Concave Vertices Research Articles

Perception Recognition Study on Long and Narrow Arcs of Polygons in Maps using Intelligent Skeleton Decomposition

<p>The paper presents an automated method for identifying elongated and narrow sections of polygons, which may arise due to uncertainties inherent in map data production and updates. It leverages a skeleton-based shape decomposition approach, encompassing the creation of skeletons and end-point sub-polygons based on the polygon boundary-constrained triangulation. Subsequently, it identifies a pair of break points using concave vertices of polygon boundaries based on the nearest neighbor principle. The optimal segmentation of the end-point sub-polygons is then determined by evaluating weighted base-height ratios, which are added to a set of candidates long and narrow arcs. Finally, the model selects the long and narrow arcs based on their base-height ratios and shape indexes. The paper reports the results of an experiment using land parcel data from Jinjiang in Fujian Province, demonstrating that the proposed method produces results that align with human perception and outperforms the internal and external buffering method. In summary, the innovative method exhibits promise in accurately identifying elongated and narrow sections of polygons, Its applicability spans diverse domains such as map data analysis and updates, where precision in delineating such features is crucial.</p> <p> </p>

Study on articular surface morphology of atlantoaxial lateral mass based on differential manifold

ObjectivesTo propose a surface reconstruction algorithm based on a differential manifold (a space with local Euclidean space properties), which can be used for processing of clinical images and for modeling of the atlantoaxial joint. To describe the ideal anatomy of the lateral atlantoaxial articular surface by measuring the anatomical data.MethodsComputed tomography data of 80 healthy subjects who underwent cervical spine examinations at our institution were collected between October 2019 and June 2022, including 46 males and 34 females, aged 37.8 ± 5.1 years (28–59 years). A differential manifold surface reconstruction algorithm was used to generate the model based on DICOM data derived by Vision PACS system. The lateral mass articular surface was measured and compared in terms of its sagittal diameter, transverse diameter, articular surface area, articular curvature and joint space height.ResultsThere was no statistically significant difference between left and right sides of the measured data in normal adults (P > 0.05). The atlantoaxial articular surface sagittal diameter length was (15.83 ± 1.85) and (16.22 ± 1.57) mm on average, respectively. The transverse diameter length of the articular surface was (16.29 ± 2.16) and (16.49 ± 1.84) mm. The lateral articular surface area was (166.53 ± 7.69) and (174.48 ± 6.73) mm2 and the curvature was (164.03 ± 5.27) and (153.23 ± 9.03)°, respectively. The joint space height was 3.05 ± 0.11mm, respectively. There is an irregular articular space in the lateral mass of atlantoaxial, and both upper and lower surfaces of the articular space are concave. A sagittal plane view shows that the inferior articular surface of the atlas is mainly concave above; however, the superior articular surface of the axis is mainly convex above. In the coronal plane, the inferior articular surface of the atlas is mostly concave above, with most concave vertices located in the medial region, and the superior articular surface of the axis is mainly concave below, with most convex vertices located centrally and laterally.ConclusionA differential manifold algorithm can effectively process atlantoaxial imaging data, fit and control mesh topology, and reconstruct curved surfaces to meet clinical measurement applications with high accuracy and efficiency; the articular surface of the lateral mass of atlantoaxial mass in normal adults has relatively constant sagittal diameter, transverse diameter and area. The distance difference between joint spaces is small, but the shape difference of articular surfaces differs greatly.

On the experiment and design of the Tachi-Miura polyhedron’s radial load-bearing capacity

Recent research has yet to note the structural performance of the radial direction. This paper experimentally verified the factors influencing the TMP’s radial load-bearing capacity and designed the new intermediate layer patterns for the radial extension. The methodology first assumed the axial motion of TMP as the approaching among sections. Based on the analysis, the relationship among the parameters was revealed according to the experiments, which marked the TMP as a high-performance structure. The results proved the positive correlation between the axial pre-compression and the radial load-bearing capacity where the folding angle has reached the value range of the self-locking state. The new intermediate layer patterns were correspondingly designed to substantiate the hypothesis regarding the specific parts. The overlapped triangular facets and the concave vertex have enhanced the radial load-bearing capacity. The combination of the relevant parameters and the spatial attributes expands the application scope of the TMP configuration.

