Perceiving Motion Empirically Figure 4. Image-source relationships derived from the virtual environment. (A) The physical speeds of 3-D objects generate a range of projected speeds over a given distance on the image plane (2u in the examples shown). As a consequence of perspective projection, relatively slow image speeds (e.g., 1u/s; solid line) are generated by objects moving at relatively slow physical speeds in 3-D space; somewhat faster image speeds (e.g., 5u/s; dashed line) arise from a wider distribution of objects in 3-D space with a larger range of physical speeds; relatively fast image speeds (e.g., 20u/s; dotted line) tend to be generated by an even wider distribution of objects moving at still greater physical speeds. Note that any given image speed can only be produced by objects moving with speeds equal to or greater than the stimulus, explaining the biased frequency distributions in (B). (B) The overall frequency distribution of image speeds generated by empirical sampling. The diamonds on the 2u projected distance function indicate the summed data from each of the three specific distributions in (A). doi:10.1371/journal.pone.0006771.g004 Figure 5. Cumulative probability distributions derived from the analyses of objects moving in the simulated environment. By transforming the frequency distribution of projected images obtained in the virtual environment (see Figure 4), the cumulative distributions order how often objects in 3-D space produced images of different speeds over different projected distances. These functions provide the basis for predicting the motion observed in psychophysical testing (see Figures 6 and 7). doi:10.1371/journal.pone.0006771.g005 PLoS ONE | www.plosone.org 5 August 2009 | Volume 4 | Issue 8 | e6771