Inductive theory of vision
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 a (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 turns out 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 image 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.