Study of transparency and coherence of motion in image sequences

As a consequence of the aperture problem, when a moving sine-grating is viewed through an aperture, the perceived motion is ambiguous. However, when we superimpose two of this gratings, the resulting pattern usually moves in a coherent way. But crossed gratings do not always cohere into a single moving pattern. It has been shown that the orientation, speed, contrast and spatial frequency of each plaid are parameters that influence the perception of coherence. We have studied the stimulus conditions under which coherence does and does not occur, using human observers who assigned a probability of coherence to each sequence of images. We then tried to find a computational method whose result would correlate with the results from the human observers. The proposed method consists on computing the optical flow field on the image sequence, using then the direction of the optical flow in each point on the image to build an histogram. This histogram can provide information about the probability of coherence of the image sequences. If the histogram presents two well marked peaks this corresponds to the situation where we perceive transparency of motion. On the other hand when we perceive coherence the corresponding histogram presents only one peak. The width of this peak is related with the probability of coherence, i.e., the narrower the peak the highest the probability of coherence. We show that the proposed method provides results very similar to the ones obtained with the human observers in terms of probability of coherence.