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Reconstruction of Convex Polytope Compositions from 3D Point-clouds [article]

Markus Friedrich, Pierre-Alain Fayolle
2021 arXiv   pre-print
Reconstructing a composition (union) of convex polytopes that perfectly fits the corresponding input point-cloud is a hard optimization problem with interesting applications in reverse engineering and  ...  We propose a pipeline that first extracts a set of planes, then partitions the input point-cloud into weakly convex clusters and finally generates a set of convex polytopes as the intersection of fitted  ...  We deal in this work with the problem of reconstructing a solid from a 3D point-cloud as a composition (union) of convex polytopes.  ... 
arXiv:2105.02956v1 fatcat:4727rbkljvcy5nyuhtoqw74ny4

CvxNet: Learnable Convex Decomposition [article]

Boyang Deng, Kyle Genova, Soroosh Yazdani, Sofien Bouaziz, Geoffrey Hinton, Andrea Tagliasacchi
2020 arXiv   pre-print
We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.  ...  Any solid object can be decomposed into a collection of convex polytopes (in short, convexes).  ...  Our method reconstruct a 3D object from an input image as a collection of convex hulls, and we visualize the explode of these convexes.  ... 
arXiv:1909.05736v4 fatcat:4xpwfjlelrgtvm3fog5bpw4tve

BSP-Net: Generating Compact Meshes via Binary Space Partitioning [article]

Zhiqin Chen and Andrea Tagliasacchi and Hao Zhang
2020 arXiv   pre-print
The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built on a set of planes.  ...  The core ingredient of BSP is an operation for recursive subdivision of space to obtain convex sets.  ...  This work was supported in part by an NSERC grant (No. 611370), a Google Faculty Research Award, and Google Cloud Platform research credits.  ... 
arXiv:1911.06971v6 fatcat:wqilhx5k3zanzm77yvcichov64

Meeting-Merging-Mission: A Multi-robot Coordinate Framework for Large-Scale Communication-Limited Exploration [article]

Yuman Gao, Yingjian Wang, Xingguang Zhong, Tiankai Yang, Mingyang Wang, Zhixiong Xu, Yongchao Wang, Chao Xu, Fei Gao
2021 arXiv   pre-print
For lower bandwidth, each robot utilizes specific polytopes to maintains free space and super frontier information (SFI) as the source for exploration decision-making.  ...  Katz et al. [3] propose to use the HPR (Hidden Point Removal) operator [4] to determine the visibility of a point cloud given a viewpoint, without reconstruction or normal estimation.  ...  Fig. 3 . 3 The process of free space and super frontier information generation. (a) Multi-raduis sampling to create point cloud used for star-convex polytopes.  ... 
arXiv:2109.07764v1 fatcat:apjwh6lacbe7jot53srhysirwa

Scaling of Convex Hull Volume to Body Mass in Modern Primates, Non-Primate Mammals and Birds

Charlotte A. Brassey, William I. Sellers, Alistair Robert Evans
2014 PLoS ONE  
We interpret such departures from isometry in the context of the 'missing mass' of soft tissues that are excluded from the convex hulling process.  ...  Convex hulling involves the calculation of minimum convex hull volumes (vol CH ) from the complete mounted skeletons of modern museum specimens, which are subsequently regressed against body mass (M b  ...  A, point cloud representing both the inner and outer surface contours of the skull; B, illustrates fit of the convex hull around the maximum extent of the skull; C, convex manifold (water-tight) polytope  ... 
doi:10.1371/journal.pone.0091691 pmid:24618736 pmcid:PMC3950251 fatcat:i5bxnrascrbxfgf54kufq3wxzq

Learning Mesh Representations via Binary Space Partitioning Tree Networks [article]

Zhiqin Chen, Andrea Tagliasacchi, Hao Zhang
2021 IEEE Transactions on Software Engineering   pre-print
The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights.  ...  The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets.  ...  This work was supported in part by an NSERC grant (No. 611370) , a Google Faculty Research Award, and Google Cloud Platform research credits.  ... 
doi:10.1109/tpami.2021.3093440 pmid:34185638 arXiv:2106.14274v1 fatcat:dpo5wecu35gwdi5px4rwgrovuy

Convex-hull mass estimates of the dodo (Raphus cucullatus): application of a CT-based mass estimation technique

Charlotte A. Brassey, Thomas G. O'Mahoney, Andrew C. Kitchener, Phillip L. Manning, William I. Sellers
2016 PeerJ  
We generate 3D volumetric renders of the articulated skeletons of 20 species of extant pigeons, and wrap minimum-fit 'convex hulls' around their bony extremities.  ...  Yet the hind limb proportions of dodo have been found to differ considerably from those of their modern relatives, particularly with regards to midshaft diameter.  ...  (Oxford Museum of Natural History), Judith White and Sandra  ... 
doi:10.7717/peerj.1432 pmid:26788418 pmcid:PMC4715441 fatcat:k2u5ksdionfi5efb2dldtznevq

Automatic Roof Plane Detection and Analysis in Airborne Lidar Point Clouds for Solar Potential Assessment

