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Accounting for spatial image transformations is a requirement for multimedia problems such as video classification and retrieval, face/object recognition or the creation of image mosaics from video sequences. We analyze a transformation invariant metric recently proposed in the machine learning literature to measure the distance between image manifolds - the tangent distance (TD) - and show that it is closely related to alignment techniques from the motion analysis literature. Exposing these relationships results in benefits for the two domains. On one hand, it allows leveraging on the knowledge acquired in the alignment literature to build better classifiers. On the other, it provides a new interpretation of alignment techniques as one component of a decomposition that has interesting properties for the classification of video. In particular, we embed the TD into a multiresolution framework that makes it significantly less prone to local minima. The new metric - multiresolution tangent distance (MRTD) - can be easily combined with robust estimation procedures, and exhibits significantly higher invariance to image transformations than the TD and the Euclidean distance (ED). For classification, this translates into significant improvements in face recognition accuracy. For video characterization, it leads to a decomposition of image dissimilarity into "differences due to camera motion" plus "differences due to scene activity" that is useful for classification. Experimental results on a movie database indicate that the distance could be used as a basis for the extraction of semantic primitives such as action and romance.