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 im-
portant 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 nite sample performance of our test.