Andreas Jochem, Bernhard Höfle, Martin Rutzinger, Norbert Pfeifer
2009 Sensors  
A relative height threshold is defined to separate potential roof points from the point cloud, followed by a segmentation of these points into homogeneous areas fulfilling the defined constraints of roof  ...  Once all roof planes are detected in the 3D point cloud, solar potential analysis is performed for each point.  ...  within the 3D point cloud.  ... 
doi:10.3390/s90705241 pmid:22346695 pmcid:PMC3274168 fatcat:k7jwuptjurh45nkddrconroa2m

A volumetric technique for fossil body mass estimation applied to Australopithecus afarensis

Charlotte A. Brassey, Thomas G. O'Mahoney, Andrew T. Chamberlain, William I. Sellers
2018 Journal of Human Evolution  
Here we present a new digital 25 reconstruction of Australopithecus afarensis (A.L. 288-1; 'Lucy') and a convex hull-based 26 volumetric estimate of body mass.  ...  Footprint area (as measured from fossil trackways) has even been used as a 64 means of reconstructing hominin body mass (Dingwall et al., 2013, Masao et al., 2016). 65 66 Whilst bivariate and multivariate  ...  may be fitted around the data whilst 1144 remaining convex, D) a larger point cloud of ~160,000 points based on the isosurface of a 1145 Macaca skull, with 136 outermost points contributing to the form  ... 
doi:10.1016/j.jhevol.2017.07.014 pmid:28838563 fatcat:wwrfmyi24jh4lno52avirsaj54


1999 International journal of computational geometry and applications  
We present an approach for the reconstruction and approximation of 3D CAD models from an unorganized collection of points.  ...  Our reconstruction approach is exible enough to permit interpolation of both smooth surfaces and sharp features, while placing few restrictions on the geometry or topology of the object.  ...  Thanks to the Computer Graphics Group, University o f W ashington and the Stanford University Computer Graphics Laboratory, for making some of the range data used in this paper publicly available.  ... 
doi:10.1142/s0218195999000236 fatcat:e6dugdyssrhuxk4zh2ykdv2one

DualSDF: Semantic Shape Manipulation using a Two-Level Representation [article]

Zekun Hao, Hadar Averbuch-Elor, Noah Snavely, Serge Belongie
2020 arXiv   pre-print
Other approaches seek to represent shapes as compositions of simple parts, which are intuitive for people to understand and easy to edit and manipulate.  ...  We are seeing a Cambrian explosion of 3D shape representations for use in machine learning. Some representations seek high expressive power in capturing high-resolution detail.  ...  This work was supported in part by grants from Facebook and by the generosity of Eric and Wendy Schmidt by recommendation of the Schmidt Futures program.  ... 
arXiv:2004.02869v1 fatcat:7ujdoqhozbb4vdujf4o3x3kobq

Reconstructing shapes with guarantees by unions of convex sets

Dominique Attali, André Lieutier
2010 Proceedings of the 2010 annual symposium on Computational geometry - SoCG '10  
In this paper, we extend this result and find convex sets C ⊂ R N , besides the unit Euclidean ball B, for which P + rC reconstructs the topology of A.  ...  A simple way to reconstruct a shape A ⊂ R N from a sample P is to output an r-offset P + rB, where B = {x ∈ R N | x ≤ 1} designates the unit Euclidean ball centered at the origin.  ...  Motivated by surface reconstruction from 3D scan data and manifold learning from point clouds, several authors have formulated precise conditions under which a reconstruction algorithm outputs a topologically  ... 
doi:10.1145/1810959.1811015 dblp:conf/compgeom/AttaliL10a fatcat:cm3li5jyafhuhel5qjg42tcguq

Wireless coverage prediction via parametric shortest paths [article]

David Applegate, Aaron Archer, David S. Johnson, Evdokia Nikolova, Mikkel Thorup, Ger Yang
2018 arXiv   pre-print
., no error) in the vast majority of cases.  ...  We prove that the IDP model can be reduced to a parametric shortest path computation on a graph derived from the walls in the floorplan.  ...  d, ℓ and enumerates extreme points of the 2D-polytope projection.  ... 
arXiv:1805.06420v1 fatcat:ibrjtbbndfcddoqlltca7zxozm

Surface reconstruction by layer peeling

Chi-Wan Lim, Tiow-Seng Tan
2006 The Visual Computer  
General Concepts The Voronoi diagram V (P ) of P is a cell decomposition of R 3 to convex polytopes.  ...  We start the reconstruction process from points that lie on the outermost layer (i.e. points that lie on the convex hull of the point set).  ... 
doi:10.1007/s00371-006-0048-9 fatcat:3fhb6ujalbdlposh7u5aaj2wwe

Controlled topology simplification

Taosong He, Lichan Hong, A. Varshney, S.W. Wang
1996 IEEE Transactions on Visualization and Computer Graphics  
Our method simplifies the topology of objects in a controlled fashion. In addition, at each level of detail, multi-layered meshes can be used for an efficient antialiased rendering.  ...  We further propose an adaptive surface generation algorithm to reduce the number of triangles generated by the standard Marching Cubes.  ...  We thank Arie Kaufman for his contribution to the original ideas of this project. The source of the Visible Human data set is the National Library of Medicine and the Visible Human Project.  ... 
doi:10.1109/2945.506228 fatcat:bid6eaon6rhfngkjfke55dy4yq
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