An optimal coverage path plan for an autonomous vehicle based on polygon decomposition and ant colony optimisation

This paper proposes a coverage path planner for the autonomous vehicle used in inspection operation. The proposed coverage path planner is developed based on a back and forth pattern (equivalent to boustrophedon pattern), producing the output path for the inspection operation with the least trajectory length and number of turns covering the entire workspace. Implementing a back and forth pattern on an arbitrary polygon (extracted from workspace boundaries) is not always viable due to the existence of concave vertices in the polygon. So, this work proposes the tree search model based on the polygon width and back and forth pattern’s sweep line, which decomposes the input polygon in numerous ways. The Dijkstra algorithm solves this tree model to obtain back and forth pattern viable polygons with the least number of turns. Later, the vehicle visits these polygons one by one during the inspection operation. The order in which polygon visits are made by the vehicle affects the overall trajectory length. So, this work proposes the ant colony optimisation based trajectory length optimiser, which finds the polygon visiting order that yields minimum trajectory length. The developed coverage path planner is versatile, and it applies to any autonomous vehicle that operates in the planar region.

A novel pre-processing approach based on colour space assessment for digestive neuroendocrine tumour grading in immunohistochemical tissue images.

The complexity of histopathological images remains achallenging issue in cancer diagnosis. Apathologist analyses immunohistochemical images to detect acolour-based stain, which is brown for positive nuclei with different intensities and blue for negative nuclei. Several issues emerge during the eyeballing tissue slide analysis, such as colour variations caused by stain inhomogeneity, non-uniform illumination, irregular cell shapes, and overlapping cell nuclei. To overcome those problems, an automated computer-aided diagnosis system is proposed to segment and quantify digestive neuroendocrine tumours. We present anovel pre-processing approach based on colour space assessment. Acriterion called pertinence degree is introduced to select the appropriate colour channel, followed by contrast enhancement. Subsequently, the adaptive local threshold technique that uses the modified Laplacian filter is applied to minimize the implementation complexity, highlight edges, and emphasize intensity variation between cells across the slide. Finally, the improved watershed algorithm based on the concave vertex graph is applied for cell separation. The performance of the algorithms for nucleus segmentation is evaluated according to both the object-level and pixel-level criteria. Our approach increases segmentation accuracy, with the F1-score equal to 0.986. There is significant agreement between the applied approach and the expert's ground truth segmentation. The proposed method outperformed the state-of-the-art techniques based on recall, precision, the F1-score, and the Dice coefficient.

Geometric Analysis of Estimability of Target Object Shape Using Location-Unknown Distance Sensors

We geometrically analyze the problem of estimating parameters related to the shape and size of a 2-D target object on the plane by using randomly distributed distance sensors whose locations are unknown. Based on the analysis using geometric probability, we discuss the estimability of these parameters: which parameters we can estimate and what conditions are required to estimate them. For a convex target object, its size and perimeter length can be estimated, and other parameters cannot be estimated. For a general polygon target object, convexity, in addition to its size and perimeter length, can be estimated. Parameters related to a concave vertex can be estimated when some conditions are satisfied. We also propose a method for estimating the convexity of a target object and the perimeter length of the target object.

On Schwarz–Christoffel mappings

We extend previous work on Schwarz-Chrsitoffel mappings, including the special cases when the image is a convex polygon or its complement. We center our analysis on the relationship between the pre-Schwrazian of such mappings and Blaschke products. For arbitrary Schwarz-Christoffel mappings, we resolve an open question in \cite{ChDO2} that relates the degrees of the associated Blaschke products with the number of convex and concave vertices of the polygon. In addition, we obtain a sharp sufficient condition in terms of the exterior angles for the injectivity of a mapping given by the Schwarz-Christoffel formula, and study the geometric interplay between the location of the zeros of the Blaschke products and the separation of the pre-vertices.

