We have considered some degeneracies that are incurred to transparent motion models and shown that to these cases linear solutions can be obtained. Under degenerate conditions, we suggest that models may be selected from the geometric mean of the eigenvalues to the model's regression matrix. The model with the largest geometric mean implies the one whose stability is highest and therefore the preferred interpretation. We have restricted our experiments to plaid patterns. However, the ideas presented in this paper may prove useful to machine algorithms that are faced with the similar problem of deciding when to combine image information into a single or transparent velocity vector(s). These problems are likely to occur under impoverished viewing conditions and especially to cases where motion boundaries occur owing to partially occluded objects.
Adrian F Clark