Redundancy in Gaussian random fields

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2020-03-13 DOI:10.1051/PS/2020010

Valentin De Bortoli, A. Desolneux, B. Galerne, Arthur Leclaire

引用次数: 2

Abstract

In this paper, we introduce a notion of spatial redundancy in Gaussian random fields. This study is motivated by applications of the a contrario method in image processing. We define similarity functions on local windows in random fields over discrete or continuous domains. We derive explicit Gaussian asymptotics for the distribution of similarity functions when computed on Gaussian random fields. Moreover, for the special case of the squared L2 norm, we give non-asymptotic expressions in both discrete and continuous periodic settings. Finally, we present fast and accurate approximations of these non-asymptotic expressions using moment methods and matrix projections.

查看原文本刊更多论文

高斯随机场中的冗余

本文在高斯随机场中引入了空间冗余的概念。本文的研究是基于反相方法在图像处理中的应用。我们定义了离散域和连续域上随机场局部窗口上的相似函数。我们导出了在高斯随机场上计算相似函数分布的显式高斯渐近性。此外，对于L2范数的平方的特殊情况，我们给出了离散和连续周期设置下的非渐近表达式。最后，我们用矩法和矩阵投影给出了这些非渐近表达式的快速和精确的逼近。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.