We study statistical detection of grayscale objects in noisy images. The
object of interest is of unknown shape and has an unknown intensity, that can
be varying over the object and can be negative. No boundary shape constraints
are imposed on the object, only a weak bulk condition for the object's interior
is required. We propose an algorithm that can be used to detect grayscale
objects of unknown shapes in the presence of nonparametric noise of unknown
level. Our algorithm is based on a nonparametric multiple testing procedure. We
establish the limit of applicability of our method via an explicit,
closed-form, non-asymptotic and nonparametric consistency bound. This bound is
valid for a wide class of nonparametric noise distributions. We achieve this by
proving an uncertainty principle for percolation on finite lattices.Comment: This paper initially appeared in January 2011 as EURANDOM Report
2011-004. Link to the abstract at EURANDOM Repository:
http://www.eurandom.tue.nl/reports/2011/004-abstract.pdf Link to the paper at
EURANDOM Repository: http://www.eurandom.tue.nl/reports/2011/004-report.pd
