A measure for mutual refinements of image segmentations

In this paper, we recover a graph interpretation of the mutual partition distance, proposed recently by Cardoso and Corte-Real. We deduce some properties of this measure, and establish a correspondence with the partition distance introduced by Almudevar and Field and Gusfield, and independently by Guigues. We also present some different formulations for the computation of the mutual partition distance. Finally, a comparison is made with similar measures.