3D Shape Recognition and Reconstruction Based on Line Element Geometry

Authors:
M. Hofer;B. Odehnal;H. Pottmann;T. Steiner;J. Wallner
Affiliations:
Technical University Wien;Technical University Wien;Technical University Wien;Technical University Wien;Technical University Wien
Venue:
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Year:
2005

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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.