M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Manuscript, 1995. Home/Search Document Details and Download
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Efficient Algorithms for Geometric Optimization - Agarwal, Sharir (1998) (9 citations) (Correct)
....Another way of measuring the resemblance between two polygons P and Q is by computing the area of their intersection (or, rather, of their symmetric difference) Suppose we wish to minimize the area of the symmetric difference between P and Q, under translation of P . For this case, de Berg et al. [86] gave an O(n log n) time algorithm, using the prune and search paradigm. Their algorithm can be extended to higher dimensions at a polylogarithmic cost, using parametric searching. 8.6 Surface simplification A generic surface simplification problem is defined as follows: Given a polyhedral ....
M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud, Computing the maximum overlap of two convex polygons under translation, Proc. 7th Annu. Internat. Sympos. Algorithms Comput., 1996.
On the Sectional Area of Convex Polytopes - Avis, Bose, Shermer, Snoeyink.. (1996) (6 citations) (Correct)
....result has consequences in shape matching in the plane. Given two convex polygons, P and Q, and a direction v, we can compute the translation of P in the direction v that has maximum intersection with Q or, equivalently, that minimizes the symmetric difference of P ffv and Q. De Berg et al. [3] have recently developed an O(n log n) algorithm to find the translation of P in any direction that has the maximum overlap with Q; their algorithm depends on this subroutine. Corollary 4.1 Given convex polygons P and Q, the magnitude ff of the translation along a given vector v that maximizes ....
M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Manuscript, 1995.
Shape Similarity Measures, Properties, and Constructions - Veltkamp, Hagedoorn (2000) (1 citation) (Correct)
....measure is a not a metric, since the triangle inequality does not hold. The invariance group is the class of di eomorphisms with unit Jacobi determinant. It turns out that translating the polygons so that their centroids coincide gives an overlap of at least 9 25 of the optimal solution [12]. For translations, the transformation that maximizes the area overlap also minimizes the area of symmetric di erence. 3.14 Area of Symmetric Di erence, Template Metric For two compact sets A and B, the area of symmetric di erence, also called template metric, is de ned as area( A B) B A) ....
Mark de Berg, Olivier Devillers, Marc van Kreveld, Otfried Schwarzkopf, and Monique Teillaud. Computing the maximum overlap of two convex polygons under translation. In Proc. 7th Annu. Internat. Sympos. Algorithms Comput., 1996.
The Area of Overlap of two Unions of Convex Objects under.. - Mark De Berg (2003) Self-citation (De berg) (Correct)
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M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. In Proc. of the 7th Internat. Symp. Algorithms and Computation (ISAAC '96), volume 1178 of LNCS, pages 126-135. Springer-Verlag, 1996.
On Finding a Guard that Sees Most and a Shop that Sells Most - Cheong, Efrat, Har-Peled (2003) (2 citations) Self-citation (Cheong) (Correct)
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M. de Berg, O. Cheong, O. Devillers, M. van Kreveld, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Theo. Comp. Sci., 31:613-628, 1998.
On the Sectional Area of Convex Polytopes - Avis, Bose, Shermer, Snoeyink.. (1996) (6 citations) (Correct)
No context found.
M. de Berg, O. Devillers, M. van Kreveld, O. Schwarzkopf, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Manuscript, 1995.
Efficient Algorithms for Shared Camera Control - Sariel Har-Peled Vladlen (2003) (Correct)
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M. de Berg, O. Cheong, O. Devillers, M. van Kreveld, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Theory of Computing Systems, 31:613--628, 1998.
Efficient Algorithms for Shared Camera Control - Har-Peled, Koltun, Song.. (2002) (Correct)
No context found.
M. de Berg, Otfried Cheong, O. Devillers, M. van Kreveld, and M. Teillaud. Computing the maximum overlap of two convex polygons under translations. Theo. Comp. Sci., 31:613--628, 1998.
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