1986 Reports

Smoothness assumptions in human and machine vision, and their implications for optimal surface interpolation

Boult, Terrance E.

In this paper we shall examine what smoothness assumptions are made about object surfaces, object motion, and image intensities. We begin by looking into the physiological limits of vision and how these might influence our perception of smoothness. We then look at a sampling of the computer vision and psychology literature, inferring smoothness constraints from the mathematical assumptions tacitly presumed by researchers. This look at computer vision and psychology of vision is not meant to be an inclusive study, but rather representative of the assumptions made, and in part representative of the mathematical models used therein. We shall conclude that prevalent assumptions are that surfaces, motion, and intensity images are functions in C2, eland c2 respectively. In the latter portion of this paper we examine one use of explicit assumptions on smoothness in the definition of existing method for obtaining "optimal" surface interpolation. We briefly introduce the nomenclature of information-based complexity originated by Traub, Wozniakowski, and their colleagues, which is the mathematical machinery used in obtaining these "optimal" surfaces. This theory requires that we know the class of functions from which our desired surface comes, and part of the definition of a class is the degree of smoothness. We then survey many possible classes for the visual interpolation problem of two dimensional surfaces, and state formulas from which one can obtain the optimal surface interpolating given depth data.