Randomized algorithms for statistical image analysis and site percolation on square lattices

Our approach uses mathematical percolation theory. Detection of objects in noisy images is the most basic problem of image analysis. Indeed, when one looks at a noisy image, the first question to ask is whether there is any object at all. This is also a primary question of interest in such diverse fields as, for example, cancer detection (Ricci-Vitiani et al. (2007)), automated urban analysis (Negri et al. (2006)), detection of cracks in buried pipes (Sinha and Fieguth (2006)), and other possible applications in astronomy, electron microscopy and neurology. Moreover, if there is just a random noise in the picture, it doesn't make sense to run computationally intensive procedures for image reconstruction for this particular picture.