Unsupervised edge map scoring: a statistical complexity approach

We propose a new Statistical Complexity Measure (SCM) to qualify edge maps without Ground Truth (GT) knowledge. The measure is the product of two indices, an \emph{Equilibrium} index $\mathcal{E}$ obtained by projecting the edge map into a family of edge patterns, and an \emph{Entropy} index $\mathcal{H}$, defined as a function of the Kolmogorov Smirnov (KS) statistic. This new measure can be used for performance characterization which includes: (i)~the specific evaluation of an algorithm (intra-technique process) in order to identify its best parameters, and (ii)~the comparison of different algorithms (inter-technique process) in order to classify them according to their quality. Results made over images of the South Florida and Berkeley databases show that our approach significantly improves over Pratt's Figure of Merit (PFoM) which is the objective reference-based edge map evaluation standard, as it takes into account more features in its evaluation.