Title: Image denoising by statistical area thresholding
Authors: D. Coupier, A. Desolneux, B. Ycart
Abstract:
Area openings and closings are morphological filters which efficiently suppress
impulse noise from an image, by removing small connected components of level
sets. The problem of an objective choice of threshold for the area
remains open. Here, a mathematical model for random images will be
considered. Under this model, a Poisson approximation for
the probability of appearance of any local
pattern can be computed. In particular, the probability to observe a
component with size larger than $k$ in pure noise has an explicit
form. This permits to define a statistical test on the significance of
connected components, thus providing an explicit formula for the area
threshold of the denoising filter, as a function of the noise
intensity. Finally, using threshold decomposition, an adaptive
denoising algorithm for gray level images is proposed.
Key words: image denoising, mathematical morphology, area
opening and closing, random image, threshold
function, Poisson approximation, lattice animals.
AMS Subject Classification: 68U10, 62H35.