Comparaison de relations spatiales floues - Approches par transport optimal et morphologie mathématique Comparison of fuzzy spatial relations - Optimal transport and mathematical morphology approaches

Observing the evolution of a pathology in medical images, or of soil occupation in remote sensing, detecting changes in video sequences, updating a spatial information system are examples that can all benefit from quantification and comparison of spatial relations between objects in the observed scenes. In this paper, we propose two approaches to compare spatial relations represented as fuzzy sets, relying on optimal transport and mathematical morphology, respectively. Examples on synthetic video sequences illustrate the interest of these approaches.