Abstract
The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The HVA, however, provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the IOC direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the HVA.
Highlights
The first stage of motion analysis is not a global estimate of the motion of an object as such, but a dense set of estimates of the motion present at each location in the visual field
In Experiment 1 we measured the effect of varying the distribution of Gabor angles in the array on the perceived global motion direction
We varied the mean angle of the Gabors and the degree of variation around this value whilst holding the global motion direction and global motion speed constant
Summary
The first stage of motion analysis is not a global estimate of the motion of an object as such, but a dense set of estimates of the motion present at each location in the visual field. These local estimates need to be grouped and combined to determine the motion of the object as a whole. This local analysis can be prone to the aperture problem (Wallach, 1935). In the case of a 1-dimensional pattern viewed through an aperture, human observers typically see motion in the direction orthogonal to the contours (Wallach, 1935; Hildreth, 1984)
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