Two current computational approaches provide interesting insights into these issues. The algorithm of Shizawa and Mase directly computes two velocity vectors for each location in the image, but does not address the problem of perceptual grouping of coherently moving regions of the scene. The algorithm of Bergen et. al. computes two global affine optical flow fields, but does not explicitly determine which portions of the scene correspond to each of these velocity fields. Furthermore, the local measurements used are only capable of determining a single velocity estimate at each point, and will thus have difficulty with pure transparency.

We have extended our previous model for layered image segmentation (ARVO-91) by incorporating the advantages of these two approaches. The previous model performs a decomposition of an image sequence into non-overlapping regions of support (``layers'') corresponding to coherent single motions in the scene. This is accomplished by testing many motion hypotheses, and enforcing mutual inhibition between hypotheses that are supported by the same image data. The new model computes direct estimates of transparent motions, using the local velocity measurements proposed by Shizawa and Mase. Each layer performs grouping based on a model of additively combined image regions, each undergoing global affine motions. The multi-layer competition scheme proceeds as before, producing a set of (possibly overlapping) layers that parsimoniously describes the visual scene. We demonstrate the use of this model on transparently moving imagery.