A new automatic image analysis method for assessing estrogen receptors’ status in breast tissue specimens

Manual assessment of estrogen receptors′ (ER) status from breast tissue microscopy images is a subjective, time consuming and error prone process. Automatic image analysis methods offer the possibility to obtain consistent, objective and rapid diagnoses of histopathology specimens. In breast cancer biopsies immunohistochemically (IHC) stained for ER, cancer cell nuclei present a large variety in their characteristics that bring various difficulties for traditional image analysis methods. In this paper, we propose a new automatic method to perform both segmentation and classification of breast cell nuclei in order to give quantitative assessment and uniform indicators of IHC staining that will help pathologists in their diagnostic. Firstly, a color geometric active contour model incorporating a spatial fuzzy clustering algorithm is proposed to detect the contours of all cell nuclei in the image. Secondly, overlapping and touching nuclei are separated using an improved watershed algorithm based on a concave vertex graph. Finally, to identify positive and negative stained nuclei, all the segmented nuclei are classified into five categories according to their staining intensity and morphological features using a trained multilayer neural network combined with Fisher's linear discriminant preprocessing. The proposed method is tested on a large dataset containing several breast tissue images with different levels of malignancy. The experimental results show high agreement between the results of the method and ground-truth from the pathologist panel. Furthermore, a comparative study versus existing techniques is presented in order to demonstrate the efficiency and the superiority of the proposed method.

On the Erdős–Szekeres [formula omitted]-interior-point problem

The n-interior-point variant of the Erdős–Szekeres problem is the following: for every n,n≥1, does there exist a g(n) such that every point set in the plane with at least g(n) interior points has a convex polygon containing exactly n interior points. The existence of g(n) has been proved only for n≤3. In this paper, we show that for any fixed r≥2, and for every n≥5, every point set having sufficiently large number of interior points and at most r convex layers contains a subset with exactly n interior points. We also consider a relaxation of the notion of convex polygons and show that for every n,n≥1, any point set with at least n interior points has an almost convex polygon (a simple polygon with at most one concave vertex) that contains exactly n interior points.

Automatic image segmentation of nuclear stained breast tissue sections using color active contour model and an improved watershed method

Automatic image segmentation of immunohistologically stained breast tissue sections helps pathologists to discover the cancer disease earlier. The detection of the real number of cancer nuclei in the image is a very tedious and time consuming task. Segmentation of cancer nuclei, especially touching nuclei, presents many difficulties to separate them by traditional segmentation algorithms. This paper presents a new automatic scheme to perform both classification of breast stained nuclei and segmentation of touching nuclei in order to get the total number of cancer nuclei in each class. Firstly, a modified geometric active contour model is used for multiple contour detection of positive and negative nuclear staining in the microscopic image. Secondly, a touching nuclei method based on watershed algorithm and concave vertex graph is proposed to perform accurate quantification of the different stains. Finally, benign nuclei are identified by their morphological features and they are removed automatically from the segmented image for positive cancer nuclei assessment. The proposed classification and segmentation schemes are tested on two datasets of breast cancer cell images containing different level of malignancy. The experimental results show the superiority of the proposed methods when compared with other existing classification and segmentation methods. On the complete image database, the segmentation accuracy in term of cancer nuclei number is over than 97%, reaching an improvement of 3–4% over earlier methods.

The Role of Figure-Ground in the Corner Enhancement Effect

The appearance of a new object in the visual field captures visual attention. Moreover, detection is faster for a probe presented in a region adjacent to the corner of a stimulus, compared to a probe adjacent to the straight edge. This corner enhancement effect is believed to show that probes near corners receive enhanced processing (Cole et al 2007, Attention, Perception and Psychophysics69, 400–412). We tested the corner effect for convex and concave corners for surfaces arranged in depth. We used coloured regions with cast shadows to specify foreground and background and a square stimulus that could be perceived as either an object or a hole (a figure-ground reversal). The probe was a small red line that could appear near a corner or a straight edge 100 msec after the stimulus onset. We asked the participants to discriminate the orientation of the probe (horizontal or vertical). The corner effect was found for both convex (Experiment 1) and concave (Experiment 2) vertices but only when the probe was ne...

CudaHull: Fast parallel 3D convex hull on the GPU

In this paper, we present a novel parallel algorithm for computing the convex hull of a set of points in 3D using the CUDA programming model. It is based on the QuickHull approach and starts by constructing an initial tetrahedron using four extreme points, discards the internal points, and distributes the external points to the four faces. It then proceeds iteratively. In each iteration, it refines the faces of the polyhedron, discards the internal points, and redistributes the remaining points for each face among its children faces. The refinement of a face is performed by selecting the furthest point from its associated points and generating three children triangles. In each iteration, concave edges are swapped, and concave vertices are removed to maintain convexity. The face refinement procedure is performed on the CPU, because it requires a very small fraction of the execution time (approximately 1%), and the intensive point redistribution is performed in parallel on the GPU. Our implementation outpaced the CPU-based Qhull implementation by 30 times for 10 million points and 40 times for 20 million points.

