Abstract
This paper presents a theoretical generalization of the circumcenter as the intersection of generalized perpendicular bisectors. We define generalized bisectors between two regions as an area where each point is the center of at least one circle crossing each of the two regions. These new notions should allow the design of new circle recognition algorithms.
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References
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)
Coeurjolly, D., Gerard, Y., Reveills, J.-P., Tougne, L.: An elementary algorithm for digital arc segmentation. Discrete Applied Mathematics 139(1-3), 31–50 (2004)
Couprie, M., Coeurjolly, D., Zrour, R.: Discrete bisector function and Euclidean skeleton in 2D and 3D. Image and Vision Computing 25(10), 1543–1556 (2007)
Dexet, M., Andres, E.: A generalized preimage for the digital analytical hyperplane recognition. Discrete Applied Mathematics 157(3), 476–489 (2009)
Farouki, R.T., Johnstone, J.K.: Computing point/curve and curve/curve bisectors. In: Fisher, R.B. (ed.) The Mathematics of Surfaces V, pp. 327–354. Oxford University, Oxford (1994)
Gonzalez, R.C., Woods, R.E., Eddins, S.L.: Digital Image Processing Using MATLAB(R). Prentice-Hall, Englewood Cliffs (2004)
Ioannou, D., Huda, W., Laine, A.F.: Circle recognition through a 2D Hough transform and radius histogramming. Image and Vision Computing 17(1), 15–26 (1999)
Peternell, M.: Geometric properties of bisector surfaces. Graphical Models 62(3), 202–236 (2000)
Roussillon, T., Tougne, L., Sivignon, I.: On three constrained versions of the digital circular arc recognition problem. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 34–45. Springer, Heidelberg (2009)
Talbot, H., Vincent, L.: Euclidean skeletons and conditional bisectors. In: Visual Comm. and Image Pricessing. SPIE, vol. 1818, pp. 862–876 (1992)
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)
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Rodríguez, M., Abdoulaye, S., Largeteau-Skapin, G., Andres, E. (2010). Generalized Perpendicular Bisector and Circumcenter. In: Barneva, R.P., Brimkov, V.E., Hauptman, H.A., Natal Jorge, R.M., Tavares, J.M.R.S. (eds) Computational Modeling of Objects Represented in Images. CompIMAGE 2010. Lecture Notes in Computer Science, vol 6026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12712-0_1
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DOI: https://doi.org/10.1007/978-3-642-12712-0_1
Publisher Name: Springer, Berlin, Heidelberg
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