperforms the original Ptr-Net regarding accuracy. Compared with traditional methods, DeepHullNet can generate a good solution quickly, and the running time is shortened by nearly 100 times based on GPU.

Particle morphology characterization of waste-tyre-stabilized rock aggregates via computational geometric modellings

This study offers a comprehensive understanding of the most important geometrical concepts for concave shape particles with very low sphericity. Study of concave hulls in three-dimensional space is performed with an emphasis on accurate and asymptotically fast algorithms. Based on that a three-dimensional concave hull algorithm is designed to generate the actual shape of irregular particles through a set of 3D surface coordinate data points captured by 3D handy laser scanner and photogrammetry. The algorithm is utilized for a wide range of large-scale waste tyre and rock aggregates to assess several fundamental theoretical hypotheses related to geometric parameters, including surface texture with concavity/convexity, concave hull volume, perimeters of projected area, and concavity computation that have not been tested before for highly irregular concave shape particles. As a result, the morphological characteristics of the waste-tyre-stabilized rock aggregate mixtures are analysed for mining operations. We also provide the details on how the application of the resulting particle morphology is employed in cloning particles with wide range of concavity distribution. The paper identifies the accuracy by implementing the proposed 3D concave hull algorithm for morphology analysis of concave particles and comparing the morphology analysis results against those of Finite Element Method (FEM), polar representation approach (PRA), and experimental data.

Point cloud registration based on concave hull association

ABSTRACT This letter presents a point cloud coarse registration method based on concave hull association. The assumption is that some internal points may be variable in different scans due to self-occlusion, but the hull vertices in overlap regions are consistent. Therefore, we only use the vertices of the concave hulls to find feature associations and reduce the number of wrong correspondences. Firstly, the method extracts the concave hulls and calculatecalculates the unique feature descriptors for each vertex of the hulls. Then, we use the sample consensus initial alignment algorithm to achieve feature matching and find the coarse registration parameters. The proposed method has been verified on different datasets and compared with state-of-the-art algorithms. The experiments demonstrate that the proposed algorithm eliminates unnecessary correspondences and obtains high efficiency and robustness.

Rangemap: An R Package to Explore Species' Geographic Ranges

Data exploration is a critical step in understanding patterns and biases in information about species’ geographic distributions. We present rangemap, an R package that implements tools to explore species’ ranges based on simple analyses and visualizations. The rangemap package uses species occurrence coordinates, spatial polygons, and raster layers as input data. Its analysis tools help to generate simple spatial polygons summarizing ranges based on distinct approaches, including spatial buffers, convex and concave (alpha) hulls, trend-surface analysis, and raster reclassification. Visualization tools included in the package help to produce simple, high-quality representations of occurrence data and figures summarizing resulting ranges in geographic and environmental spaces. Functions that create ranges also allow generating extents of occurrence (using convex hulls) and areas of occupancy according to IUCN criteria. A broad community of researchers and students could find in rangemap an interesting means by which to explore species’ geographic distributions.

Towards footwear manufacturing 4.0: shoe sole robotic grasping in assembling operations

In this paper, we present a robotic workcell for task automation in footwear manufacturing such as sole digitization, glue dispensing, and sole manipulation from different places within the factory plant. We aim to make progress towards shoe industry 4.0. To achieve it, we have implemented a novel sole grasping method, compatible with soles of different shapes, sizes, and materials, by exploiting the particular characteristics of these objects. Our proposal is able to work well with low density point clouds from a single RGBD camera and also with dense point clouds obtained from a laser scanner digitizer. The method computes antipodal grasping points from visual data in both cases and it does not require a previous recognition of sole. It relies on sole contour extraction using concave hulls and measuring the curvature on contour areas. Our method was tested both in a simulated environment and in real conditions of manufacturing at INESCOP facilities, processing 20 soles with different sizes and characteristics. Grasps were performed in two different configurations, obtaining an average score of 97.5% of successful real grasps for soles without heel made with materials of low or medium flexibility. In both cases, the grasping method was tested without carrying out tactile control throughout the task.

Assigning occurrence data to cryptic taxa improves climatic niche assessments: Biodecrypt, a new tool tested on European butterflies

