A theoretical and empirical investigation into three computational strategies for structure from motion perception in Euclidean and projective geometries

Motion information processing can yield percepts of frame-of-reference based structure. In Part 1 we provided a theoretical characterization of three computational-level strategies for the extraction of frame-of-reference based structure from motion perception. Each of these assumes a different type of input information. The 'velocity feature integration strategy' (e.g. Olshausen et al, 1993) takes as input the absolute Cartesian velocity field of the retinal image, and assumes that only local absolute velocity magnitudes are detected automatically: focal attention based integration, operating in conjunction with internal representational assumptions, is required to infer 3D structural percepts from 2D retinal image information. The 'Euclidean vector analysis strategy' (e.g. Cutting & Proffitt, 1981) takes as input optic flow, defined in terms of the Euclidean velocity field. It assumes that structured relations between absolute velocities in the velocity field, directly informative of frame-of-reference based structure and invariant over absolute velocity values, may be automatically extracted by vector analytic operations. The 'projective vector analysis strategy' (e.g. Johansson, 1973) takes as input optic flow defined in projective geometry which differs from Euclidean optic flow in as far as the information detected is necessarily relativistic. It assumes that structural properties of the world in relation to the viewer can be detected directly as object-centred and viewer-centred projective-geometry vectors, without the mediation of a 2D velocity field.;In Part 2 we empirically tested between these three computational strategies using a parametric 'match to sample', direction-of-motion judgment task, using two concentric 'centre-surround' squares as stimuli, one of which enclosed the other. The surround square was assumed to provide the frame of reference for the enclosed square (Rock, 1990). Two experiments were conducted. In Experiment 1, square motions were defined in viewer-centred XY space; in Experiment 2, square motions were defined in proximal projection Z/...