Output-Sensitive Computation of Force-Closure Grasps of a Semi-Algebraic Object

We propose a technique which significantly simplifies the computation of frictionless force-closure grasps of a curved planar part <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$P$</tex></formula> . We use a colored projection scheme from the three-dimensional wrench space to two-dimensional screens, which allows us to reduce the problem of identifying combinations of arcs and concave vertices of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> that admit frictionless force-closure grasps, to colored intersection searching problems in the screens. We show how to combine this technique with existing intersection searching algorithms to obtain efficient, output-sensitive algorithms to compute all force-closure grasps of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$P$</tex></formula> , where at most four hard, frictionless point contacts exert exactly four wrenches on <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$P$</tex></formula> . If the boundary of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$P$</tex></formula> consists of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$n$</tex></formula> algebraic arcs of constant complexity and <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$m$</tex></formula> concave vertices, we show how to compute all force-closure grasps with: <orderedlist continuation="restarts" numeration="bullet" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <listitem><para>four contacts along four arcs in <formula formulatype="inline"> <tex Notation="TeX">$O(n^{8/3}\log ^{1/3}n+K)$</tex></formula> time;</para></listitem></orderedlist>

Testing a rotation axis to drain a 3D workpiece

Given a triangular mesh defining the geometry of a 3D workpiece filled with water, we propose an algorithm to test whether, for an arbitrary given axis, the workpiece will be completely drained under gravity when the rotation axis is set parallel to the ground and the workpiece is rotated around the axis. Observing that all water traps contain a concave vertex, we solve our problem by constructing and analyzing a directed “ draining graph” whose nodes correspond to concave vertices of the geometry and whose edges are set according to the transition of trapped water when we rotate the workpiece around the given axis. Our algorithm to test whether or not a given rotation axis drains the workpiece outputs a result in about a second for models with more than 100,000 triangles after a few seconds of preprocessing.

An algorithm for determining concave vertex of object based on vector product

Concave vertex of an object is an important parameter for analyzing an object’s shape. A new algorithm for searching concave vertex is proposed in this paper. The new algorithm requires tracking the border firstly, and then uses sampling border to obtain coordinates sequence of discrete boundary points. Each sampling point of the discrete border is determined to be either concave or convex according to the value of vector product. Two inflexions can be searched by the change of concavo-convex trend. The region between two inflexions is defined as concave area. The values of distance are calculated between all boundary points on the concave area and a straight line connected by two inflexions. The boundary point corresponding to the greatest distances is max concave vertex, or the object’s concave vertex. Experimental results have proved that the new algorithm can extract the max concave vertexes of an object accurately and reliably.

Grasping Non-stretchable Cloth Polygons

In this paper, we examine non-stretchable two-dimensional polygonal cloth, and place bounds on the number of fingers needed to immobilize it. For any non-stretchable cloth polygon, it is always necessary to pin all of the convex vertices. We show that for some shapes, more fingers are necessary. No more than one-third of the concave vertices need to be pinned for simple polygons, and no more than one-third of the concave vertices plus two fingers per hole are necessary for polygons with holes.

