ADAPTIVE MULTISCALE DETECTION OF FILAMENTARY STRUCTURES IN A BACKGROUND OF UNIFORM RANDOM POINTS 1
ADAPTIVE MULTISCALE DETECTION OF FILAMENTARY STRUCTURES IN A BACKGROUND OF UNIFORM RANDOM POINTS 1
复制标题
均匀随机点背景下丝状结构的自适应多尺度检测1
DOI：
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复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
X. Huo
中科院分区：
文献类型：
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作者：
E. Arias;D. Donoho;X. Huo
给定n个点的集合，这些点可能均匀分布在单位正方形[0,1]2中。我们希望测试这个集合，虽然主要由均匀分散的点组成，但是否也包含从一些（先验未知的）C α -范数以β为界的曲线中采样的一小部分点。该问题存在一个渐近检测阈值；对于常数T−(α,β) > 0，如果从曲线上采样的点数小于T−(α,β) n 1 / (1+ α)，则对于较大的n不可能进行可靠的检测。我们描述了一种多尺度显著运行算法，该算法可以可靠地检测光滑曲线附近的数据集中，而无需事先知道平滑信息α或β，只要曲线上的点数超过T∗(α,β) n 1 / (1+ α)。因此，该算法有一个最优检测阈值，达到因子T * /T−。我们方法的核心是通过计算多尺度多各向异性条带的隶属度来分析数据。条带的面积为2 /n，具有不同的长度、方向和各向异性。条带被划分为各向异性类；每个类都被组织成一个有向图，其顶点都是具有相同各向异性的条，其边将这些条与它们的“良好延续”连接起来。点云数据被简化为测量条带成员的计数。每个各向异性图被简化为由具有显著计数的条带组成的子图。当某些这样的子图包含连接许多连续有效计数的路径时，算法拒绝h0。
We are given a set of n points that might be uniformly distributed in the unit square [0 , 1] 2 . We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled from some (a priori unknown) curve with C α -norm bounded by β . An asymptotic detection threshold exists in this problem; for a constant T − ( α,β ) > 0, if the number of points sampled from the curve is smaller than T − ( α,β ) n 1 / (1+ α ) , reliable detection is not possible for large n . We describe a multiscale significant-runs algorithm that can reliably detect concentration of data near a smooth curve, without knowing the smoothness information α or β in advance, provided that the number of points on the curve exceeds T ∗ ( α,β ) n 1 / (1+ α ) . This algorithm therefore has an optimal detection threshold, up to a factor T ∗ /T − . At the heart of our approach is an analysis of the data by counting membership in multiscale multianisotropic strips. The strips will have area 2 /n and exhibit a variety of lengths, orientations and anisotropies. The strips are partitioned into anisotropy classes; each class is organized as a directed graph whose vertices all are strips of the same anisotropy and whose edges link such strips to their “good continuations.” The point-cloud data are reduced to counts that measure membership in strips. Each anisotropy graph is reduced to a subgraph that consist of strips with significant counts. The algorithm rejects H 0 whenever some such subgraph contains a path that connects many consecutive significant counts.
影响因子：
1.8
作者：
Levi, DM;Klein, SA
通讯作者：
Klein, SA
DOI：
10.1364/josaa.4.000391
发表时间：
1987-02-01
影响因子：
1.9
作者：
LEGGE, GE;KERSTEN, D;BURGESS, AE
通讯作者：
BURGESS, AE