In motion transparency, one surface is very often seen on top of the other in spite of no proper depth cue in the display. We investigated the dynamics of depth assignment in motion transparency stimuli composed of random dots moving in opposite directions. Similarly to other bistable percepts, which surface is seen in front is arbitrary and changes over time. In addition, we found that helping the segregation of the two surfaces by giving the same color to all dots of one surface significantly slowed down the initial rate of depth reversals. We also measured preferences to see one particular motion direction in front. Unexpectedly, we found that all of our 34 observers had a strong bias to see a particular motion direction in front, and this preferred direction was usually either downward or rightward. In contrast, there was no consistency in seeing the fastest or slowest surface in front. Finally, the preferred motion direction seen in front for one observer was very stable across several days, suggesting that a trace of this arbitrary motion preference is kept in memory.

*no-segmentation*condition (Figure 1A), half of the black dots moved in one direction and the other half in the opposite direction. The same was true for the white dots. Therefore, each surface was composed of half black and half white dots. In contrast, in the

*two-color*condition (Figure 1B), all the black dots moved in one direction and all the white dots moved in the opposite direction. Therefore, in this second condition, the color of the dots was a cue to help segment the stimulus into two surfaces. Which surface color moved to the right rather than left was randomized between runs. Both conditions contained the same number of black and white dots, and the same number of dots moving in each direction, the only difference being whether the dot color was a cue to segment the two surfaces. Each condition was repeated 48 times. The total of 96 runs was presented in random order in 12 blocks of 8 runs and participants were authorized to take short breaks between blocks.

*τ*

_{1}(respectively,

*τ*

_{2}) the critical time to reach the stationary regime in the no-segmentation condition (respectively, the two-color condition) and

*α*

_{1}(respectively,

*α*

_{2}) the reversal rate in the stationary regime in the no-segmentation condition (respectively, the two-color condition). We note that for this observer the time to reach the stationary regime is longer in the two-color condition than in the no-segmentation condition (

*τ*

_{1}= 11.1 s vs.

*τ*

_{2}= 13.8 s). In contrast, there was no difference in the reversal rate in the stationary regime between the two conditions. These two observations for this particular observer generalize across our population of participants. The time to reach the stationary regime is longer in the two-color condition than in the no-segmentation condition (Figure 2C). In contrast, there was no difference in the reversal rate in the stationary regime between the two conditions (Figure 2D).

*θ,*the probability

*p*to see the black surface in front is characterized by the following logit model:

*θ*

_{0}is the preferred direction,

*β*

_{ θ }represents the strength of the effect of motion direction on the depth percept, and

*γ*is a constant. In this equation, ∣ ∣

_{ π }stands for the absolute value modulo

*π,*i.e., ∣

*x*∣

_{ π }= acos(cos(

*x*)). The parameter

*β*

_{ θ }shows how sensitive an observer is for small variations of motion directions (its unit is in rad

^{−1}when motion directions are expressed in radians). Some observers, such as BC, are very sensitive to the direction of motion in the sense that rotating the display by just a few degrees makes the black surface perceived always behind to always in front. These observers will display a large value of the parameter

*β*

_{ θ }. Other observers, such as PW, will be less affected by the motion direction and will display a smaller value of the parameter

*β*

_{ θ }.

*θ*

_{0}that represents the motion direction of the black dots that leads to the largest probability to see these black dots in front. Figure 3B shows the distribution of these preferred motion directions leading to a surface seen in front. This distribution is bimodal with a peak for downward motion and the other peak for rightward motion.

*κ,*the probability

*p*to see the black surface in front is characterized by the following logit model:

*β*

_{ κ }represents the strength of the effect of motion speed on the depth percept. Positive values of the parameter

*β*

_{ κ }represent a preference to see the fast surface in front, and negative values represent a preference to see the slow surface in front. Note that the logarithm is used on the right-hand side because the variable of interest is a ratio (as a consequence,

*β*

_{ κ }is unitless). Equation 2 can be rewritten to give a simple form for the probability

*p*

*β*

_{ κ }close to zero). Overall, most observers showed little effect of speed (Figure 4C). If anything, there is a small bias to see the slow surface in front.

*β*

_{ κ }as a measure of the speed bias strength: the larger the value, the stronger the effect of speed. For instance, in Figure 4B, observer PW was more influenced by speed than observer BC and this is well captured by the magnitude of

*β*

_{ κ }. We can also perform a similar analysis with the data collected in the previous experiment. The strength with which motion direction determined which surface was seen in front is characterized by the magnitude of the parameter

*β*

_{ θ }. When these two parameters are compared, we observe a trade-off (Figure 5). There is a significant negative correlation between the directional bias and the speed bias strengths (Pearson's correlation

*R*= 0.680). In other words, those observers who were very much influenced by the stimulus speed were less influenced by its direction and conversely.