On the Shape of a Set of Points and Lines in the Plane
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Date
2011
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd.
Abstract
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 a-shape: an extension of the well known a-shape that uses lines (guides) to indicate preferred locations for the boundary of the shape. The guided a-shape uses (parts of) these lines as boundary where the points suggest that this is appropriate. We prove that the guided a-shape can be constructed in O((n+m) log(n+m)) time, from an input of n points and m guides. We apply guided a-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 a-shapes of both synthetic and real data and show they are consistently better than a-shapes for this application.
Description
@article{:10.1111/j.1467-8659.2011.02029.x,
journal = {Computer Graphics Forum},
title = {{On the Shape of a Set of Points and Lines in the Plane}},
author = {Kreveld, Marc van and Lankveld, Thijs van and Veltkamp, Remco C.},
year = {2011},
publisher = {The Eurographics Association and Blackwell Publishing Ltd.},
ISSN = {1467-8659},
DOI = {/10.1111/j.1467-8659.2011.02029.x}
}