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To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller and Younes (Int J Comput Vis 41(1):61\u201384, 2001) and Trouv\u00e9 and Younes (Found Comput Math 5(2):173\u2013198, 2005). For this model, a variational time discretization of the Riemannian path energy is presented and the existence of discrete geodesic paths minimizing this energy is demonstrated. Furthermore, convergence of discrete geodesic paths to geodesic paths in the time continuous model is investigated. The spatial discretization is based on a finite difference approximation in image space and a stable spline approximation in deformation space; the fully discrete model is optimized using the iPALM algorithm. Numerical experiments indicate that the incorporation of semantic deep features is superior to intensity-based approaches.<\/jats:p>","DOI":"10.1007\/s10851-020-00974-5","type":"journal-article","created":{"date-parts":[[2020,7,19]],"date-time":"2020-07-19T13:03:32Z","timestamp":1595163812000},"page":"309-327","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Image Morphing in Deep Feature Spaces: Theory and Applications"],"prefix":"10.1007","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5936-048X","authenticated-orcid":false,"given":"Alexander","family":"Effland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erich","family":"Kobler","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Pock","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marko","family":"Rajkovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Rumpf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,7,19]]},"reference":[{"key":"974_CR1","doi-asserted-by":"crossref","unstructured":"Arnold, V.: Sur la g\u00e9om\u00e9trie diff\u00e9rentielle des groupes de Lie de dimension infinie et ses applications \u00e0 l\u2019hydrodynamique des fluides parfaits. 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