On convergence of the Horn and Schunck optical-flow estimation method

Authors:
A. Mitiche;A. -R. Mansouri
Affiliations:
Inst. Nat. de la Recherche Scientifique, Montreal, Que., Canada;-
Venue:
IEEE Transactions on Image Processing
Year:
2004

Citing 0
Cited 4

Sub-Pixel Estimation Error Cancellation on Area-Based Matching

International Journal of Computer Vision
Optical Flow 3D Segmentation and Interpretation: A Variational Method with Active Curve Evolution and Level Sets

IEEE Transactions on Pattern Analysis and Machine Intelligence
A convergence proof for the Horn-Schunck optical-flow computation scheme using neighborhood decomposition

IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
Dense point trajectories by GPU-accelerated large displacement optical flow

ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I

Quantified Score

Hi-index	0.01

Visualization

Abstract

The purpose of this study is to prove convergence results for the Horn and Schunck optical-flow estimation method. Horn and Schunck stated optical-flow estimation as the minimization of a functional. When discretized, the corresponding Euler-Lagrange equations form a linear system of equations. We write explicitly this system and order the equations in such a way that its matrix is symmetric positive definite. This property implies the convergence Gauss-Seidel iterative resolution method, but does not afford a conclusion on the convergence of the Jacobi method. However, we prove directly that this method also converges. We also show that the matrix of the linear system is block tridiagonal. The blockwise iterations corresponding to this block tridiagonal structure converge for both the Jacobi and the Gauss-Seidel methods, and the Gauss-Seidel method is faster than the (sequential) Jacobi method.