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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Bibliographic Details
Published in:Computer graphics forum Vol. 30; no. 5; pp. 1553 - 1562
Main Authors: van Kreveld, M., van Lankveld, T., Veltkamp, R. C.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.08.2011
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:istex:A6C1F2BC16F5D1B385534BA8FCB7C7DBD7D5AF58
ArticleID:CGF2029
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2011.02029.x