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Estimation of local orientations in multivariate signals is an important problem in image processing and computer vision. This general problem formulation also covers optical flow estimation, which can be regarded as orientation estimation in space-time-volumes. Modelling a signal using only a single orientation, however, is often too restrictive, since occlusions and transparencies occur frequently, thus necessitating the modelling and analysis of multiple orientations. We, therefore, develop a unifying mathematical model for multiple orientations: Beyond describing an arbitrary number of orientations in scalar- and vector-valued image data such as color image sequences, it allows the unified treatment of additively and occludingly superimposed oriented structures as well as of combinations of these. Based on this model, we describe estimation schemes for an arbitrary number of additively or occludingly superimposed orientations in images. We confirm the performance of our framework on both synthetic and real image data.