Shortest paths and convex hulls in 2D complexes with non-positive curvature

Lubiw, Anna; Maftuleac, Daniela; Owen, Megan

doi:10.1016/j.comgeo.2020.101626

Cited by 6 publications

(6 citation statements)

References 53 publications

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“…Using the convex hull in MDS space to start our approach helped reduce the geodesic distance matrix size used to create the visualizations. In a way, we treat the convex hull in MDS space as an approximation of the convex hull in treespace (Lubiw et al 2020; Lin et al 2017). However, we believe that the hull defined by MDS allows us to investigate good and best trees within its boundary.…”

Section: Discussionmentioning

confidence: 99%

Geodesics to Characterize the Phylogenetic Landscape

Khodaei

Owen

Beerli

2022

Preprint

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Phylogenetic trees are fundamental for understanding the evolutionary history of a set of species. The local neighborhoods of a phylogenetic tree provide important information, but since trees are high-dimensional objects, characterizing these neighborhoods is difficult. Based on the Billera-Holmes-Vogtmann (BHV) distance between pairs of trees, we describe a method to generate intermediate trees on the shortest path between two arbitrary trees, called pathtrees. These pathtrees give a structured way to investigate intermediate neighborhoods between trees of interest in the BHV treespace and can also be used to find high likelihood trees independently of traditional heuristic search mechanisms. We implemented our algorithm in the Python package Pathtrees, which enables the construction of the continuous tree landscape interior of the convex hull of starting trees, low-dimensional visualization of the generated tree landscape, identifying clusters of trees with the same topologies, and searching for the best tree.

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Section: Discussionmentioning

confidence: 99%

Geodesics to Characterize the Phylogenetic Landscape

Khodaei

Owen

Beerli

2022

Preprint

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“…The screw thread surface point cloud is a 3D cloud that contains a massive amount of data. The random incremental algorithm is used to calculate the CH effectively and quickly [20]. The calculation process is as follows:…”

Section: ) Processing Of the Point Set Of The 3d Chmentioning

confidence: 99%

“…When the number of particles is low, the iteration speed is high and premature convergence can easily occur. When fitting a loworder objective function for the central axis of a screw thread, high efficiency is achieved when the number of particles is <100 [21]. After many experiments, the number of particles was set as 50 in this study.…”

Section: ) Processing Of the Point Set Of The 3d Chmentioning

confidence: 99%

Improved Particle Swarm Optimization Algorithm Based on a Three-Dimensional Convex Hull for Fitting a Screw Thread Central Axis

et al. 2021

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“…The convex hull method is used for calculating the volume of these plants. The recent research in reference [26] deals also with this method in the aim to find the shortest path in 2D complexes with non-positive curvatures. The convex hull method is often used for the determination of an area and perimeter in 2D shapes.…”

Section: Related Workmentioning

confidence: 99%

Advanced Methods for Point Cloud Processing and Simplification

et al. 2020

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Nowadays, mobile robot exploration needs a rangefinder to obtain a large number of measurement points to achieve a detailed and precise description of a surrounding area and objects, which is called the point cloud. However, a single point cloud scan does not cover the whole area, so multiple point cloud scans must be acquired and compared together to find the right matching between them in a process called registration method. This method requires further processing and places high demands on memory consumption, especially for small embedded devices in mobile robots. This paper describes a novel method to reduce the burden of processing for multiple point cloud scans. We introduce our approach to preprocess an input point cloud in order to detect planar surfaces, simplify space description, fill gaps in point clouds, and get important space features. All of these processes are achieved by applying advanced image processing methods in combination with the quantization of physical space points. The results show the reliability of our approach to detect close parallel walls with suitable parameter settings. More importantly, planar surface detection shows a 99% decrease in necessary descriptive points almost in all cases. This proposed approach is verified on the real indoor point clouds.

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Shortest paths and convex hulls in 2D complexes with non-positive curvature

Cited by 6 publications

References 53 publications

Geodesics to Characterize the Phylogenetic Landscape

Geodesics to Characterize the Phylogenetic Landscape

Improved Particle Swarm Optimization Algorithm Based on a Three-Dimensional Convex Hull for Fitting a Screw Thread Central Axis

Advanced Methods for Point Cloud Processing and Simplification

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