Distribution on Warp Maps for Alignment of Open and Closed Curves.
Distribution on Warp Maps for Alignment of Open and Closed Curves.
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DOI：
10.1080/01621459.2019.1632066
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发表时间：
2020
影响因子：
3.7
通讯作者：
Kurtek S
中科院分区：
文献类型：
--
作者：
Bharath K;Kurtek S
曲线数据的对齐是其统计分析的一个组成部分，并且可以使用基于模型或优化的方法来实现。参数空间通常是域的单调、连续扭曲映射的集合。参数空间的无限维性质鼓励基于采样的方法，这需要在扭曲图集上进行分布。此外，该分布还应该能够在限制扭曲图的曲线上存在重要地标信息的情况下进行采样。对于 , d = 1, 2, 3 中的闭合曲线和开放曲线的对齐，可能带有地标信息，我们提供了一个构造性的、基于点过程的定义，对 [0, 1] 和单位圆 的扭曲图集上的分布进行定义，即（1）易于采样，（2）拥有将具有地标约束的对齐问题分解为多个无约束问题的需求。对于 [0, 1] 上的扭曲贴图，分布与狄利克雷过程相关。我们通过将其用作贝叶斯模型中扭曲图上的先验分布来对齐两条单变量曲线，以及用作随机算法中的建议分布来展示其实用性，以优化高维曲线的合适对齐函数。提供了来自模拟和真实数据集的几个示例。
Alignment of curve data is an integral part of their statistical analysis, and can be achieved using modelor optimization-based approaches. The parameter space is usually the set of monotone, continuous warp maps of a domain. Infinite-dimensional nature of the parameter space encourages sampling based approaches, which require a distribution on the set of warp maps. Moreover, the distribution should also enable sampling in the presence of important landmark information on the curves which constrain the warp maps. For alignment of closed and open curves in , d = 1, 2, 3, possibly with landmark information, we provide a constructive, point-process based definition of a distribution on the set of warp maps of [0, 1] and the unit circle , that is, (1) simple to sample from, and (2) possesses the desiderata for decomposition of the alignment problem with landmark constraints into multiple unconstrained ones. For warp maps on [0, 1], the distribution is related to the Dirichlet process. We demonstrate its utility by using it as a prior distribution on warp maps in a Bayesian model for alignment of two univariate curves, and as a proposal distribution in a stochastic algorithm that optimizes a suitable alignment functional for higher-dimensional curves. Several examples from simulated and real datasets are provided.
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