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Sparse 3D Topological Graphs for Micro-Aerial Vehicle Planning [article]

Helen Oleynikova, Zachary Taylor, Roland Siegwart, Juan Nieto
2018 arXiv   pre-print
We use a Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram (GVD), and obtain a thin skeleton diagram representing the topological structure of the environment.  ...  We then convert this skeleton diagram into a sparse graph, which we show is resistant to noise and changes in resolution.  ...  GVD Generation In order to generate the original Generalized Voronoi Diagram, we follow the common approach of finding "ridges" in the signed distance function [18] , [7] .  ... 
arXiv:1803.04345v2 fatcat:zi7hlluz2bh4xdaygrl7rd65vm

Visualization and Analysis of Second-Order Tensors: Moving Beyond the Symmetric Positive-Definite Case

A. Kratz, C. Auer, M. Stommel, I. Hotz
2012 Computer graphics forum (Print)  
For interactive exploration of the data, we propose to combine diagram views with three-dimensional hybrid visualizations.  ...  We show that this facilitates familiarizing with the data and leads to exciting analytic queries. If a geometric data reduction is possible, we focus on glyph-and texture-based methods.  ...  To ensure a time-efficient solution, we apply a distance measure that has already been successfully used in previous work [Labelle and Shewchuk, 2003; Feng et al., 2008] to generalize Voronoi diagrams  ... 
doi:10.1111/j.1467-8659.2012.03231.x fatcat:bamlrmjhvjfwxcnekmddn7bzm4

Computational Geometry-Based Surface Reconstruction for Volume Estimation: A Case Study on Magnitude-Frequency Relations for a LiDAR-Derived Rockfall Inventory

Paul-Mark DiFrancesco, David A. Bonneau, D. Jean Hutchinson
2021 ISPRS International Journal of Geo-Information  
Given various point cloud imperfections, it is difficult for methods to generate digital surface representations of rockfall with detailed geometry and correct topology.  ...  The Alpha Solid approach is to be used on small-scale point clouds, characterized with high curvatures relative to their sampling density, which challenge the Power Crust sampling assumptions.  ...  Note that all proximity and distance metrics utilized in the definitions refer to Euclidean distance. The Delaunay triangulation (blue), which is the dual graph of the Voronoi diagram (black).  ... 
doi:10.3390/ijgi10030157 fatcat:jld4lorsk5hdlb3q3ibh5eltiq

Geometric Detection Algorithms for Cavities on Protein Surfaces in Molecular Graphics: A Survey

Tiago Simões, Daniel Lopes, Sérgio Dias, Francisco Fernandes, João Pereira, Joaquim Jorge, Chandrajit Bajaj, Abel Gomes
2017 Computer graphics forum (Print)  
Furthermore, these surveys agree on a simplified classification of cavity detection algorithms into the following classes: sphere-based, grid-based, and Voronoi-based.  ...  Such cavities correspond to pockets, clefts, invaginations, voids, tunnels, channels, and grooves on the surface of a given protein.  ...  Zhang and Bajaj's method Zhang and Bajaj [ZB07] introduced a new cavity detection method based on a signed distance function in relation to the molecular surface.  ... 
doi:10.1111/cgf.13158 pmid:29520122 pmcid:PMC5839519 fatcat:5t4rhndtunhvtmkm32niknst7i

Protein pocket detection via convex hull surface evolution and associated Reeb graph

Rundong Zhao, Zixuan Cang, Yiying Tong, Guo-Wei Wei
2018 Bioinformatics  
This work introduces a computational tool based on differential geometry, algebraic topology and physics-based simulation to address this pressing issue.  ...  The surface evolution induced Morse function and Reeb graph are utilized to characterize the hierarchical pocket and sub-pocket structure in controllable detail.  ...  Voronoi based methods, introduced by Liang et al. (1998) , have been proposed to compare the differences between alpha shapes and the Delaunay triangulation (dual structure to Voronoi diagram) to find  ... 
doi:10.1093/bioinformatics/bty598 pmid:30423105 pmcid:PMC6129271 fatcat:qkgmoznncnd3jf7kewi2opuy6e

