Visions of a generalized probability theory

Fabio Cuzzolin
Ph.D. Thesis, University of Padua, Italy, March 2001

Computer vision is an increasingly growing discipline with the ambitious purpose of enabling machines to mimic the visual skills humans and animals are provided by the nature, allowing them to move effortless inside complex, dynamic environments. Designing automatic recognition and sensing systems involves a number of very difficult tasks and requires a large variety of interesting and even sophisticated mathematical tools. In most cases the knowledge the animal or automatic agent has of the external world is at least uncompleted or even missing at all. The need of a mathematical description of uncertain models and measurements naturally arises. The theory of evidence is perhaps one of the most successful approaches to uncertainty theory and surely the most straightforward and intuitive attempt to produce a generalized probability theory. Coming out from a deep criticism of the classical Bayesian theory of inference, it stimulated a wide discussion about the epistemic nature of beliefs and chances. During the last decade, a renewed interest in generalized probabilities or belief functions has seen the born of many applications of this theory, mainly in the field of sensor fusion. In this thesis we are going to show how the mutual interaction of vision and evidential reasoning can produce a number of new interesting results on both sides. We will describe some theoretical advances about the geometrical and algebraic properties of belief functions, and introduce in the theory a well-known concept of probability theory such as that of total function. The introduction of tools widely used in computer and system engineering is definitively necessary to achieve the goal of a valid alternative to the classical Bayesian formalism. On the other side we will explain how these questions arise from classical computer vision problems, namely articulated object tracking, data association and feature integration. All these problems will find a natural solution in the framework of the evidential reasoning and stimulate the comparison between evidential and probabilistic approaches.
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 BibTeX Entry

  AUTHOR = "Fabio Cuzzolin", 
  TITLE = "Visions of a generalized probability theory", 
  SCHOOL = "Department of Information Engineering, University of Padua",
  TYPE = "{PhD} Dissertation",
  YEAR = "2001" 

INRIA Rhone-Alpes