On the shape of a set of points and lines in the plane

Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free‐form shape of a p...

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Vydané v:	Computer graphics forum Ročník 30; číslo 5; s. 1553 - 1562
Hlavní autori:	van Kreveld, M., van Lankveld, T., Veltkamp, R. C.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Oxford, UK Blackwell Publishing Ltd 01.08.2011
Predmet:	and systems Boundaries Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-Boundary representations Computer Graphics [I.3.5]: Computational Geometry and Object Modeling-Geometric algorithms Computer Graphics [I.3.5]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems Construction Geometry languages Lidar Marketing Mathematical models Planes Reconstruction Studies Three dimensional models
ISSN:	0167-7055, 1467-8659
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Popis
Shrnutí:	Detailed geometric models of the real world are in increasing demand. LiDAR data is appropriate to reconstruct urban models. In urban scenes, the individual surfaces can be reconstructed and connected to form the scene geometry. There are various methods for reconstructing the free‐form shape of a point sample on a single surface. However, these methods do not take the context of the surface into account. We present the guided α‐shape: an extension of the well known α‐shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided α‐shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided α‐shape can be constructed in O((n + m) log (n + m)) time, from an input of n points and m guides. We apply guided α‐shapes to urban reconstruction from LiDAR, where neighboring surfaces can be connected conveniently along their intersection lines into adjacent surfaces of a 3D model. We analyze guided α‐shapes of both synthetic and real data and show they are consistently better than α‐shapes for this application.
Bibliografia:	istex:A6C1F2BC16F5D1B385534BA8FCB7C7DBD7D5AF58 ArticleID:CGF2029 ark:/67375/WNG-03GKWTGH-T SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0167-7055 1467-8659
DOI:	10.1111/j.1467-8659.2011.02029.x