Parallel centerline extraction on the GPU

Baoquan Liu, Alexandru C. Telea, Jos B.T.M. Roerdink, Gordon J. Clapworthy, David Williams, Po Yang, Feng Dong, Valeriu Codreanu, Alessandro Chiarini
2014 Computers & graphics  
In this paper, we present a new parallel centerline extraction algorithm suitable for implementation on a GPU to produce highly accurate, 26-connected, one-voxel-thick centerlines at interactive speed.  ...  Some methods based on distance mapping are accurate, but these are sequential algorithms which have limited performance when running on the CPU.  ...  The DFB field is stored as a signed floating-point distance field, that is, it has positive values for voxels inside ∂ Ω, zero values on ∂ Ω, and negative values outside ∂ Ω.  ... 
doi:10.1016/j.cag.2014.02.003 fatcat:iq3e6ypz7bcpfd2duwvsnt4qvm

Time-efficient sparse analysis of histopathological whole slide images

Chao-Hui Huang, Antoine Veillard, Ludovic Roux, Nicolas Loménie, Daniel Racoceanu
2011 Computerized Medical Imaging and Graphics  
It relies on specific high and generic low resolution image analysis algorithms embedded in a multi-scale framework to rapidly identify the high power fields of interest used by the pathologist to assess  ...  The time processing to achieve automatic WSI analysis is on a par with the pathologist's performance (about ten minutes a WSI), which constitutes by itself a major contribution of the proposed methodology  ...  Acknowledgment This study has been partially supported by the MMed-Web 3 grant A*STAR SERC 052 101 0103 (NUS R-252-000-319-305) and by the ONCO-MEDIA 4 . We would like to thank Dr.  ... 
doi:10.1016/j.compmedimag.2010.11.009 pmid:21145705 fatcat:fqjtr4wfabftxa7m4bzrxgvrwy

Multi-architecture Monte-Carlo (MC) simulation of soft coarse-grained polymeric materials:SOft coarse grained Monte-carlo Acceleration (SOMA)

L. Schneider, M. Müller
2018 Computer Physics Communications  
We achieve efficiency of the simulations commissioning accelerators like GPUs on both workstations as well as supercomputers.  ...  The Single-Chain-in-Mean-Field (SCMF) algorithm in conjunction with a soft, coarse-grained polymer model is an established technique to investigate these soft-matter systems.  ...  We are planning to further develop SOMA, to integrate additional features, and to tune execution efficiency for other accelerators and invite researchers at other institutions to use the program and contribute  ... 
doi:10.1016/j.cpc.2018.08.011 fatcat:dle4e32syvapzl5pi5s7v2tsu4

Interactive Modeling of Cellular Structures on Surfaces with Application to Additive Manufacturing

P. Stadlbauer, D. Mlakar, H.‐P. Seidel, M. Steinberger, R. Zayer
2020 Computer graphics forum (Print)  
Unfortunately, interactive control of such patterns-as modeled by Voronoi diagrams, is limited to the simple two dimensional case and does not extend well to freeform surfaces.  ...  Together with shells, they can be conveniently packed to save on production time.  ...  A workaround is the so called restricted Voronoi diagrams, i.e., the intersection of the surface and a volumetric Voronoi diagram.  ... 
doi:10.1111/cgf.13929 fatcat:xmy6wgjmvrcsrjuzwlzryx7cje

Algorithms for Interactive Editing of Level Set Models

Ken Museth, David E. Breen, Ross T. Whitaker, Sean Mauch, David Johnson
2005 Computer graphics forum (Print)  
This paper describes the collection of techniques and algorithms (some new, some pre-existing) needed to overcome these challenges and to create an interactive editing system for this new type of geometric  ...  Level set models combine a low-level volumetric representation, the mathematics of deformable implicit surfaces, and powerful, robust numerical techniques to produce a novel approach to shape design.  ...  Based on this observation, a 3D Voronoi diagram is built for the faces, edges and vertices of the mesh, with each Voronoi cell defined by a polyhedron.  ... 
doi:10.1111/j.1467-8659.2005.00904.x fatcat:wb6d7cwg6jbuzae2dsgppcljgq

