M. Bauer, M. Grasmair, C. Kirisits:
"Optical flow on moving manifolds";
SIAM Journal on Imaging Sciences, 8 (2015), 1; S. 484 - 512.

Kurzfassung englisch:
Optical flow is a powerful tool for the study and analysis of motion in a sequence of images. In this paper we study a Horn--Schunck-type spatio-temporal regularization functional for image sequences that have a non-Euclidean, time varying image domain. To that end we construct a Riemannian metric that describes the deformation and structure of this evolving surface. The resulting functional can be seen as a natural geometric generalization of previous work by Weickert and Schnörr in 2001 and Lefèvre and Baillet in 2008 for static image domains. In this paper we show the existence and well-posedness of the corresponding optical flow problem and derive necessary and sufficient optimality conditions. We demonstrate the functionality of our approach in two experiments using both synthetic and real data.

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