Discrete Geometry for Computer Imagery: 10th International by Walter G. Kropatsch (auth.), Achille Braquelaire,

By Walter G. Kropatsch (auth.), Achille Braquelaire, Jacques-Olivier Lachaud, Anne Vialard (eds.)

This e-book constitutes the refereed lawsuits of the tenth foreign convention on electronic Geometry for desktop Imagery, DGCI 2002, held in Bordeaux, France, in April 2002.
The 22 revised complete papers and thirteen posters awarded including three invited papers have been conscientiously reviewed and chosen from sixty seven submissions. The papers are geared up in topical sections on topology, combinatorial photo research, morphological research, form illustration, types for discrete geometry, segmentation and form acceptance, and purposes.

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Extra info for Discrete Geometry for Computer Imagery: 10th International Conference, DGCI 2002 Bordeaux, France, April 3–5, 2002 Proceedings

Example text

Using the terminology of the graph-theoretical approach, a simple closed curve γd is a connected graph in which any vertex has degree two. An arc is defined as an k-connected set of points, denoted with α, with each of its points satisfying the conditions SCC1-3, except two points which are kadjacent to just one other point of α. In [13], Rosenfeld has shown that no simple closed curve in ZZ 2 is both a 4-connected curve and an 8-connected curve. Curves in ZZ n (a) (b) 37 (c) Fig. 1. Simple closed curves: (a) a 4-connected set to be ruled out, (b) an 8-connected set to be ruled out, (c) a valid 8-connected curve.

Closed quasi curves admit – like simple closed curves – a unique parameterization, that has been identified as one of the fundamental features of curves to be kept in discrete space. Loosely speaking, a closed quasi curve is obtained by adding “triangles” to the adjacency graph of simple closed curves following certain rules. This is illustrated for an example in Fig. 2(b). The notation of closed quasi curves are generally stated for graphs in [8] and for 18-connected closed quasi curves in [7].

Note, that this condition is actually too restrictive for 8-connected curves. An example is given in Fig. 1(c) for which an 8-connected curve separates ZZ 2 into two components and consists itself of four points. Using the terminology of the graph-theoretical approach, a simple closed curve γd is a connected graph in which any vertex has degree two. An arc is defined as an k-connected set of points, denoted with α, with each of its points satisfying the conditions SCC1-3, except two points which are kadjacent to just one other point of α.

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