Image Morphing in Deep Feature Spaces: Theory and Applications

Alexander Effland*, Erich Kobler, Thomas Pock, Marko Rajkovic, Martin Rumpf

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper combines image metamorphosis with deep features. 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):61–84, 2001) and Trouvé and Younes (Found Comput Math 5(2):173–198, 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.

Original languageEnglish
Pages (from-to)309-327
Number of pages19
JournalJournal of Mathematical Imaging and Vision
Issue number2
Early online date19 Jul 2020
Publication statusPublished - Feb 2021


  • Convolutional neural networks
  • Image morphing
  • Metamorphosis model
  • Mosco convergence
  • Variational time discretization

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Applied Mathematics
  • Geometry and Topology
  • Computer Vision and Pattern Recognition
  • Statistics and Probability
  • Modelling and Simulation


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