Visions of a generalized probability theory

Abstract

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.

Cited by in corpus (5)

• Evidential Sparsification of Multimodal Latent Spaces in Conditional Variational Autoencoders
• Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces
• A geometric approach to conditioning belief functions
• Uncertainty measures: The big picture
• Belief likelihood function for generalised logistic regression