AbstractAimOccurrence data are fundamental to macroecology, but accuracy is often compromised when multiple units are lumped together (e.g., in recently separated cryptic species or in citizen science records). Using amalgamated data leads to inaccuracy in species mapping, to biased beta‐diversity assessments and to potentially erroneously predicted responses to climate change. We provide a set of R functions (biodecrypt) to objectively attribute unidentified occurrences to the most probable taxon based on a subset of identified records.InnovationBiodecrypt assumes that unidentified occurrences can only be attributed at certain distances from areas of sympatry. The function draws concave hulls based on the subset of identified records; subsequently, based on hull geometry, it attributes (or not) unidientified records to a given taxon. Concavity can be imposed with an alpha value and sea or land areas can be excluded. A cross‐validation function tests attribution reliability and another function optimises the parameters (alpha, buffer, distance ratio between hulls). We applied the procedure to 16 European butterfly complexes recently separated into 33 cryptic species for which most records were amalgamated. We compared niche similarity and divergence between cryptic taxa, and re‐calculated and contributed updated climatic niche characteristics of the butterflies in Europe (CLIMBER).Main conclusionsBiodecrypt showed a cross‐validated correct attribution of known records always ≥ 98% and attributed more than 80% of unidientified records to the most likely taxon in parapatric species. The functions determined where records can be assigned even for largely sympatric species, and highlighted areas where further sampling is required. All the cryptic taxa showed significantly diverging climatic niches, reflected in different values of mean temperature and precipitation compared to the values originally provided in the CLIMBER database. The substantial fraction of cryptic taxa existing across different taxonomic groups and their divergence in climatic niches highlight the importance of using reliably assigned occurrence data in macroecology.

SeededclustR: Using Cluster Analysis of Mitochondria to Improve Cell Segmentation and Automated Quantification of mtDNA in Smooth Muscle Cells.

IntroSegmentation of fluorescently labelled cells is essential to pipelines of automated image analysis. Identifying regions of interest (ROIs) around labelled nuclei is relatively easy using tools available in ImageJ/Fiji, but determining the bounds of cells can be much harder. We asked if fluorescently labelled mitochondria could be used to improve the automated generation of cellular ROIs.MethodThe perimeter coordinates of nuclear ROIs and the centroid coordinates, area, mean intensity, angle, and solidity of ROIs around MitoTracker Orange (MTO)‐labelled mitochondria were generated in ImageJ and exported to R. Using the nuclei as seeds for a recursive k‐Nearest Neighbour search extending from each nucleus, MTO particles were assigned to their nearest‐neighbouring cells. A concave hull was created around MTO particles assigned to each cell using the concaveman package. We determined the sensitivity of this algorithm by comparing the accuracy of the generated concave hulls to the corresponding hand‐drawn ROIs, and ROIs from Voronoi expanded distance mapsResultsWhen we compared seededClustR ROIs to those drawn by hand, the Intersection‐Over‐Union (IOU) was 68 ± 8% (mean ± SD), Precision was 88 ± 6% and Recall 95 ± 3%. In contrast, Voronoi expansion of nuclei resulted in the IOU of 46 ± 18%, Precision of 83 ± 17%, and Recall of 91 ± 11%. Optimal IOU and Recall were observed when each MTO particle was compared to its 7–10 nearest neighbours. IOU and Recall were maximized using recursive steps of 40–200 μm, while Precision decreased from 94% to 88% as step size increased from 7–40 μm. Unexpectedly, extending seededClustR to an n‐dimensional kd‐tree calculation that included varying weights of MTO particle mean intensity, area, standard deviation, angle and solidity reduced cell tracing accuracy. Similarly, using Wilks’‐test to identify outliers decreased IOU by 17 percentage points (pp) and Recall by 20 pp, though it increased Precision by 6 pp. Finally, we tested whether if the more accurate cell ROI from seededClustR versus Voronoi ROIs could improve our ability to detect changes in optical measures of mtDNA in A7r5 smooth muscle cells treated with angiotensin II, 5,6‐dideoxycytidine, and H2O2, where results showed promising gains.ConclusionseededClustR is a generalizable algorithm that can use simple XY coordinates of puncta‐like features of cells to generate cellular ROIs around labelled nuclei with measures of accuracy that exceed simple dilation of nuclear ROIs. This approach should facilitate improved precision in automated screens of cellular phenotypes.Support or Funding InformationNatural Sciences and Engineering Research Council of Canada

On the numerical solution of a minimax control problem with a positional functional

We consider a minimax feedback control problem for a linear dynamic system with a positional quality index, which is the norm of the set of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A numerical method is given for finding an approximation of the game value and constructing an optimal (minimax and maximin) control law. The method is based on the recursive construction of upper convex (concave) hulls of auxiliary program functions. In addition, we use the “pixel” approximation of the domains of convexified functions and the approximate construction of the upper convex hull of a function as the lower envelope of a finite set of support hyperplanes of its subgraph.

