Abstract
This article deals with the problem of detecting the weak-symmetry of a simple polygon. The main application of this work is the automatic reconstruction of 3D polygons (planar or non-planar polylines) symmetric with respect to a plane from free hand sketching 2D polygons. We propose a provable approach to check on the weak-symmetry of a simple polygon. The worst time complexity of the proposed algorithm is O(n 3) where n is the number of the vertices of the input polygon.
This is a preview of subscription content, log in via an institution to check access.
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
Olsen, L., Samavati, F.F., Costa Sousa, M., Jorge, J.-A.: Sketch-based modeling: A survey. Computers & Graphics 33(1), 85–103 (2009)
Cordier, F., Seo, H., Park, J., Noh, J.: Sketching of Mirror-symmetric Shapes. IEEE Transactions on Visualization and Computer Graphics (2011)
Kanade, T.: Recovery of the Three-Dimensional Shape of an Object from a Single View. Artificial Intelligence 17, 409–460 (1981)
Posch, S.: Detecting skewed symmetries. In: International Conference on Pattern Recognition, The Hague, pp. 602–606 (1992)
Shen, D., Horace, H.-S Ip., Teoh, E.K.: Robust detection of skewed symmetries by combining local and semi-local affine invariants. Pattern Recognition 34(7), 1417–1428 (2001)
Shen, D., Horace, H.-S Ip., Teoh, E.K.: Robust Detection of Skewed Symmetries. In: International Conference on Pattern Recognition, pp. 7022–7025 (2000)
Yip Raymond, K.-K.: A Hough transform technique for the detection of reflectional symmetry and skew-symmetry. Pattern Recognition Letters 21(2), 117–130 (2000)
Melkemi, M., Cordier, F., Sapidis, N.: A provable algorithm to detect the symmetry of a simple polygon. Technical Report LMIA, pp. 1–30 (2010)
Okabe, A., Boots, B., Sugihara, K.: Spatial tessellations: Concepts and Applications of Voronoi Diagrams. John Wiley and Sons, Chichester (1992)
O’Rourke, J.: Computational geometry in C. Cambridge University Press, Cambridge (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Melkemi, M., Cordier, F., Sapidis, N.S. (2011). An Algorithm to Detect the Weak-Symmetry of a Simple Polygon. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2011. Lecture Notes in Computer Science, vol 6753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21593-3_37
Download citation
DOI: https://doi.org/10.1007/978-3-642-21593-3_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21592-6
Online ISBN: 978-3-642-21593-3
eBook Packages: Computer ScienceComputer Science (R0)