Smooth Anatomical Models From 3D Imaging

3D imaging has become a standard tool in medical diagnostics and, while software is available to visualize volumetric data sets, we do not yet have software that can efficiently transform 3D scan data to solid models that are useful for engineering design and analysis. Why not? Currently, deriving solid models from 3D scans involves 3 steps: (1) segmentation: identification of voxels associated with the structure; (2) polygonization: computing a set of polygons that approximate the surface of the structure; and (3) repair: removing stray voxels and polygons, specifying connectivity, and establishing consistent orientation. Significant progress has been made on accurate, automated segmentation (recent work by Hu et al. (Image Segmentation and Registration for the Analysis of Joint Motion From 3D MRI,” Proc SPIE 6141, pp. 133–142, Medical Imaging: Visualization, Image-Guided Procedures, &amp; Display, 2006), combining graph cuts with level sets is of particular interest) but effective polygonization cannot be guaranteed. In the worst case, manual repairs are needed to patch holes and remove stray elements. Even if a valid boundary representation (b-rep) model is obtained, accurate models contain so many polygons that modeling operations become unfeasible. Moreover, regardless of accuracy, the surface of a polyhedral model will never be truly smooth. In previous work (Storti, D., et al., Artifact vs. Anatomy: Dealing With Conflict of Geometric Modeling Descriptions,” SAE 2007 Transactions Journal of Passenger Cars: Electronic and Electrical Systems, Paper No. 2007-01-2450, Vol. 116, pp. 813–823, 2007), we proposed overcoming the barriers to creating solid models from 3D scans by employing a new solid modeling description, wavelet SDF-reps, that lies much closer to the native 3D scan format and eliminates polygonization. Here, we focus on the ability to produce models with smooth surfaces that are important for various biomedical simulations. For example, careful studies of joint function involve detailed modeling of ligament wrapping; i.e., connective tissue moving across bone surface as the joint configuration changes. Realistic behavior cannot be obtained if the ligament is snagging on or snapping across convex vertices of a polyhedral model. Similarly, haptic simulation of a catheter navigating through the circulatory system cannot be realistic if the catheter gets stuck in concave vertices of the anatomical model. How can the new modeling format address such issues? Wavelet SDF-reps take advantage of a by-product of the segmentation algorithm (Hue et al.) which converts the raw voxel intensity values to a grid of signed distance values. Applying an appropriate interpolant such as Daubechies wavelets (Daubechies, I., Wavelets, CBMS-NS Series in Applied Mathematics, SIAM Publications, Philadelphia, 1992) then produces an implicit or function-based (f-rep) solid model of the segmented structure. Wavelet SDF-reps are inherently multi-resolution and support significant data compression and medial axis computation. We illustrate the capability of wavelet SDF-reps to support smooth models and enable analysis of curvature features.

Detection of convexity and concavity in context.

Sensitivity to shape changes was measured, in particular detection of convexity and concavity changes. The available data are contradictory. The author used a change detection task and simple polygons to systematically manipulate convexity/concavity. Performance was high for detecting a change of sign (a new concave vertex along a convex contour or a new convex vertex along a concave contour). Other things being equal, there was no evidence of an advantage for detecting a new concavity compared with a new convexity, for detecting a change of angle to a concave vertex compared with a convex vertex, for detecting a change within a concave region compared with a change within a convex region, or for an interaction between convexity and concavity and changes affecting or not affecting a vertex. The author concludes that change detection is affected by changes of sign of curvature (leading to changes in part structure). However, contrary to previous proposals, there is no special role for negative curvature or minima of curvature in guiding attention.

Boundary Mapping and Boundary-State Routing (BSR) in Ad Hoc Networks

This paper presents a geographic routing protocol, boundary state routing (BSR), which consists of two components. The first is an improved forwarding strategy, greedy-bounded compass, which can forward packets around concave boundaries, where the packet moves away from the destination without looping. The second component is a boundary mapping protocol (BMP), which is used to maintain link state information for boundaries containing concave vertices. The proposed forwarding strategy greedy-bounded compass is shown to produce a higher rate of path completion than Greedy forwarding and significantly improves the performance of greedy perimeter state routing (GPSR) in sparse networks when used in place of greedy forwarding. The proposed geographic routing protocol BSR is shown to produce significant improvements in performance in comparison to GPSR in sparse networks due to informed decisions regarding the direction of boundary traversal at local minima.

Automatic image analysis of histopathology specimens using concave vertex graph.

Automatic image analysis of histopathology specimens would help the early detection of blood cancer. The first step for automatic image analysis is segmentation. However, touching cells bring the difficulty for traditional segmentation algorithms. In this paper, we propose a novel algorithm which can reliably handle touching cells segmentation. Robust estimation and color active contour models are used to delineate the outer boundary. Concave points on the boundary and inner edges are automatically detected. A concave vertex graph is constructed from these points and edges. By minimizing a cost function based on morphological characteristics, we recursively calculate the optimal path in the graph to separate the touching cells. The algorithm is computationally efficient and has been tested on two large clinical dataset which contain 207 images and 3898 images respectively. Our algorithm provides better results than other studies reported in the recent literature.