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- Title
A proper generalized decomposition approach for optical flow estimation.
- Authors
El Hamidi, Abdallah; Saleh, Marwan; Papadakis, Nicolas; Senneville, B. Denis
- Abstract
This paper introduces the use of the proper generalized decomposition (PGD) method for the optical flow (OF) problem in a classical framework of Sobolev spaces, ie, optical flow methods including a robust energy for the data fidelity term together with a quadratic penalizer for the regularization term. A mathematical study of PGD methods is first presented for general regularization problems in the framework of (Hilbert) Sobolev spaces, and their convergence is then illustrated on OF computation. The convergence study is divided in two parts: (a) the weak convergence based on the Brézis‐Lieb decomposition and (b) the strong convergence based on a growth result on the sequence of descent directions. A practical PGD‐based OF implementation is then proposed and evaluated on freely available OF data sets. The proposed PGD‐based OF approach outperforms the corresponding non‐PGD implementation in terms of both accuracy and computation time for images containing a weak level of information, namely, low image resolution and/or low signal‐to‐noise ratio (SNR).
- Subjects
OPTICAL flow; SOBOLEV spaces; SIGNAL-to-noise ratio; MATHEMATICAL regularization
- Publication
Mathematical Methods in the Applied Sciences, 2020, Vol 43, Issue 8, p5339
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.6275