By Jean-Marc Chassery, Isabelle Sivignon (auth.), Rocio Gonzalez-Diaz, Maria-Jose Jimenez, Belen Medrano (eds.)

This publication constitutes the completely refereed complaints of the seventeenth foreign convention on Discrete Geometry for laptop Imagery, DGCI 2013, held in Seville, Spain, in March 2013. The 34 revised complete papers awarded have been conscientiously chosen from fifty six submissions and concentrate on geometric transforms, discrete and combinatorial instruments for picture segmentation and research, discrete and combinatorial topology, discrete form illustration, popularity and research, types for discrete geometry, morphological research and discrete tomography.

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**Additional resources for Discrete Geometry for Computer Imagery: 17th IAPR International Conference, DGCI 2013, Seville, Spain, March 20-22, 2013. Proceedings**

**Example text**

We have previously seen that each point needs a min-heap indexed structure of size 2n for each of the dim part, and ﬁnally a trie composed by nodes of size n. A larger upper bound of the number of nodes is given by the number of points n multiplied by the depth dim in the trie and the size of a node. We consider sizeof (node) ≈ n because we are interested in discrete geometry problems and then we can use an index table for distances in order to use less memory as possible by compacting the table pointer of each node.

The number of partition in each classes can be computed by this recursive function: k 1 j=i pj #[ pi+1 , . . , pk ] , #[ pi , pi+1 , . . , pk ] = Ai pi where Ai is the number of parts in [ pi , pi+1 , . . , pk ] which value equals pi . The number of classes of dimension n is highly unevenly distributed; the cardinal of the metric bases class is minimal and is far smallest than the cardinal of the other classes. 3 Algorithm In this section we describe some methods to determine if a given partition is resolving.

J. Jimenez, B. ): DGCI 2013, LNCS 7749, pp. 35–46, 2013. c Springer-Verlag Berlin Heidelberg 2013 36 A. Hoarau and T. Monteil (a) r = 28 (b) r = 29 Fig. 1. The spike coded by 0011 appears in the digitization of big integer circles (a) 0011 (b) 001011 (c) 000101 Fig. 2. The most elementary spikes A word is said to be persistent if it appears in the Freeman code of integer discrete circles for inﬁnitely many radii. Their complete description is the aim of this paper. As we can consider the dual point of view where the circle radius does not grow but the grid mesh vanishes, we know that persistent words are tangent convex words, which were introduced in [9].