title: Variational optical flow computation in real time.
abstract: This paper investigates the usefulness of bidirectional multigrid methods for variational optical flow computations. Although these numerical schemes are among the fastest methods for solving equation systems, they are rarely applied in the field of computer vision. We demonstrate how to employ those numerical methods for the treatment of variational optical flow formulations and show that the efficiency of this approach even allows for real-time performance on standard PCs. As a representative for variational optic flow methods, we consider the recently introduced combined local-global method. It can be considered as a noise-robust generalization of the Horn and Schunck technique. We present a decoupled, as well as a coupled, version of the classical Gauss-Seidel solver, and we develop several multgrid implementations based on a discretization coarse grid approximation. In contrast, with standard bidirectional multigrid algorithms, we take advantage of intergrid transfer operators that allow for nondyadic grid hierarchies. As a consequence, no restrictions concerning the image size or the number of traversed levels have to be imposed. In the experimental section, we juxtapose the developed multigrid schemes and demonstrate their superior performance when compared to unidirectional multgrid methods and nonhierachical solvers. For the well-known 316 x 252 Yosemite sequence, we succeeded in computing the complete set of dense flow fields in three quarters of a second on a 3.06-GHz Pentium4 PC. This corresponds to a frame rate of 18 flow fields per second which outperforms the widely-used Gauss-Seidel method by almost three orders of magnitude.
authors.affiliation: Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, 66041 Saarbrücken, Germany. bruhn@mia.uni-saarland.de
authors.forename: Andrés
authors.initials: A
authors.lastname: Bruhn
authors.forename: Joachim
authors.initials: J
authors.lastname: Weickert
authors.forename: Christian
authors.initials: C
authors.lastname: Feddern
authors.forename: Timo
authors.initials: T
authors.lastname: Kohlberger
authors.forename: Christoph
authors.initials: C
authors.lastname: Schnörr
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D003199:Computer Systems; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D009068:Movement; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013382:Subtraction Technique; D014741:Video Recording / Q000379:methods*