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Michael S. Langer, Richard Mann; Computation of heading from motion parallax in 3-D cluttered scenes. Journal of Vision 2004;4(8):611. doi: https://doi.org/10.1167/4.8.611.
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Computational models of heading perception from motion parallax typically assume the observer estimates an image velocity field and uses this field as an input to a subsequent heading computation. Examples of the heading computation are (Rieger and Lawton, JOSA 1985) who use local differences of velocity and (Perrone and Stone, Vision Research 1994) who use velocity field templates. Because such heading computations assume a pre-computed velocity field as input, they do not fully explain heading perception in many common scenes, such as transparency or a 3-D cloud of dots. When an observer moves through such cluttered scenes, multiple image velocity vectors are present near each image position because of multiple depths, and so a velocity field in the classical sense of a vector field is poorly defined. Here we introduce an alternative computational model of heading perception from motion parallax in 3-D cluttered scenes. Rather than computing a velocity field, we estimate a distribution of velocity vectors over local image regions. We show: (1) that the 3-D spatiotemporal power spectrum in such regions has a bowtie pattern, thus extending the motion plane model of (Watson and Ahumada, JOSA 1985) to motion parallax; (2) the spatial frequency axis of this bowtie points toward the instantaneous direction of heading; (3) the axis direction can be estimated using a method analogous to (Rieger and Lawton, 1985), namely nulling the rotation components of the image velocity distributions. Data from computer vision experiments is presented for several difficult stimuli — both natural and computer graphics generated. These stimuli include a single ground plane, two-layered transparency, and a 3-D cloud of polygons.
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