Abstract
This paper deals with the problem of shape reconstruction from an unorganized and not necessarily uniformly distributed point cloud with outliers. A shape reconstruction method based on a Delaunay filtration called LDA-α-shapes has been introduced in 2010 [1]. This method may be used to reconstruct 2-D or 3-D shapes from a non necessary uniformly distributed point cloud but unfortunately it faces problems when there are outliers. For this reason, a little modification of the LDA-α-shapes definition is proposed in this article to deal with this kind of point clouds. The resulting new algorithm is still simple and efficient.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Maillot, Y., Adam, B., Melkemi, M.: Shape Reconstruction from Unorganized Set of Points. In: Campilho, A., Kamel, M. (eds.) ICIAR 2010, Part I. LNCS, vol. 6111, pp. 274–283. Springer, Heidelberg (2010) 10.1007/978-3-642-13772-3_28
Amenta, N., Bern, M.: Surface reconstruction by voronoi filtering. Discrete and Computational Geometry 22, 481–504 (1999)
Amenta, N., Choi, S., Dey, T., Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. In: ACM Symposium on Computational Geometry, pp. 213–222 (2000)
Edelsbrunner, H.: The union of balls and its dual shape. In: Proceedings of the Ninth Annual Symposium on Computational Geometry, SCG 1993, pp. 218–231. ACM, New York (1993)
Amenta, N., Choi, S., Kolluri, R.K.: The power crust. In: SMA 2001: Proceedings of the Sixth ACM Symposium on Solid Modeling and Applications, pp. 249–266. ACM, New York (2001)
Dey, T.K., Goswami, S.: Provable surface reconstruction from noisy samples. Comput. Geom. Theory Appl. 35(1), 124–141 (2006)
Edelsbrunner, H., Kirkpatrick, D., Seidel, R.: On the shape of a set of points in the plane. IEEE Transactions on Information Theory 29(4), 551–559 (1983)
Chevallier, N., Maillot, Y.: Boundary of a non-uniform point cloud for reconstruction: Extended abstract. In: Symposium on Computational Geometry, pp. 510–518 (2011)
Goodman, J.E., O’Rourke, J. (eds.): Handbook of discrete and computational geometry. CRC Press, Inc., Boca Raton (1997)
Presles, B., Debayle, J., Maillot, Y., Pinoli, J.-C.: Automatic Recognition of 2D Shapes from a Set of Points. In: Kamel, M., Campilho, A. (eds.) ICIAR 2011, Part I. LNCS, vol. 6753, pp. 183–192. Springer, Heidelberg (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maillot, Y., Presles, B., Debayle, J. (2012). Shape Reconstruction from an Unorganized Point Cloud with Outliers. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2012. Lecture Notes in Computer Science, vol 7324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31295-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-31295-3_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31294-6
Online ISBN: 978-3-642-31295-3
eBook Packages: Computer ScienceComputer Science (R0)