H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 703-716. Springer-Verlag, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on such graphical data are very complicated and expensive. An error criterion de nes the goodness of t in terms of the deviations between the approximated and approximating objects. Di erent error criteria have been used in solving various polygonal curve approximation problems (e.g. see [1, 2, 5, 7 18, 21 28]) In this paper, we consider two commonly used error criteria for studying polygonal curve approximations: The error criterion used in [5, 12,14,18] which we call the tolerance zone criterion, and the criterion used in [9, 14,24] which we call the in nite beam criterion (the in nite beam ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. Proc. 10th Coll. on Autom., Lang., and Prog. (ICALP), pages 703-716, 1990.

....we give several examples in section 4. In section 4. 1 we sketch an algorithm that uses Theta(log n) time to compute chords of a given length and direction in a convex n gon, answering a question posed by Mount [13] This improves algorithms on approximating convex polygons by rectangles [1, 17]. In section 4.2 we cast an old problem of computing the separation distance between two disjoint convex polygons [4] as a fixed point problem. In subsection 4.3 we solve the inscribed triangle homothet problem: given a convex polygon P , find the largest homothet of a given triangle T that can ....

....parallel to direction ff that were half the length of the longest chord. We describe a logarithmic time algorithms for the longest chord parallel to ff and parallel chords with specified lengths. These algorithms improve the running time of algorithms that approximate convex polygons by rectangles [1, 17]. 10 Let us assume that ff is vertical and polygon P is given by a hierarchical representation [3] which here means that middle points of a polygonal chain and their tangents are available. Hierarchical representations can be implemented by storing the vertices of P in order in an array or ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Seventeenth ICALP, number 443 in LNCS, pages 703--716. Springer-Verlag, 1990.

.... point, can done in time O(mn log(mn) The corresponding computation problem, computing the Fr echet distance, can be solved in time O(mn(log(mn) 2 ) AG95] For convex contours curves, the Fr echet distance is equal to the Hausdor distance, which can be computed in time O(mn log(mn) ABGW90] 6.3 Hausdor distance Given two polygons A and B, the directed Hausdor distance from A to B can be computed using the Voronoi diagram of B, which assigns to each vertex and edge of A a region of points that lie closer to that vertex or edge than to any other, see Figure 12. If the edges in ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proceedings of the 17th International Colloquium on Automata, Languages, and Programming (ICALP), Lecture Notes in Computer Science 443, pages 703-716. Springer, 1990.

....of M and area(s) area(t) is minimal. Moreover we prove an O(n log n) lower bound for the one dimensional version of the problem. 1 Introduction Computing approximated, concise representations of complex shapes is a standard problem in computer graphics, pattern recognition and robotics. [1] shows how a convex polygon can be approximated by means of circles, rectangles or k gons. An algorithm for computing a pair of parallel circumscribed and inscribed rectangles for a convex polygon with n vertices is described in [6] its complexity is O(log 3 n) if vertices are given in a sorted ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Automata, Languages and Programming (Proc. of the 17th ICALP, Univ. of Warwick, England, July 1990), Lecture Notes in Computer Science 443, pages 703--716, 1990.

.... here is to compute the similarity or distance between two polygons which could represent the boundaries of shapes or the convex hulls of sets of points [To84] This problem is in turn closely related to the problem of approximating polygons by smoother ones or by polygons with fewer vertices [ABGW90], To85a] 4. Computational Morphology and Shape Analysis Computational morphology is concerned with the analysis, description, and synthesis of shapes and patterns from a computational point of view. It is therefore of central concern to document analysis. Once the objects in an image have been ....

Alt, H., Blomer, J., Godau, M. and Wagener, H., "Approximation of convex polygons, " ICALP, 1990.

....the individual algorithms used are characterized and classified, the properties of these heuristic combinations are not. Criteria much like our fattening [5, 26, 29] may then be used a posteriori to test the quality of the resulting approximations. Imai and Iri [16, 17, 18] and other researchers [2, 4, 8, 13, 23, 25, 31] have chosen mathematical criterion for the approximations and then sought efficient algorithms to find best approximations. The algorithms they have developed, however, have quadratic or greater running times especially for those that use original data points as vertices of the approximation. ....

Helmut Alt, Johannes Blomer, Michael Godau, and Hubert Wagener. Approximation of convex polygons. In Seventeenth International Colloquium on Automata, Languages and Programming, number 443 in Lecture Notes in Computer Science, pages 703--716. Springer-Verlag, 1990.

....we give several examples in section 3. In section 3. 1 we sketch an algorithm that uses Theta(log n) time to compute chords of a given length and direction in a convex n gon, answering a question posed by Mount [13] This improves algorithms for approximating convex polygons by rectangles [1, 17]. In section 3.2 we cast an old problem of computing the separation distance between two disjoint convex polygons [4] as a fixed point problem. In section 3.3 we solve the inscribed triangle homothet problem: given a convex polygon P , find the largest homothet of a given triangle T that can be ....

