Does this computational theory solve the right problem? Marr, Gibson, and the goal of vision

David Marr's book Vision attempted to formulate athoroughgoing formal theory of perception. Marr borrowed much of the "computational" level from James Gibson: a proper understanding of the goal of vision, the natural constraints, and the available information are prerequisite to describing the processes and mechanisms by which the goal is achieved. Yet, as a research program leading to a computational model of human vision, Marr's program did not succeed. This article asks why, using the perception of 3D shape as a morality tale. Marr presumed that the goal of vision is to recover a general-purpose Euclidean description of the world, which can be deployed for any task or action. On this formulation, vision is underdetermined by information, which in turn necessitates auxiliary assumptions to solve the problem. But Marr's assumptions did not actually reflect natural constraints, and consequently the solutions were not robust. We now know that humans do not in fact recover Euclidean structure--rather, they reliably perceive qualitative shape (hills, dales, courses, ridges), which is specified by the second-order differential structure of images. By recasting the goals of vision in terms of our perceptual competencies, and doing the hard work of analyzing the information available under ecological constraints, we can reformulate the problem so that perception is determined by information and prior knowledge is unnecessary.