Diffused Expectation Maximisation for image segmentation

Diffused Expectation Maximisation (DEM) is a novel algorithm for image segmentation. The method models an image as a finite mixture, where each mixture component corresponds to a region class and uses a maximum likelihood approach to estimate the parameters of each class, via the expectation maximisation (EM) algorithm, coupled with anisotropic diffusion on classes, in order to account for the spatial dependencies among pixels. Introduction: Any image can be considered a set of N unlabelled samples F = {f1, f2, . . . fN}, on a 2-D discrete support Ω ⊆ Z, with N = |Ω|. Thus, an image segmentation/classification problem can be defined in probabilistic terms as the problem of assigning a label k to each site i, given the observed data F , and where each label k ∈ [1, · · · , K] defines a particular region/model. Different models are selected with probability P (k), and a sample is generated with probability distribution p(fi|k, θ) where θ = {θk, k = 1, · · ·K} and θk is the vector of the parameters associated to label k. Thus p(fi|k, θ) is the probability of fi given the parameters of all models and the fact that we have selected model (label) k. Each image can be conceived as drawn from a mixture density, so that, for any site (pixel), p(fi|θ) = ∑K k=1 p(fi|k, θ)P (k), and the likelihood of the data is L = p(f |θ) = Ni=1 p(fi|θ). For clarity’s sake, we define p(fi) and π(f), two probability distributions; the former is the probability that a given gray level f is assigned