We investigate the cumulative scenery process associated with random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramér’s condition. We prove moderate deviation principles in dimensions d ≥ 2, covering all those regimes where rate and speed do not depend on the actual distribution of the scenery. In the case d ≥ 4 we eve...

This work focuses on characterizing scenery images. We semantically divide the objects in natural landscape scenes into background and foreground and show that the shapes of the regions associated with these two types are statistically different. We then focus on the background regions. We study statistical properties such as size and shape, location and relative location, the characteristics o...

Let {~(n)}nEZbe a 2-color random scenery, that is a random coloration of in two colors, such that the ~(i)'s are i.i.d. Bernoulli variables with parameter~. Let {S(n)}nEN be a symmetric random walk starting at O. Our main result shows that a.s., ~ 0 S (the composition of ~ and S) determines ~ up to translation and reflection. In other words, by observing the scenery ~ along the random walk path...

This paper proposes an optimization procedure of a spatial filter in a water level detection system. The water level of running water of a river is detected by applying a temporal filter and a spatial filter to a video of various river scenery. Previously, we have proposed an algorithm based on “addition” of frames and “horizontal” detection of edges. We have confirmed its superiority to the ex...