A New Version of KKM Theorem with Geodesic Convex Hull with an Application on Hadamard Manifold

2019 ◽  
Vol 10 (1si) ◽  
pp. 247
Author(s):  
J.C. Yao
Keyword(s):  
Convex Hull ◽  
Hadamard Manifold ◽  
Kkm Theorem ◽  
Geodesic Convex

Two classes of graphs in which some problems related to convexity are efficiently solvable

2018 ◽  
Vol 10 (03) ◽  
pp. 1850042
Author(s):  
Marina Moscarini ◽  
Francesco M. Malvestuto
Keyword(s):  
Convex Hull ◽  
Polynomial Time ◽  
Convex Set ◽  
Linear Time ◽  
Shortest Paths ◽  
Minimum Cardinality ◽  
Vertex Set ◽  
Geodesic Convex ◽  
Cyclic Graph

Monophonic, geodesic and 2-geodesic convexities ([Formula: see text]-convexity, [Formula: see text]-convexity and [Formula: see text]-convexity, for short) on graphs are based on the families of induced paths, shortest paths and shortest paths of length [Formula: see text], respectively. We introduce a class of graphs, the class of cross-cyclicgraphs, in which every connected [Formula: see text]-convex set is also [Formula: see text]-convex and [Formula: see text]-convex. We show that this class is properly contained in the class, say [Formula: see text], of graphs in which geodesic and monophonic convexities are equivalent and properly contains the class of distance-hereditary graphs. Moreover, we show that (1) an [Formula: see text]-hull set (i.e., a subset of vertices, with minimum cardinality, whose [Formula: see text]-convex hull equals the whole vertex set) and, hence, the m-hull number and the g-hull number of a graph in [Formula: see text] can be computed in polynomial time and that (2) both the geodesic-convex hull and the monophonic-convex hull can be computed in linear time in a cross-cyclic graph without cycles of length [Formula: see text] and, hence, in a bipartite distance-hereditary graph.

Convex hull of chain-coded blob

1989 ◽  
Vol 136 (6) ◽  
pp. 530
Author(s):  
G.R. Wilson ◽  
B.G. Batchelor
Keyword(s):  
Convex Hull

Saliency Detection Based on Improved Manifold Ranking via Convex Hull

2019 ◽  
Vol 31 (5) ◽  
pp. 761
Author(s):  
Xiao Lin ◽  
Zuxiang Liu ◽  
Xiaomei Zheng ◽  
Jifeng Huang ◽  
Lizhuang Ma
Keyword(s):  
Convex Hull ◽  
Saliency Detection ◽  
Manifold Ranking

scholarly journals On the expected diameter, width, and complexity of a stochastic convex hull

2019 ◽  
Vol 82 ◽  
pp. 16-31 ◽  
Author(s):  
Jie Xue ◽  
Yuan Li ◽  
Ravi Janardan
Keyword(s):  
Convex Hull

Spherical object recognition based on the number of contour edges extracted by fitting and convex hull processing

2020 ◽  
pp. 095440702096950
Author(s):  
Bochang Zou ◽  
Huadong Qiu ◽  
Yufeng Lu
Keyword(s):  
Convex Hull ◽  
Target Object ◽  
Identification Accuracy ◽  
Detection Accuracy ◽  
Morphological Operations ◽  
Circle Detection ◽  
Spherical Object ◽  
Single Feature ◽  
Contour Fitting ◽  
Rgb Images

The detection of spherical targets in workpiece shape clustering and fruit classification tasks is challenging. Spherical targets produce low detection accuracy in complex fields, and single-feature processing cannot accurately recognize spheres. Therefore, a novel spherical descriptor (SD) for contour fitting and convex hull processing is proposed. The SD achieves image de-noising by combining flooding processing and morphological operations. The number of polygon-fitted edges is obtained by convex hull processing based on contour extraction and fitting, and two RGB images of the same group of objects are obtained from different directions. The two fitted edges of the same target object obtained at two RGB images are extracted to form a two-dimensional array. The target object is defined as a sphere if the two values of the array are greater than a custom threshold. The first classification result is obtained by an improved K-NN algorithm. Circle detection is then performed on the results using improved Hough circle detection. We abbreviate it as a new Hough transform sphere descriptor (HSD). Experiments demonstrate that recognition of spherical objects is obtained with 98.8% accuracy. Therefore, experimental results show that our method is compared with other latest methods, HSD has higher identification accuracy than other methods.

scholarly journals The construction of local convex hull on the task of pattern recognition

2021 ◽  
Vol 186 ◽  
pp. 360-365
Author(s):  
Kamilov Mirzoyan ◽  
Hudayberdiev Mirzaakbar ◽  
Khamroev Alisher
Keyword(s):  
Pattern Recognition ◽  
Convex Hull ◽  
Local Convex

scholarly journals Enhanced CD4+ and CD8+ T cell infiltrate within convex hull defined pancreatic islet borders as autoimmune diabetes progresses

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander J. Dwyer ◽  
Jacob M. Ritz ◽  
Jason S. Mitchell ◽  
Tijana Martinov ◽  
Mohannad Alkhatib ◽  
...  
Keyword(s):  
T Cells ◽  
T Cell ◽  
Convex Hull ◽  
Pancreatic Islets ◽  
Immune Cell ◽  
Nod Mice ◽  
Cell Infiltration ◽  
Immune Cell Infiltration ◽  
Analytical Strategy ◽  
Islet Mass

AbstractThe notion that T cell insulitis increases as type 1 diabetes (T1D) develops is unsurprising, however, the quantitative analysis of CD4+ and CD8+ T cells within the islet mass is complex and limited with standard approaches. Optical microscopy is an important and widely used method to evaluate immune cell infiltration into pancreatic islets of Langerhans for the study of disease progression or therapeutic efficacy in murine T1D. However, the accuracy of this approach is often limited by subjective and potentially biased qualitative assessment of immune cell subsets. In addition, attempts at quantitative measurements require significant time for manual analysis and often involve sophisticated and expensive imaging software. In this study, we developed and illustrate here a streamlined analytical strategy for the rapid, automated and unbiased investigation of islet area and immune cell infiltration within (insulitis) and around (peri-insulitis) pancreatic islets. To this end, we demonstrate swift and accurate detection of islet borders by modeling cross-sectional islet areas with convex polygons (convex hulls) surrounding islet-associated insulin-producing β cell and glucagon-producing α cell fluorescent signals. To accomplish this, we used a macro produced with the freeware software ImageJ equipped with the Fiji Is Just ImageJ (FIJI) image processing package. Our image analysis procedure allows for direct quantification and statistical determination of islet area and infiltration in a reproducible manner, with location-specific data that more accurately reflect islet areas as insulitis proceeds throughout T1D. Using this approach, we quantified the islet area infiltrated with CD4+ and CD8+ T cells allowing statistical comparison between different age groups of non-obese diabetic (NOD) mice progressing towards T1D. We found significantly more CD4+ and CD8+ T cells infiltrating the convex hull-defined islet mass of 13-week-old non-diabetic and 17-week-old diabetic NOD mice compared to 4-week-old NOD mice. We also determined a significant and measurable loss of islet mass in mice that developed T1D. This approach will be helpful for the location-dependent quantitative calculation of islet mass and cellular infiltration during T1D pathogenesis and can be combined with other markers of inflammation or activation in future studies.

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