Abstract
This paper present an adaptive pixel resizing method based on a parameter space approach. The pixel resizing is designed for both multiscale recognition and reconstruction purposes. The general idea is valid in any dimension. In this paper we present an illustration of our method in 2D. Pixels are resized according to the local curvature of the curve to control the local error margin of the reconstructed Euclidean object. An efficient 2D algorithm is proposed.
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
Andres, E.: Discrete linear objects in dimension n: the standard model. Graphical Models 65, 92–111 (2003)
Andres, E.: The supercover of an m-flat is a discrete analytical object. Theoretical Computer Science 406, 8–14 (2008); Discrete Tomography and Digital Geometry: In memory of Attila Kuba
Andres, E., Acharya, R., Sibata, C.: Discrete analytical hyperplanes. Graphical Models and Image Processing 59, 302–309 (1997)
Breton, R., Sivignon, I., Dexet, M., Andres, E.: Towards an invertible euclidean reconstruction of a discrete object. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 246–256. Springer, Heidelberg (2003)
Bullard, J.W., Garboczi, E.J., Carter, W.C., Fuller Jr., E.R.: Numerical methods for computing interfacial mean curvature. Computational Materials Science 4, 103–116 (1995)
Coeurjolly, D., Sivignon, I., Dupont, F., Feschet, F., Chassery, J.M.: On digital plane preimage structure. Discrete Applied Mathematics, 78–92 (2005)
De Berg, M., Cheong, O., Van Kreveld, M., Overmars, M.: Computational Geometry: Algorithms and Applications, 3rd edn. Springer, Heidelberg (2008)
Debled-Rennesson, I., Feschet, F., Rouyer-Degli, J.: Optimal blurred segments decomposition of noisy shapes in linear time. Computer & Graphics 30 (2006)
Debled Rennesson, I., Tabbone, S., Wendling, L.: Multiorder polygonal approximation of digital curves. Electonic Letters on Computer Vision and Image Analysis 5, 98–110 (2005)
Dexet, M., Andres, E.: A generalized preimage for the digital analytical hyperplane recognition. Discrete Applied Mathematics 157, 476–489 (2009)
Edelsbrunner, H.: Finding transversals for sets of simple geometric figures. Theoretical Computer Science 35, 55–69 (1985)
Hough, P.V.C.: Method and means for recognizing complex patterns. In: United States Pattent 3069654, pp. 47–64 (1962)
Lachaud, J.O., Vialard, A., De Vieilleville, F.: Analysis and comparative evaluation of discrete tangent estimators. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 240–251. Springer, Heidelberg (2005)
Largeteau-Skapin, G., Andres, E.: Discrete-euclidean operations. Discrete Applied Mathematics 157, 510–523 (2009)
Reveillés, J.P.: Géometrie Discrete, calcul en nombre entiers et algorithmique. PhD thesis, Université Louis Pasteur (1991)
Rodríguez, M., Largeteau-Skapin, G., Andres, E.: Adaptive pixel size reconstruction with topological control. In: Wiederhold, P., Barneva, R.P. (eds.) Progress in Combinatorial Image Analysis. Research Publishing Services, Singapore (to appear 2009)
Sivignon, I., Dupont, F., Chassery, J.: Reversible vectorisation of 3d digital planar curves and applications. Image Vision and Computing 25, 1644–1656 (2007)
Vialard, A.: Geometrical parameters extraction from discrete paths. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 24–35. Springer, Heidelberg (1996)
Vittone, J., Chassery, J.M.: (n,m)-cubes and farey nets for naive planes understanding. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 76–90. Springer, Heidelberg (1999)
Vittone, J., Chassery, J.M.: Recognition of digital naive planes and polyhedrization. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 296–307. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rodríguez, M., Largeteau-Skapin, G., Andres, E. (2009). Adaptive Pixel Resizing for Multiscale Recognition and Reconstruction. In: Wiederhold, P., Barneva, R.P. (eds) Combinatorial Image Analysis. IWCIA 2009. Lecture Notes in Computer Science, vol 5852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10210-3_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-10210-3_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10208-0
Online ISBN: 978-3-642-10210-3
eBook Packages: Computer ScienceComputer Science (R0)