We propose that this predictive cue to depth is combined with available sensory information (see
Figure 8). We are agnostic about the specific nature of the cue integration process and propose that the simplest way of combining sensory and predictive information is through a weighted sum, where the weights sum to 1. We postulate that the visual system performs a rough estimate of the velocity in depth to determine the final position of the projectile. However, this estimate varies depending on the trajectory. When the trajectory confines the position of the object close to the edge, the velocity in depth is estimated based on the strong signal provided by the relative disparity between the projectile and the edge. When the projectile falls far from the edge, the velocity estimate relies solely on changes in ocular vergence and looming, as the binocular information is outside of the fusion range. Consequently, the weight of predictive information decreases as the falling location of the ball gets closer to the observer. The weight of sensory information (
ws) thus varies as a function of depth,
z, according to the following equation:
\begin{eqnarray}
{w_s} = {w_{s\left( {{\rm{min}}} \right)}} + \frac{{\left( {{w_{s\left( {{\rm{max}}} \right) - }}{w_{s\left( {{\rm{min}}} \right)}}} \right)}}{{\left( {{z_{{\rm{max}}}} - {z_{{\rm{min}}}}} \right)}}\left( {z - {z_{{\rm{min}}}}} \right)\quad
\end{eqnarray}
where
zmax and
zmin represent the maximum and minimum possible depths in our display (116.50 and 34.25 mm, respectively).The minimum weight of the sensory information,
ws(min), and the maximum weight of the sensory information,
ws(max), are the only free parameters in our model. When the displayed depth,
z, is identical to minimum possible depth,
zmin, the weight of the sensory information is at its lowest, and it is highest when the displayed depth equals
zmax. Importantly, these boundary conditions set by
zmax and
zmin ensure that
ws is uniquely determined by these parameters.