Functional Liftings of Vectorial Variational Problems with Laplacian Regularization

Thomas Vogt, Jan Lellmann


We propose a functional lifting-based convex relaxation of variational problems with Laplacian-based second-order regularization. The approach rests on ideas from the calibration method as well as from sublabel-accurate continuous multilabeling approaches, and makes these approaches amenable for variational problems with vectorial data and higher-order regularization, as is common in image processing applications. We motivate the approach in the function space setting and prove that, in the special case of absolute Laplacian regularization, it encompasses the discretization-first sublabel-accurate continuous multilabeling approach as a special case. We present a mathematical connection between the lifted and original functional and discuss possible interpretations of minimizers in the lifted function space. Finally, we exemplarily apply the proposed approach to 2D image registration problems.

Original languageEnglish
Title of host publicationScale Space and Variational Methods in Computer Vision: 7th International Conference, SSVM 2019
Number of pages13
PublisherSpringer International Publishing
Publication date05.06.2019
ISBN (Print)978-3-030-22367-0
ISBN (Electronic)978-3-030-22368-7
Publication statusPublished - 05.06.2019
Event7th International Conference on Scale Space and Variational Methods in Computer Vision
- Hofgeismar, Germany
Duration: 30.06.201904.07.2019
Conference number: 227689


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