2 research outputs found
Consistent transformations of belief functions
Consistent belief functions represent collections of coherent or
non-contradictory pieces of evidence, but most of all they are the counterparts
of consistent knowledge bases in belief calculus. The use of consistent
transformations cs[.] in a reasoning process to guarantee coherence can
therefore be desirable, and generalizes similar techniques in classical logic.
Transformations can be obtained by minimizing an appropriate distance measure
between the original belief function and the collection of consistent ones. We
focus here on the case in which distances are measured using classical Lp
norms, in both the "mass space" and the "belief space" representation of belief
functions. While mass consistent approximations reassign the mass not focussed
on a chosen element of the frame either to the whole frame or to all supersets
of the element on an equal basis, approximations in the belief space do
distinguish these focal elements according to the "focussed consistent
transformation" principle. The different approximations are interpreted and
compared, with the help of examples
Visions of a generalized probability theory
In this Book we argue that the fruitful interaction of computer vision and
belief calculus is capable of stimulating significant advances in both fields.
From a methodological point of view, novel theoretical results concerning the
geometric and algebraic properties of belief functions as mathematical objects
are illustrated and discussed in Part II, with a focus on both a perspective
'geometric approach' to uncertainty and an algebraic solution to the issue of
conflicting evidence. In Part III we show how these theoretical developments
arise from important computer vision problems (such as articulated object
tracking, data association and object pose estimation) to which, in turn, the
evidential formalism is able to provide interesting new solutions. Finally,
some initial steps towards a generalization of the notion of total probability
to belief functions are taken, in the perspective of endowing the theory of
evidence with a complete battery of estimation and inference tools to the
benefit of all scientists and practitioners