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Most approaches for motion analysis and interpretation rely on restrictive parametric models and involve iterative methods which depend heavily on initial conditions and are subject to instability. Further difficulties are encountered in image regions where motion is not smooth-typically around motion boundaries. This work addresses the problem of visual motion analysis and interpretation by formulating it as an inference of motion layers from a noisy and possibly sparse point set in a 4D space. The core of the method is based on a layered 4D representation of data and a voting scheme for affinity propagation. The inherent problem caused by the ambiguity of 2D to 3D interpretation is usually handled by adding additional constraints, such as rigidity. However, enforcing such a global constraint has been problematic in the combined presence of noise and multiple independent motions. By decoupling the processes of matching, outlier rejection, segmentation, and interpretation, we extract accurate motion layers based on the smoothness of image motion, and then locally enforce rigidity for each layer in order to infer its 3D structure and motion. The proposed framework is noniterative and consistently handles both smooth moving regions and motion discontinuities without using any prior knowledge of the motion model.