Computing Optical Flow via Variational Techniques
- 1 January 1999
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Applied Mathematics
- Vol. 60 (1) , 156-182
- https://doi.org/10.1137/s0036139998340170
Abstract
Defined as the apparent motion in a sequence of images, the optical flow is very important in the computer vision community where its accurate estimation is necessary for many applications. It is one of the most studied problems in computer vision. In spite of this, not much theoretical analysis has been done. In this article, we first present a review of existing variational methods. Then, we will propose an extended model that will be rigorously justified on the space of functions of bounded variations. Finally, we present an algorithm whose convergence will be carefully demonstrated. Some results showing the capabilities of this method conclude the paper.Keywords
This publication has 28 references indexed in Scilit:
- A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$SIAM Journal on Mathematical Analysis, 1999
- A Variational Method in Image RecoverySIAM Journal on Numerical Analysis, 1997
- A fast scalable algorithm for discontinuous optical flow estimationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1996
- Analysis of bounded variation penalty methods for ill-posed problemsInverse Problems, 1994
- Variational approach to optical flow estimation managing discontinuitiesImage and Vision Computing, 1993
- Multimodal estimation of discontinuous optical flow using Markov random fieldsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1993
- Affine structure from motionJournal of the Optical Society of America A, 1991
- Differential techniques for optical flowJournal of the Optical Society of America A, 1990
- On the estimation of optical flow: Relations between different approaches and some new resultsArtificial Intelligence, 1987
- Some results on regularity for solutions of non-linear elliptic systems and quasi-regular functionsDuke Mathematical Journal, 1975