Contours from Apparent Motion: A Computational Theory

Abstract

509Human vision readily constructs subjective contours from displays of kinetic occlusion and color from motion. To construct these contours from kinetic displays it is argued that human vision must solve the point-aperture problem, a problem more general and more difficult than the well-known aperture problem. In the aperture problem one is given a contour and its orthogonal velocity field, and must compute the full velocity field; in the point-aperture problem one is given neither the curve nor any components of its velocity field, and must constn,ict both the curve and its full velocity field . We formalize the point-aperture problem and present, in special cases, two simple algorithms for its solution.

From Flashes to Edges to Objects: Recovery of Local Edge Fragments Initiates Spatiotemporal Boundary Formation

“…The demonstration that SBF can occur for short edge fragments indicates that such fragments can be recovered without more global shape information and that such fragments are the likely basic units in SBF. This is in agreement with our current SBF models (Shipley and Kellman, 1994 , 1997 ; Erlikhman and Kellman, 2015 ) and is inconsistent with others that rely on the detection of a large object region (Prophet et al, 2001 ). According to formal models (e.g., Shipley and Kellman, 1997 ), edge orientation and local motion can be extracted from the transformations of three, non-collinear elements given only their relative positions and the timing of the transformation events.…”

“…Here, as in other applications of motion energy filter responses, there are ambiguity and/or aperture problems. Several models exist that combine motion vectors into global percepts (e.g., Weiss et al, 2002 ), but SBF displays pose some additional ambiguities (Shipley and Kellman, 1994 ; Prophet et al, 2001 ). First, the output of such motion models is typically a global motion signal, not an edge orientation.…”

“…Third, orientation information of an object's boundary may often be explicit in the image, but in SBF displays when the elements are circles, no edge orientation information about the virtual object is available in a static image. This describes a nefarious type of aperture problem that exists in SBF, which has elsewhere been called the “point-aperture problem” (Prophet et al, 2001 ). Unlike the classic aperture problem in which concurrently available motion vectors orthogonal to moving edges are integrated across several small apertures (Wallach, 1935 ; Adelson and Movshon, 1982 ; Nakayama and Silverman, 1988a , b ; Shimojo et al, 1989 ), in SBF, in which each element may itself be treated as a small aperture, there are no edges to which the motion vectors are orthogonal, and their direction is therefore ambiguous.…”

“…For collinear elements, the timing of element transformations is not affected by edge orientation. This is a form of an aperture problem that occurs in SBF (Shipley and Kellman, 1994 , 1997 ; Prophet et al, 2001 ).…”

Non-rigid illusory contours and global shape transformations defined by spatiotemporal boundary formation

“…Depending on the transformation used to produce SBF, there may be local orientation changes (when element orientation change is used) or local motions (when element displacement is used), but these events not only provide no information about a larger form and moving contours, they provide what would appear to be contradictory information. This more extreme version of the aperture problem in SBF has been referred to as the “point-aperture problem” (Prophet et al, 2001 ).…”