Representation of shape mediated by environmental stimuli in Physarum polycephalum and a multi-agent model

The slime mould Physarum polycephalum is known to construct protoplasmic transport networks which approximate proximity graphs by foraging for nutrients during its plasmodial life cycle stage. In these networks, nodes are represented by nutrients and edges are represented by protoplasmic tubes. These networks have been shown to be efficient in terms of length and resilience of the overall network to random damage. However, relatively little research has been performed in the potential for Physarum transport networks to approximate the overall shape of a data-set. In this paper we distinguish between connectivity and shape of a planar point data-set and demonstrate, using scoping experiments with plasmodia of P. polycephalum and a multi-agent model of the organism, how we can generate representations of the external and internal shapes of a set of points. As with proximity graphs formed by P. polycephalum, the behaviour of the plasmodium (real and model) is mediated by environmental stimuli. We further explore potential morphological computation approaches with the multi-agent model, presenting methods which approximate the Convex Hull and the Concave Hull. We demonstrate how a growth parameter in the model can be used to transition between Convex and Concave Hulls. These results suggest novel mechanisms of morphological computation mediated by environmental stimuli.

On Binary-State Phyllosilicate Automata

Phyllosilicate is a sheet of silicate tetrahedra bound by basal oxygens. A phyllosilicate automaton is a regular network of finite state machines, which mimics the structure of phyllosilicate. A node of a binary state phyllosilicate automaton takes states 0 and 1. A node updates its state in discrete time depending on a sum of states of its three (silicon nodes) or six (oxygen nodes) closest neighbors. We phenomenologically select the main types of patterns generated by phyllosilicate automata based on their shape: convex and concave hulls, almost circularly growing patterns, octagonal patterns, and those with dendritic growth; and, the patterns' interior: disordered, solid, labyrinthine. We also present the rules exhibiting traveling localizations.

Convex and concave hulls for classification with support vector machine

The training of a support vector machine (SVM) has the time complexity of O(n3) with data number n. Normal SVM algorithms are not suitable for classification of large data sets. Convex hull can simplify SVM training, however the classification accuracy becomes lower when there are inseparable points. This paper introduces a novel method for SVM classification, called convex–concave hull. After grid pre-processing, the convex hull and the concave (non-convex) hull are found by Jarvis march method. Then the vertices of the convex–concave hull are applied for SVM training. The proposed convex–concave hull SVM classifier has distinctive advantages on dealing with large data sets with higher accuracy. Experimental results demonstrate that our approach has good classification accuracy while the training is significantly faster than the other training methods.

A New Concave Hull Algorithm and Concaveness Measure for n-dimensional Datasets

Convex and concave hulls are useful concepts for a wide variety of application areas, such as pattern recognition, image processing, statistics, and classification tasks. Concave hull performs better than convex hull, but it is difficult to formulate and few algorithms are suggested. Especially, an n-dimensional concave hull is more difficult than a 2- or 3-dimensional one. In this paper, we propose a new concave hull algorithm for n-dimensional datasets. It is simple but creative. We show its application to dataset analysis. We also suggest a concaveness measure and a graph that captures geometric shape of an n-dimensional dataset. Proposed concave hull algorithm and concaveness measure/graph are implemented using java, and are posted to http://user.dankook.ac.kr/~bitl/dkuCH.

Influences on the formation and evolution of Physarum polycephalum inspired emergent transport networks

The single-celled organism Physarum polycephalum efficiently constructs and minimises dynamical nutrient transport networks resembling proximity graphs in the Toussaint hierarchy. We present a particle model which collectively approximates the behaviour of Physarum. We demonstrate spontaneous transport network formation and complex network evolution using the model and show that the model collectively exhibits quasi-physical emergent properties, allowing it to be considered as a virtual computing material. This material is used as an unconventional method to approximate spatially represented geometry problems by representing network nodes as nutrient sources. We demonstrate three different methods for the construction, evolution and minimisation of Physarum-like transport networks which approximate Steiner trees, relative neighbourhood graphs, convex hulls and concave hulls. We extend the model to adapt population size in response to nutrient availability and show how network evolution is dependent on relative node position (specifically inter-node angle), sensor scaling and nutrient concentration. We track network evolution using a real-time method to record transport network topology in response to global differences in nutrient concentration. We show how Steiner nodes are utilised at low nutrient concentrations whereas direct connections to nutrients are favoured when nutrient concentration is high. The results suggest that the foraging and minimising behaviour of Physarum-like transport networks reflect complex interplay between nutrient concentration, nutrient location, maximising foraging area coverage and minimising transport distance. The properties and behaviour of the synthetic virtual plasmodium may be useful in future physical instances of distributed unconventional computing devices, and may also provide clues to the generation of emergent computation behaviour by Physarum.

Gradients of local linear hulls in finite-difference operators for the Hamilton-Jacobi equations

A finite-difference operator (FDO) for the Hamilton-Jacobi equation is presented in which the non-existent solution gradients are replaced by the gradients of linear hulls. The approximation scheme (AS) corresponding to this FDO is proved to be minorized and majorized by ASs with FDOs based on the construction of sub-differentials and superdifferentials of local convex and concave hulls. This makes it possible to verify that the ASs converge to the linear constructions. Modifications of the FDO taking into account the configuration of local attainability domains are considered. The results of numerical experiments are presented.