Statistics and Probability Commons^™

Detectability Of Convex-Shaped Objects In Digital Images, Its Fundamental Limit And Multiscale Analysis, Xiaoming Huo, Xuelei (Sherry) Ni

Faculty and Research Publications

Given a convex-shape inhomogeneous region embedded in a noisy image, we consider the conditions under which such an embedded region is detectable. The existence of low order-of-complexity detection algorithms is also studied. The main results are (1) an analytical threshold (of a statistic) that specifies what is detectable, and (2) the existence of a multiscale detection algorithm whose order of complexity is roughly the optimal O(n(2) log(2) (n)).

Our analysis has two main components. We first show that in a discrete image, the number of convex sets increases faster than any finite degree polynomial of the image size n. Hence …