Computing the direction of heading from affine image flow

Abstract

Observers moving through a three-dimensional environment can use optic flow to determine their direction of heading. Existing heading algorithms use cartesian flow fields in which image flow is the displacement of image features over time. I explore a heading algorithm that uses affine flow instead. The affine flow at an image feature is its displacement modulo an affine transformation defined by its neighborhood. Modeling the observer's instantaneous motion by a translation and a rotation about an axis through its eye, affine flow is tangent to the translational field lines on the observer's viewing sphere. These field lines form a radial flow field whose center is the direction of heading. The affine flow heading algorithm has characteristics that can be used to determine whether the human visual system relies on it. The algorithm is immune to observer rotation and arbitrary affine transformations of its input images; its accuracy improves with increasing variation in environmental depth; and it cannot recover heading in an environment consisting of a single plane because affine flow vanishes in this case. Translational field lines can also be approximated through differential cartesian motion. I compare the performance of heading algorithms based on affine flow, differential cartesian flow, and least-squares search.

Method for recovery of heading from motion

“…These are essentially the same equations as (6). It indicates that the virtual radial flow is quite similar to the flow pattern generated by translation toward the frontoparallel plane with average depth.…”

“…It is also important for computer vision. A large number of heading recovery algorithms from image sequences have been presented for computer vision [1][2][3][4] and several algorithms were proposed as method in which biological visual systems may recover heading from motion [5][6][7][8][9] . The algorithm of Rieger and Lawton 5 based on the method of Longuet-Higgins & Prazdny 2 is one of the methods which might be used by biological visual systems.…”

Effects of roll and pitch components in retinal flow on heading judgement

“…Since the perception of the curved path has little effect on the judgement, the bias observed in our experiment cannot be explained by the perceived curved path. Several models of human heading recovery successfully explain the bias with stimuli which simulate a small depth range (Hildreth, 1992;Beusmans, 1993;Hanada & Ejima, in press). The bias appears to arise from the limitation of computation in the human visual system.…”

“…When an observer rotates due to head, body or eye movement, it is not trivial to recover heading from the retinal flow alone. A large number of algorithms to recover heading have been presented for computer vision (e.g., Bruss and Horn, 1983;Louguet-Higgins and Prazdny, 1980;Kanatani, 1993) and several models of human heading perception have been proposed (e.g, Rieger & Lawton, 1985;Hildreth, 1992;Beusmans, 1993;Lappe & Rauschecker, 1993;Perrone, 1992;Royden, 1997;Beintema & van den Berg, 1998).…”

Receptive Field Dynamics Underlying MST Neuronal Optic Flow Selectivity

“…One such attribute is the increasing divergence of visual motion elements that define the outward radial pattern seen during forward self-movement van Doorn 1975, 1981), potentially implemented by a normalization of motion properties across a segment of the visual field to derive the affine motion of elements in that segment (Beusmans 1993). Extension of a subspace algorithm led to a biologically plausible two-layered population encoding network for heading estimation that accommodates eye rotation and depth of field effects (Lappe and Rauschecker 1993).…”