
Visions of a generalized probability theory 


Fabio Cuzzolin
Ph.D. Thesis, University of Padua, Italy, March 2001 
Abstract 
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 wellknown 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 
@PHDTHESIS{cuzzolin01thesis,
AUTHOR = "Fabio Cuzzolin",
TITLE = "Visions of a generalized probability theory",
SCHOOL = "Department of Information Engineering, University of Padua",
TYPE = "{PhD} Dissertation",
YEAR = "2001"
} 