scholarly journals $S$-Hypersimplices, Pulling Triangulations, and Monotone paths

10.37236/8457 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Sebastian Manecke ◽  
Raman Sanyal ◽  
Jeonghoon So
Keyword(s):  
Convex Hull ◽  
Monotone Path ◽  
Monotone Paths

An $S$-hypersimplex for $S \subseteq \{0,1, \dots,d\}$ is the convex hull of all $0/1$-vectors of length $d$ with coordinate sum in $S$. These polytopes generalize the classical hypersimplices as well as cubes, crosspolytopes, and halfcubes. In this paper we study faces and dissections of $S$-hypersimplices. Moreover, we show that monotone path polytopes of $S$-hypersimplices yield all types of multipermutahedra. In analogy to cubes, we also show that the number of simplices in a pulling triangulation of a halfcube is independent of the pulling order.

Monotone Descent Path Queries on Dynamic Terrains

2014 ◽  
Vol 14 (1) ◽  
Author(s):  
Xiangzhi Wei ◽  
Ajay Joneja ◽  
Yaobin Tian ◽  
Yan-An Yao
Keyword(s):  
Data Structure ◽  
Engineering Design ◽  
Linear Time ◽  
Monotone Path ◽  
Path Queries ◽  
Contour Tree ◽  
Monotone Paths

Monotone paths are useful in many engineering design applications. In this paper, we address the problem of answering monotone descent path queries on terrains that are continually changing. A terrain can be represented by a unique contour tree. Such a contour tree belongs to a class of graphs called arbitrarily directed trees (ADTs). Let T be an ADT with n nodes. In this paper, we present a new linear time preprocessing algorithm for decomposing a static ADT T into a forest F, with which we can answer lowest common descendent (LCA) queries in O(1) time. This is useful in answering monotone path queries on the corresponding terrain. We show how to maintain this data structure, and thereby answer LCA queries efficiently, for dynamic ADTs. We also show how to maintain the data structure of dynamic terrains, while simultaneously maintaining the corresponding contour tree. This allows us to efficiently answer monotone path queries between any two points on dynamic terrains.

Monotone Paths on Zonotopes and Oriented Matroids

2001 ◽  
Vol 53 (6) ◽  
pp. 1121-1140
Author(s):  
Christos A. Athanasiadis ◽  
Francisco Santos
Keyword(s):  
Lower Bound ◽  
Coxeter Groups ◽  
Natural Generalization ◽  
Oriented Matroids ◽  
Oriented Matroid ◽  
Monotone Path ◽  
Maximal Chains ◽  
Monotone Paths

AbstractMonotone paths on zonotopes and the natural generalization to maximal chains in the poset of topes of an oriented matroid or arrangement of pseudo-hyperplanes are studied with respect to a kind of local move, called polygon move or flip. It is proved that any monotone path on a $d$-dimensional zonotope with $n$ generators admits at least $\left\lceil 2n/\left( n-d+2 \right) \right\rceil -1$ flips for all $n\ge d+2\ge 4$ and that for any fixed value of $n-d$, this lower bound is sharp for infinitely many values of $n$. In particular, monotone paths on zonotopes which admit only three flips are constructed in each dimension $d\ge 3$. Furthermore, the previously known 2-connectivity of the graph of monotone paths on a polytope is extended to the 2-connectivity of the graph of maximal chains of topes of an oriented matroid. An application in the context of Coxeter groups of a result known to be valid for monotone paths on simple zonotopes is included.

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.

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