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We consider in some detail the case of image metrics given in terms of the structure tensor and compute some cases of such a tensor for video. Then we comment on the connections with variational formulations of image diffusion comparing the anisotropies that appear. Finally, we include numerical experiments illustrating some of the models. Namely, we compare some examples for still images using the Laplace--Beltrami flow and some variational models. We also consider several examples in video: the mean curvature motion and the extension of the morphological and Galilean invariant scale spaces to the video manifold case, and the Laplace--Beltrami flow. We point out that the number of models that appear is huge, and we have restricted ourselves to such cases for the sake of brevity and illustration.<\/jats:p>","DOI":"10.1137\/130923142","type":"journal-article","created":{"date-parts":[[2014,6,3]],"date-time":"2014-06-03T15:17:52Z","timestamp":1401808672000},"page":"1108-1170","source":"Crossref","is-referenced-by-count":3,"title":["Multiscale Analysis for Images on Riemannian Manifolds"],"prefix":"10.1137","volume":"7","author":[{"given":"Felipe","family":"Calderero","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vicent","family":"Caselles","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2014,6,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/36.992791"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00375127"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/0729052"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s002080000122"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-010-0418-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-008-0160-y"},{"key":"atypb7","unstructured":"C. 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