  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.
