The 'ecological' probability density function for linear optic flow: implications for neurophysiology

Local statistics of retinal optic flow for self-motion through natural sceneries

Image analysis in the visual system is well adapted to the statistics of natural scenes. Investigations of natural image statistics have so far mainly focused on static features. The present study is dedicated to the measurement and the analysis of the statistics of optic flow generated on the retina during locomotion through natural environments. Natural locomotion includes bouncing and swaying of the head and eye movement reflexes that stabilize gaze onto interesting objects in the scene while walking. We investigate the dependencies of the local statistics of optic flow on the depth structure of the natural environment and on the ego-motion parameters. To measure these dependencies we estimate the mutual information between correlated data sets. We analyze the results with respect to the variation of the dependencies over the visual field, since the visual motions in the optic flow vary depending on visual field position. We find that retinal flow direction and retinal speed show only minor statistical interdependencies. Retinal speed is statistically tightly connected to the depth structure of the scene. Retinal flow direction is statistically mostly driven by the relation between the direction of gaze and the direction of ego-motion. These dependencies differ at different visual field positions such that certain areas of the visual field provide more information about ego-motion and other areas provide more information about depth. The statistical properties of natural optic flow may be used to tune the performance of artificial vision systems based on human imitating behavior, and may be useful for analyzing properties of natural vision systems.

Neuromagnetic evoked responses to complex motions are greatest for expansion

We analysed evoked magnetic responses to moving random dot stimuli, initially using a 19-channel magnetoencephalography (MEG) system, and subsequently using a 151-channel MEG system. Random dot displays were used to construct complex motion sequences, which we refer to as expansion, contraction, deformation, and rotation. We also investigated lateral translation and a condition in which the directions of the dots were randomised. In all stimulus conditions, the dots were first stationary, then traveled for a brief period (317 s or 542 ms), and were then stationary again. In all conditions, evoked magnetic responses were observed with a widespread bilateral distribution over the observers' heads. Initial recordings revealed a substantially larger evoked magnetic response to the expansion condition than the other conditions. In a revised study, we used a 151-channel MEG system and two stimulus diameters (9.3 and 48 deg), the smaller comparable with the first experiment. The responses were analysed using a nonparametric approach and confirmed our initial observations. In a third study, speed gradients were removed and a new design permitted direct comparisons between motion conditions. The results from all three experiments are consistent with the greater ecological validity of the expansion stimulus.

Broad direction bandwidths for complex motion mechanisms

Growing evidence from psychophysics and single-unit recordings suggests specialised mechanisms in the primate visual system for the detection of complex motion patterns such as expansion and rotation. Here we used a subthreshold summation technique to determine the direction tuning functions of the detecting mechanisms. We measured thresholds for discriminating noise and signal+noise for pairs of superimposed complex motion patterns (signal A and B) carried by random-dot stimuli in a circular 5 degrees field. For expansion, rotation, deformation and translation we found broad tuning functions approximated by cos(d), where d is the difference in dot directions for signal A and B. These data were well described by models in which either: (a) cardinal mechanisms had direction bandwidths (half-widths) of around 60 degrees; or (b) the number of mechanisms was increased and their half-width was reduced to about 40 degrees. When d=180 degrees we found summation to be greater than probability summation for expansion, rotation and translation, consistent with the idea that mechanisms for these stimuli are constructed from subunits responsive to relative motion. For deformation, however, we found sensitivity declined when d=180 degrees, suggesting antagonistic input from directional subunits in the deformation mechanism. This is a necessary property for a mechanism whose job is to extract the deformation component from the optic flow field.

Classical and inverted White's effects

In classical White's effect, intermediate-luminance targets appear lighter when they interrupt the dark stripes of a grating and darker when they interrupt the light stripes. The effect is reversed when targets are of double-increment or double-decrement luminance, relative to the luminances of grating stripes. To find a common explanation for classical and inverted effects, we ran two experiments. In experiment 1, we utilised intermediate-target displays to show that perceived transparency dominates over occlusion only when the target luminance is close to the luminances of top regions. This result weakens transparency-based accounts of White's effect. In experiment 2, we varied grating contrast and target luminance to measure the classical effect in seven intermediate-target cases, as well as the inverted effect in four double-increment and four double-decrement cases. Both types of effect are explained by a common model, based on assimilation to the top region and contrast with the interrupted region, weighted by adjacency along the luminance continuum.

Mechanisms for seeing transparency-from-motion and orientation-from-motion

Structure-from-motion (SFM) perception is hypothesised to be mediated by units that sense the near-far relationships in transparency-from-motion (TFM) and orientation-from-motion (OFM). The frequency of subjective reversals during observation of ambiguous SFM displays is considerably decreased when either the direction of rotation or the surface orientation is oscillated during the inspection. Such manipulations impede adaptation of units selectively sensitive to TFM and OFM. The results show that both OFM and TFM units are direction-selective, and that the reversal rate is unaffected by reducing TFM to zero; and support the view that depth order, when both TFM and OFM are present, is estimated by common neural units.