Abstract
All the polygonalisation algorithms we can find in the literature proceed on 4-connected or 8-connected discrete arcs. In this article, we aim to polygonalise “thick arcs”. A first step consists in giving a definition of such arcs based on morphological properties. In a second step, we propose two methods in order to polygonalise such arcs. The first one is based on a squelettisation of the arc and uses the fuzzy arc polygonalisation. The second one is based on a grouping of the cells in order to obtain heterogeneous pixels and then, the polygonalisation of heterogeneous arcs is applied.
This work is supported by the french ACI GeomDiGIT (http://liris.cnrs.fr/geodigit/)
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
Andrès, E.: Modélisation analytique discrète d’objets géométriques. Master’s thesis, Laboratoire IRCOM-SIC, Université de Poitiers (2000)
Buzer, L.: An incremental linear algorithm for digital line and plane recognition using a linear incremental feasibility problem. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 372–381. Springer, Heidelberg (2002)
Carré, P., Andrès, É.: Ridgelet transform based on reveillès discrete lines. In: Braquelaire, A., Lachaud, J.-O., Vialard, A. (eds.) DGCI 2002. LNCS, vol. 2301, pp. 313–325. Springer, Heidelberg (2002)
Coeurjolly, D., Debled-Rennesson, I., Teytaud, O.: Segmentation and length estimation of 3d discrete curves. In: Digital and Image Geometry, pp. 295–313 (2001)
Coeurjolly, D.: Supercover model and digital straight line recognition on irregular isothetic grids. In: Andrès, É., Damiand, G., Lienhardt, P. (eds.) DGCI 2005. LNCS, vol. 3429, pp. 311–322. Springer, Heidelberg (2005) (To appear)
Coeurjolly, D., Tougne, L.: Digital straight line recognition on heterogeneous grids. In: Vision Geometry, pp. 283–294. SPIE, San Jose (2004)
Debled-Rennesson, I.: Etude et reconnaissance des droites et plans discrets. PhD thesis, Université Louis Pasteur, Strasbourg (1995)
Debled-Renesson, I., Reveillès, J.P.: A linear algorithm for segmention of digital curves. International Journal of Pattern Recognition and Artificial Intelligence 9, 635–662 (1995)
Debled, I., Rémy, J.L., Rouyer-Degli, J.: Segmentation of discrete curves into fuzzy segments. In: International Workshop on Combinatorial Image Analysis, IWCIA 2003 (2003)
Dorst, L., Smeulders, A.W.M.: Discrete representation of straight lines. IEEE Transaction on Pattern Analysis and Machine Intelligence 6, 450–463 (1984)
Freeman, H.: Computer processing of line-drawing images. ACM Computing Surveys 6(1), 457–497 (1974)
Feschet, F., Tougne, L.: On the min dss problem of the closed discrete curves. In: International Workshop on Combinatorial Image Analysis, IWCIA 2003 (2003)
Klette, R., Bülow, T.: Minimum-length polygons in simple cube-curves. In: Nyström, I., Sanniti di Baja, G., Borgefors, G. (eds.) DGCI 2000. LNCS, vol. 1953, pp. 467–478. Springer, Heidelberg (2000)
Klette, R., Kovalevsky, V.A., Yip, B.: Length estimation of digital curves, pp. 117–129. SPIE, San Jose (1999)
Kovalevsky, V.A.: New definition and fast recognition of digital straight segments and arcs. In: Proceedings of the tenth international conference on Pattern Analysis and Machine Intelligence (1990)
Li-De, W.: On the chain code of a line. IEEE Transaction on Pattern Analysis and Machine Intelligence 4, 347–353 (1982)
Reveillès, J.-P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d’etat, Université Louis Pasteur, Strasbourg (1991)
Rosenfeld, A.: Digital straight line segments. IEEE Transaction on Computers 23(12), 1264–1269 (1974)
Slobada, F., Zatko, B.: On one-dimensional grid continua in ℝ2. Technical report, Institute of Control Theory and Robotics, Bratislava (1996)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alhalabi, F., Tougne, L. (2005). Toward Polygonalisation of Thick Discrete Arcs. In: Gagalowicz, A., Philips, W. (eds) Computer Analysis of Images and Patterns. CAIP 2005. Lecture Notes in Computer Science, vol 3691. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556121_25
Download citation
DOI: https://doi.org/10.1007/11556121_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28969-2
Online ISBN: 978-3-540-32011-1
eBook Packages: Computer ScienceComputer Science (R0)