Summary on Several Key Techniques in 3D Geological Modeling

Gang Mei
2014 The Scientific World Journal  
Note that these techniques are generic and widely used in various applications but play a key role in 3D geological modeling.  ...  There are two essential procedures in 3D geological modeling: the first is the simulation of geological interfaces using geometric surfaces and the second is the building of geological objects by means  ...  Conflict of Interests The author declares that there is no conflict of interests regarding the publication of this paper.  ... 
doi:10.1155/2014/723832 pmid:24772029 pmcid:PMC3948591 fatcat:33c23hcuarhrzpzb4swe5cdc3m

Medical image processing on the GPU – Past, present and future

Anders Eklund, Paul Dufort, Daniel Forsberg, Stephen M. LaConte
2013 Medical Image Analysis  
This review presents the past and present work on GPU accelerated medical image processing, and is meant to serve as an overview and introduction to existing GPU implementations.  ...  The review covers GPU acceleration of basic image processing operations (filtering, interpolation, histogram estimation and distance transforms), the most commonly used algorithms in medical imaging (image  ...  Acknowledgement We would like to acknowledge the helpful comments and suggestions of Cyrus Eierud. Daniel Forsberg was funded by the Swedish Research Council (grant 2007-4786).  ... 
doi:10.1016/j.media.2013.05.008 pmid:23906631 fatcat:vsoek36pb5cuxdcmhlvfojwjuu

Hydra: A Real-time Spatial Perception Engine for 3D Scene Graph Construction and Optimization [article]

Nathan Hughes, Yun Chang, Luca Carlone
2022 arXiv   pre-print
We evaluate Hydra on simulated and real data and show it is able to reconstruct 3D scene graphs with an accuracy comparable with batch offline methods, while running online.  ...  Our first contribution is to develop real-time algorithms to incrementally construct the layers of a scene graph as the robot explores the environment; these algorithms build a local Euclidean Signed Distance  ...  The authors in [50] use Voxblox [43] to integrate semantically-labeled point clouds into a monolithic Truncated Signed Distance Field (TSDF) and an ESDF of the environment, while also performing Bayesian  ... 
arXiv:2201.13360v1 fatcat:o2pcudstnnha7oeugwog2uvz2e

Modeling and Visualization of Multi-material Volumes

P.-A. Fayolle, L. McLoughlin, M. Sanchez, G. Pasko, A. Pasko
2021 Scientific Visualization  
The classification of the multimaterial volumes is given from the spatial partitions, spatial domain for material distribution, types of involved scalar fields and types of models for material distribution  ...  In addition to the technical challenges of multi-material volume representations, a range of key challenges are considered before such representations can be adopted as mainstream practice.  ...  One approach consists in introducing connectivity by computing the Delaunay triangulation (or its dual the Voronoi diagram) of the points to find the natural neighbors of a given evaluation point and then  ... 
doi:10.26583/sv.13.2.09 fatcat:js26xkn6qrdrpa6chzeif5vtbm

Tracing the dark matter sheet in phase space

Tom Abel, Oliver Hahn, Ralf Kaehler
2012 Monthly notices of the Royal Astronomical Society  
Because of gravitational forces this three dimensional manifold evolves in phase space without ever tearing, conserving phase-space volume and preserving the connectivity of nearby points.  ...  Particles are considered as the vertices of an unstructured three dimensional mesh, moving in six dimensional phase-space. On this mesh, mass density and momentum are uniquely defined.  ...  ACKNOWLEDGEMENTS T.A. is grateful for numerous conversations with Greg Bryan in the past ten years on how one might solve for dark matter dynamics directly in phase-space and acknowledges support by the  ... 
doi:10.1111/j.1365-2966.2012.21754.x fatcat:xms5ytgspvfzjelkoqhdouja6u
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