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This paper describes a new method for estimating optical flow that strikes a balance between the flexibility of local dense computations and the robustness and accuracy of global parameterized flow models. An affine model of image motion is used within local image patches while a spatial smoothness constraint on the affine flow parameters of neighboring patches enforces continuity of the motion. We refer to this as a ``Skin and Bones'' model in which the affine patches can be thought of as rigid ``bones'' connected by a flexible ``skin''. Since local image patches may contain multiple motions we use a layered representation for the affine bones. To regularize this layered motion representation we develop a new framework for "regularization with transparency".