Abstract:
This paper presents a new method for the recognition and reconstruction of surfaces from 3D data. Line element geometry, which generalizes both line geometry and the Laguerre geometry of oriented planes, enables us to recognize a wide class of surfaces (spiral surfaces, cones, helical surfaces, rotational surfaces, cylinders, etc.) by fitting linear subspaces in an appropriate seven-dimensional image space. In combination with standard techniques such as PCA and RANSAC, line element geometry is employed to effectively perform the segmentation of complex objects according to surface type. Examples show applications in reverse engineering of CAD models and testing mathematical hypotheses concerning the exponential growth of sea shells.
Bibtex:
@inproceedings{hofer-2005-3dsr,
title = "{3D} shape recognition and reconstruction based on
line element geometry",
author = "M. Hofer and B Odehnal and H. Pottmann and T. Steiner
and J. Wallner",
booktitle = "Tenth IEEE International
Conference on Computer Vision",
year = 2005,
volume = 2,
pages = "1532--1538",
publisher="IEEE Computer Society",
isbn="0-7695-2334-X",
}
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