What Is a 'Degenerate' View?

Abstract

In this paper, we attempt to quantify what is meant by the terms view, and its relatives, view, visual event, and viewing position. We propose that the definition of degeneracy is itself degenerate, taking on differing meanings at different times. We claim (at least for the case of polyhedra) that one can only speak of a two-dimensional stimulus as being degenerate with respect to a given heuristic for inverting the image function. Additionally, we show that given the finite viewing resolution of a two-dimensional retina, in practice the concept of a characteristic view is often not characteristic of real imagery. Even precisely defined general viewing positions are sensitive to camera acuity: any viewpoint ceases to be characteristic at some resolution, and non-characteristic views are not vanishingly improbable. We provide initial quantitative estimates on these probabilities for some simple cases, and relate them to a minimal disambiguation distance. It follows that an aspect graph is less a discrete graph, and more properly a partitioning of the surface of the viewing sphere into fuzzy regions of non-zero area: an aspect map. This viewpoint is more in keeping with recent and proposed work on optimal viewing strategies.