Variational optic flow computation with a spatio-temporal smoothness constraint

Weickert, Joachim ; Schnörr, Christoph

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URN: urn:nbn:de:bsz:180-madoc-18436
Document Type: Working paper
Year of publication: 2000
The title of a journal, publication series: Technical Reports
Volume: 00-015
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Subject: 004 Computer science, internet
Classification: MSC: 68T45 68U99 ,
Subject headings (SWD): Bildfolge , Variationsrechnung , Partielle Differentialgleichung , Finite-Differenzen-Methode
Keywords (English): optic flow , differential techniques , variational methods , spatio-temporal regularization , partial differential equations , finite differences
Abstract: Nonquadratic variational regularization is a well-known and powerful approach for the discontinuity-preserving computation of optic flow. In the present paper, we consider an extension of flow-driven spatial smoothness terms to spatio-temporal regularizers. Our method leads to a rotationally invariant and time symmetrie convex optimization problem. It has a unique minimum that can be found in a stable way by standard algorithms such as gradient descent. Since the convexity guarantees global convergence, the result does not depend on the flow initialization. An iterative algorithm is presented that is not difficult to implement. Qualitative and quantitative results for synthetic and real-world scenes show that our spatio-temporal approach (i) improves optic flow fields significantly, (ii) smoothes out background noise efficiently, and (iii) preserves true motion boundaries. The computational costs are only 50 % higher than for a pure spatial approach applied to all subsequent image pairs of the sequence.

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