4 Methods

Our experiments are based upon moving plaid patterns, like the ones shown in figure 1. To these images we manipulated relative grating speed, contrast and orientation. We calculated each model's certainty measurement following the example given by equation ( 21 ) for a phase (1-d), coherent, and transparent velocity. The pre-processing filters were Difference of Gaussian (DoG) smoothing kernels and their first and second order derivatives. Two different DoG filters were used with peak tuning frequencies that were two octaves apart. The magnitude of the Lagrange multiplier used to stabilize the transparent model (equations (7) and (8)) was unity. Lagrange multipliers were omitted for the phase (1-d) and coherent models.

   
Figure 3: Motion certainties for coherence, additive transparency and phase (1-d) velocity. We varied: (A) : Image speed. The two sinusoidal gratings were equal in contrast and orthogonal in spatial orientation. (B) : Relative grating contrast. The coherent velocity was fixed at 0.707 pixels per frame. The two gratings were orthogonal in spatial orientation. (C) : Relative orientation. The magnitude of spatial frequency and temporal frequency was fixed. The grating's speed was also fixed at 0.3 pixels per frame. For these experiments each grating's spatial frequency differed by 2 octaves.