On set distances and their application to image registration

In this paper we study set distances that are used in image processing. We propose a generalization of sum of minimal distances and show that its special case includes a metric by symmetric difference. The Hausdorff metric and the Chamfer matching distances are also closely related with the presented framework. In addition, we define the complement set distance of a given set distance. We evaluate the observed distances with respect to applicability to image object registration. We perform comparative evaluation with respect to noise sensitivity, as well as with respect to rigid body transformations. We conclude that the family of generalized sum of minimal distances has many desirable properties for this application.