On the estimation of optical flow: relations between different approaches and some new results
Artificial Intelligence
Performance of optical flow techniques
International Journal of Computer Vision
Two-dimensional imaging
Uncalibrated obstacle detection using normal flow
Machine Vision and Applications
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Applied numerical linear algebra
Applied numerical linear algebra
Computational Cardiology: Modeling Of Anatomy, Electrophysiology, And Mechanics (LECTURE NOTES IN COMPUTER SCIENCE)
On convergence of the Horn and Schunck optical-flow estimation method
IEEE Transactions on Image Processing
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In this paper, we prove the convergence property of the Horn-Schunck optical-flow computation scheme. Horn and Schunck derived a Jacobi-method-based scheme for the computation of optical-flow vectors of each point of an image from a pair of successive digitised images. The basic idea of the Horn-Schunck scheme is to separate the numerical operation into two steps: the computation of the average flow vector in the neighborhood of each point and the refinement of the optical flow vector by the residual of the average flow vectors in the neighborhood. Mitiche and Mansouri proved the convergence property of the Gauss-Seidel- and Jacobi-method-based schemes for the Horn-Schunck-type minimization using algebraic properties of the matrix expression of the scheme and some mathematical assumptions on the system matrix of the problem. In this paper, we derive an alternative proof for the original Horn-Schunck scheme. To prove the convergence property, we develop a method of expressing shift-invariant local operations for digital planar images in the matrix forms. These matrix expressions introduce the norm of the neighborhood operations. The norms of the neighborhood operations allow us to prove the convergence properties of iterative image processing procedures.