Paper: INDUCTIVE THEORY OF VISION

[Lev Goldfarb]

My apologies if you receive multiple copies of this message.


The following paper 

(also TR96-108, April 1996, Faculty of Computer
Science, University of New Brunswick, Fredericton, Canada) 

will be presented at the workshop WHAT IS INDUCTIVE LEARNING held in
Toronto on May 20-21, 1996 in conjunction with the 11th Canadian biennial
conference on Artificial Intelligence.

It is available via anonymous ftp (45 pages) 
ftp://ftp.cs.unb.ca/incoming/theory.ps.Z 


It goes without saying that comments and suggestions are appreciated.


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			INDUCTIVE THEORY OF VISION

 	   Lev Goldfarb, Sanjay S. Deshpande, Virendra C. Bhavsar    
      
	 		Faculty of Computer Science 
			University of New Brunswick,
	 	     Fredericton, N.B., Canada E3B 5A3 
		    
                    Ph: (506)453-4566,  FAX: (506)453-3566 
		   E-mail: goldfarb, d23d, bhavsar  @unb.ca

			       
			       Abstract
                              ---------- 

In spite of the fact that some of the outstanding physiologists and
neurophysiologists (e.g. Hermann von Helmholtz and Horace Barlow) 
insisted on the central role of inductive learning processes in vision as
well as in other sensory processes, there are absolutely no
(computational) theories of vision that are guided by these processes. It
appears that this is mainly due to the lack of understanding of what
inductive learning processes are. 

We strongly believe in the central role of inductive learning processes
around which, we think, all other (intelligent) biological processes have
evolved. In this paper we outline the first (computational) theory of
vision completely built around the inductive learning processes for all
levels in vision. The development of such a theory became possible with
the advent of the formal model of inductive learning--evolving
transformation system (ETS). The proposed theory is based on the concept
of structured measurement device, which is motivated by the formal model
of inductive learning and is a far-reaching generalization of the concept
of classical measurement device, whose output measurements are not numbers
but structured entities ("symbols") with an appropriate metric geometry.

	We propose that the triad of object structure, image structure and
the appropriate mathematical structure (ETS)--to capture the latter two
structures--is precisely what computational vision should be about. And it
is the inductive learning process that relates the members of this triad.
We suggest that since the structure of objects in the universe has evolved
in a combinative (agglomerative) and hierarchical manner, it is quite
natural to expect that biological processes have also evolved (to learn)
to capture the latter combinative and hierarchical structure. In
connection with this, the inadequacy of the classical mathematical
structures as well as the role of mathematical structures in information
processing are discussed. 

	We propose the following postulates on which we base the theory. 
 
POSTULATE 1. The objects in the universe have emergent combinative
hierarchical structure. Moreover, the term "object structure" cannot be
properly understood and defined outside the inductive learning process. 

POSTULATE 2. The inductive learning process is an evolving process that
tries to capture the emergent object (class)  structure mentioned in
Postulate 1. The mathematical structure on which the inductive learning
model is based should have the intrinsic capability to capture the
evolving object structure. 
(It appears that the corresponding mathematical structure is
fundamentally different from the classical mathematical structures.)

POSTULATE 3.  All basic representations in vision processes are
constructed on the basis of the inductive class representation, which, 
in turn, is constructed by the inductive learning process (see Postulate
2). Thus, the inductive learning processes form the core around which all
vision processes have evolved. 

 	We present simple examples to illustrate the proposed theory for the
case of "low-level" vision.

                _______________________________________________


KEYWORDS: vision, low-level vision, object structure, inductive learning,
learning from examples, evolving transformation system, symbolic image
representation, image structure, abstract measurement device. 


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-- Lev Goldfarb         

http://wwwos2.cs.unb.ca/profs/goldfarb/goldfarb.htm