Two new Bayesian approximations of belief functions based on convex geometry

Fabio Cuzzolin (1)

1 PERCEPTION - Interpretation and Modelling of Images and Videos

In this paper, we analyze from a geometric perspective the meaningful relations taking place between belief and probability functions in the framework of the geometric approach to the theory of evidence. Starting from the case of binary domains, we identify and study three major geometric entities relating a generic belief function (b.f.) to the set of probabilities P: 1) the dual line connecting belief and plausibility functions; 2) the orthogonal complement of P; and 3) the simplex of consistent probabilities. Each of them is in turn associated with a different probability measure that depends on the original b.f. We focus in particular on the geometry and properties of the orthogonal projection of a b.f. onto P and its intersection probability, provide their interpretations in terms of degrees of belief, and discuss their behavior with respect to affine combination.

Mots clés: Bayesian belief functions (b.f.); commutativity; geometric approach; intersection probability; orthogonal projection; theory of evidence

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Fabio Cuzzolin. Two new Bayesian approximations of belief functions based on convex geometry. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2007, 37 (4), pp.993-1008. ⟨10.1109/TSMCB.2007.895991⟩. ⟨hal-00171417⟩