Multi-labelled Image Segmentation in Irregular, Weighted Networks: A Spatial Autocorrelation Approach.

Image segmentation and spatial clustering both face the same primary problem, namely to gather together spatial entities which are both spatially close and similar regarding their features. The parallelism is partic- ularly obvious in the case of irregular, weighted networks, where methods borrowed from spatial analysis and general data analysis (soft K-means) may serve at segmenting images, as illustrated on four examples. Our semi-supervised approach considers soft memberships (fuzzy clustering) and attempts to minimize a free energy functional made of three ingredients : a within-cluster features dispersion (hard K-means), a network partitioning objective (such as the Ncut or the modularity) and a regularizing entropic term, enabling an itera- tive computation of the locally optimal soft clusters. In particular, the second functional enjoys many possible formulations, arguably helpful in unifying various conceptualizations of space through the probabilistic selec- tion of pairs of neighbours, as well as their relation to spatial autocorrelation (Moran’s I).