Motion detection in interleaved random dot patterns: evidence for a rectifying nonlinearity preceding motion analysis

Failure of direction identification for briefly presented second-order motion stimuli: evidence for weak direction selectivity of the mechanisms encoding motion

We sought to investigate why the direction of second-order motion, unlike first-order motion, cannot be identified when the stimulus exposure duration is brief (<200 ms). In a series of experiments observers identified both the orientation (vertical or horizontal) and the direction (left, right, down or up) of a drifting sinusoidal modulation (0.93 c/ degrees ) in either the luminance (first order) or the contrast (second order) of a two-dimensional noise carrier. All motion stimuli were equated for visibility, and the duration was varied using the method of constant stimuli. Performance was measured for second-order motion over a range of drift temporal frequencies (0.63-5.04 Hz) and for first-order motion stimuli composed of two, opposite drifting modulations in luminance of unequal modulation depth. Orientation-identification performance was nearly 100% correct for both first-order and second-order motion stimuli, even at the briefest stimulus duration tested (26.49 ms). Direction identification for first-order motion was also typically good with brief presentations, but was poor for second-order motion when the exposure duration was < approximately 200 ms. Importantly increasing either the drift temporal frequency of second-order motion or the bidirectional nature of the first-order motion patterns produced comparable levels of performance for the two varieties of motion (i.e. the minimum duration required for reliable direction identification could be equated). As orientation-identification performance for the first-order and second-order motion stimuli was comparably good and minimally affected by duration, the marked differences on the direction-identification task must be specific to mechanisms that encode drift direction, rather than spatial structure. We propose that second-order motion detectors are much less selective for stimulus direction than first-order motion sensors, and thus are more susceptible to the deleterious effects of limiting stimulus duration (which introduces spurious motion in the opposite direction, particularly at low drift rates). Alternative explanations based on the delayed propagation of second-order motion signals or the temporal characteristics of the underlying motion mechanisms are not supported by our findings.

Second-order processing of four-stroke apparent motion

In four-stroke apparent motion displays, pattern elements oscillate between two adjacent positions and synchronously reverse in contrast, but appear to move unidirectionally. For example, if rightward shifts preserve contrast but leftward shifts reverse contrast, consistent rightward motion is seen. In conventional first-order displays, elements reverse in luminance contrast (e.g. light elements become dark, and vice-versa). The resulting perception can be explained by responses in elementary motion detectors turned to spatio-temporal orientation. Second-order motion displays contain texture-defined elements, and there is some evidence that they excite second-order motion detectors that extract spatio-temporal orientation following the application of a non-linear 'texture-grabbing' transform by the visual system. We generated a variety of second-order four-stroke displays, containing texture-contrast reversals instead of luminance contrast reversals, and used their effectiveness as a diagnostic test for the presence of various forms of non-linear transform in the second-order motion system. Displays containing only forward or only reversed phi motion sequences were also tested. Displays defined by variation in luminance, contrast, orientation, and size were effective. Displays defined by variation in motion, dynamism, and stereo were partially or wholly ineffective. Results obtained with contrast-reversing and four-stroke displays indicate that only relatively simple non-linear transforms (involving spatial filtering and rectification) are available during second-order energy-based motion analysis.

A computational model of selective deficits in first and second-order motion processing

Recent neurological studies of selective impairments in first and second-order motion processing are of considerable relevance in elucidating the mechanisms of motion perception in normal human observers. We examine the stimuli which have been used to assess first and second-order motion processing capabilities in clinical subjects, and discuss the nature of the computations necessary to extract their motion. We find that a simple computational model of first and second-order motion processing is able to account for the data. The model consists of a first-order channel computing motion at coarse and fine scales, and a coarse scale second-order channel. The second-order channel is sensitive to motion information defined by variations in luminance, contrast, spatial frequency and flicker. When elements of the model are disabled, its performance on either first or second-order motion can be selectively impaired in line with the neurological data.

Nonlinear preprocessing in short-range motion

The phenomenon of non-Fourier motion (visually perceived motion that cannot be explained simply on the basis of the autocorrelation structure of the visual stimulus) is well recognized, and is generally considered to be due to nonlinear preprocessing of the visual stimulus prior to a stage of standard motion analysis. We devised a sequence of novel visual stimuli in which the availability of a motion stimulus depends on the nature of the nonlinear preprocessing: an nth order stimulus Pn will generate a perception of motion if it is preprocessed by a nonlinearity of polynomial order n or greater, but not if preprocessed by a nonlinearity of polynomial order less than n. We found that unambiguous motion direction was perceived for P2, P3, and P4, but not for higher-order stimuli, and we measured the contrast thresholds for direction discrimination with superimposed noise. We found that an asymmetric compressive nonlinearity can, in a unified fashion, account for these results, while a purely quadratic nonlinearity or a rectification of the form T(p) = magnitude of p cannot. We compared velocity discrimination judgements for second-order non-Fourier stimuli (P2) with standard drifting gratings. Although velocity comparisons were veridical, uncertainties were greater for the non-Fourier stimuli. This could be reproduced by substituting a Fourier grating with superimposed noise for the non-Fourier grating. These findings are consistent with a single pathway which processes both Fourier and non-Fourier short-range motion, and are discussed in the context of other investigations which have been interpreted as demonstrating separate pathways.