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Gilles Brassard, Anne Broadbent, Alain Tapp (auth.), Frank's Algorithms and Data Structures: 8th International Workshop, PDF

By Gilles Brassard, Anne Broadbent, Alain Tapp (auth.), Frank Dehne, Jörg-Rüdiger Sack, Michiel Smid (eds.)

This booklet constitutes the refereed lawsuits of the eighth overseas Workshop on Algorithms and knowledge buildings, WADS 2003, held in Ottawa, Ontario, Canada, in July/August 2003.

The forty revised complete papers provided including four invited papers have been conscientiously reviewed and chosen from 126 submissions. A vast number of present features in algorithmics and information constructions is addressed.

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Read Online or Download Algorithms and Data Structures: 8th International Workshop, WADS 2003, Ottawa, Ontario, Canada, July 30 - August 1, 2003. Proceedings PDF

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Extra info for Algorithms and Data Structures: 8th International Workshop, WADS 2003, Ottawa, Ontario, Canada, July 30 - August 1, 2003. Proceedings

Example text

Giesen, and S. Goswami It is not completely obvious, but it can be shown that this flow is well defined [8]. It is also easy to see that the orbits of φ are piecewise linear curves that are linear in Voronoi objects. See Figure 2 for some examples of orbits. Under some mild non-degeneracy condition the stable manifolds of the critical points have a nice recursive structure. A stable manifold of index k, 0 ≤ k ≤ d, has dimension k and its boundary is made up from stable manifolds of index k − 1 critical points.

Dey, J. Giesen, and S. Goswami The final algorithm to compute a feature segmentation of a shape Σ ⊆ R3 from a sample P is described below. Some examples are shown in Figure 4. Segment(P, ρ) 1 StableManifold(P ); 2 Merge all ρ-mergeable segments and output the resulting decomposition. Fig. 4. Segmentation of 2D and 3D models. In the leftmost picture of the first row we zoom in the tail of the camel to show that the point sample is noisy as it is derived from the boundary extraction of a 2D image. The second row shows that the 3D models are segmented into so-called features.

Observation 2 The flow φ induced by a finite point set P is given as follows. For all critical points x of the distance function associated with P we set φ(t, x) = x , t ∈ [0, ∞). Otherwise let d(x) be the driver of x and R be the ray originating at x and shooting in the direction v(x) = x − d(x)/ x − d(x) . Let z be the first point on R whose driver is different from d(x). Note that such a z need not exist in Rd if x is contained in an unbounded Voronoi object. In this case let z be the point at infinity in the direction of R.

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