منابع مشابه
Adaptive Estimation of Planar Convex Sets
In this paper, we consider adaptive estimation of an unknown planar compact, convex set from noisy measurements of its support function. Both the problem of estimating the support function at a point and that of estimating the whole convex set are studied. For pointwise estimation, we consider the problem in a general non-asymptotic framework, which evaluates the performance of a procedure at e...
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The process of learning the shape of an unknown convex planar object through an adaptive process of simple measurements called Line probings, which reveal tangent lines to the object, is considered. A systematic probing strategy is suggested and an upper bound on the number of probings it requires for achieving an approximation with a pre-specified precision to the unknown object is derived. A ...
متن کاملk-Sets of Convex Inclusion Chains of Planar Point Sets
Given a set V of n points in the plane, we introduce a new number of k-sets that is an invariant of V : the number of k-sets of a convex inclusion chain of V . A convex inclusion chain of V is an ordering (v1, v2, ..., vn) of the points of V such that no point of the ordering belongs to the convex hull of its predecessors. The k-sets of such a chain are then the distinct k-sets of all the subse...
متن کاملCounting Convex Polygons in Planar Point Sets
Given a set S of n points in the plane, we compute in time O(n) the total number of convex polygons whose vertices are a subset of S. We give an O(m n) algorithm for computing the number of convex k-gons with vertices in S, for all values k = 3; : : : ;m; previously known bounds were exponential (O(ndk=2e)). We also compute the number of empty convex polygons (resp., k-gons, k m) with vertices ...
متن کاملEmpty Convex Hexagons in Planar Point Sets
Erdős asked whether every sufficiently large set of points in general position in the plane contains six points that form a convex hexagon without any points from the set in its interior. Such a configuration is called an empty convex hexagon. In this paper, we answer the question in the affirmative. We show that every set that contains the vertex set of a convex 9-gon also contains an empty co...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2018
ISSN: 0090-5364
DOI: 10.1214/17-aos1576