....parallel to direction ff that were half the length of the longest chord. We describe logarithmic time algorithms for the longest chord parallel to ff and parallel chords with specified lengths. These algorithms improve the running time of algorithms that approximate convex polygons by rectangles [1, 17]. Let us assume that ff is vertical and polygon P is given by a hierarchical representation [3] which here means that middle points of a polygonal chain and their tangents are available. Hierarchical representations can be implemented by storing the vertices of P in order in an array or storing ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Seventeenth ICALP, number 443 in LNCS, pages 703--716. Springer-Verlag, 1990.

.... here is to compute the similarity or distance between two polygons which could represent the boundaries of shapes or the convex hulls of sets of points [To84] This problem is in turn closely related to the problem of approximating polygons by smoother ones or by polygons with fewer vertices [ABGW90], To85] 4. Computational Morphology Computational morphology is concerned with the analysis, description, and synthesis of shapes and patterns from a computational point of view. It is therefore of central concern to computer vision. Once the objects in an image have been normalized, smoothed, ....

Alt, H., Blomer, J., Godau, M. and Wagener, H., "Approximation of convex polygons, " ICALP, 1990.

No context found.

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 703-716. Springer-Verlag, 1990.

....weak Fr echet distance having a large Fr echet distance. For given polygonal curves P; Q with n and m vertices, respectively, one can compute H (P; Q) in O (m n) log(m n) time, see [2] and F (P; Q) as well as F (P; Q) in O(mn log(m n) time, see [4] The following result from [3] (see also [8] shows that for certain classes of curves the three distance measures are closely related, so we can do better than mn) when we want to compute the Fr echet distance. Theorem 1. For any pair of convex closed curves P and Q, H (P; Q) F (P; Q) F (P; Q) Let us now turn ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 703-716. Springer-Verlag, 1990.

.... n) time, see [1] and F (P; Q) in O(mn log(m n) time, see [3] Here, a polygonal curve is a curve P : 0; n] R 2 with n 2 N, such that for all i 2 f0; 1; n 1g each P i : P j [i;i 1] is ane, i.e. P (i ) 1 )P (i) P (i 1) for all 2 [0; 1] The following result from [2] (see also [4] shows that for certain classes of curves the two distance measures are closely related, so we can do better than mn) when we want to compute the Fr echet distance. Theorem (Alt et. al, 2] For any pair of convex closed curves P and Q, F (P; Q) H (P; Q) In the following we ....

....i.e. P (i ) 1 )P (i) P (i 1) for all 2 [0; 1] The following result from [2] see also [4] shows that for certain classes of curves the two distance measures are closely related, so we can do better than mn) when we want to compute the Fr echet distance. Theorem (Alt et. al, [2]) For any pair of convex closed curves P and Q, F (P; Q) H (P; Q) In the following we will consider straight curves; for these curves the arclength between any two points is at most a constant times their Euclidean distance. De nition 1 ( Straightness) A planar curve P is called ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes Comput. Sci., pages 703-716. Springer-Verlag, 1990.

....of area(F ) when no confusion arises. The symmetric difference ffi is one of the standard error measures considered in the theory of convex approximation, see the surveys of Gruber [G83, G93] In the area of computational geometry, ffi has been investigated only in a few papers so far, including [ABGW90] where simplification problems are addressed, and a recent paper of de Berg et al. BDK 96] which is also concerned with matching problems under translations. In some applications, ffi is more appropriate than the Hausdorff distance. Consider the case when F 1 is an image disturbed by ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., Lecture Notes in Computer Science, Vol. 443, pp. 703--716. Springer-Verlag, 1990.

....In this context the probably most natural distance measure between two shapes is the area of their symmetric difference. However, this measure seems to be much more difficult to handle than Hausdorff distance. Within computational geometry it was first considered in a paper by Alt et al. ABGW90] in connection with the very special problem of optimally approximating a convex polygon by an axes parallel rectangle. Only recently some more results on the symmetric difference have been obtained. In fact, de Berg et al. in [dBDvK 96] consider matching algorithms maximizing the area of ....

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Proc. 17th Internat. Colloq. Automata Lang. Program., volume 443 of Lecture Notes in Computer Science, pages 703--716. Springer-Verlag, 1990.

No context found.

H. Alt, J. Blomer, M. Godau, and H. Wagener. Approximation of convex polygons. In Seventeenth International Colloquium on Automata, Languages and Programming, number 443 in Lecture Notes in Computer Science, pages 703--716. SpringerVerlag, 1990.

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