Robust nonparametric detection of objects in noisy images

Abstract

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.

This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pdf

References in corpus (3)

• Detection of objects in noisy images and site percolation on square lattices
• Spatial statistics, image analysis and percolation theory
• Computationally efficient algorithms for statistical image processing. Implementation in R

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• Unsupervised nonparametric detection of unknown objects in noisy images based on percolation theory
• Asymptotic convergence rate of the longest run in an inflating Bernoulli net
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