Computing the Local Continuity Order of Optical Flow Using Fractional Variational Method
We introduce variational optical flow computation involving priors with fractional order differentiations. Fractional order differentiations are typical tools in signal processing and image analysis. The zero-crossing of a fractional order Laplacian yields better performance for edge detection than the zero-crossing of the usual Laplacian. The order of the differentiation of the prior controls the continuity class of the solution. Therefore, using the square norm of the fractional order differentiation of optical flow field as the prior, we develop a method to estimate the local continuity order of the optical flow field at each point. The method detects the optimal continuity order of optical flow and corresponding optical flow vector at each point. Numerical results show that the Horn-Schunck type prior involving the n + ε order differentiation for 0 < ε< 1 and an integer n is suitable for accurate optical flow computation.
KeywordsOptical Flow Fractional Order Fractional Derivative Total Variational Regularisation Continuity Order
Unable to display preview. Download preview PDF.
- 7.Zhang, J., Wei, Z.-H.: Fractional variational model and algorithm for image denoising. In: Proceedings of 4th International Conference on Natural Computation, vol. 5, pp. 524–528 (2008)Google Scholar
- 10.Oldham, K.B., Spanier, J.: The Fractional Calculus: Theory And Applications of Differentiation And Integration to Arbitrary Order (Dover Books on Mathematics). Dover (2004)Google Scholar
- 19.Debbi. L., Explicit solutions of some fractional partial differential equations via stable subordinators. J. of Applied Mathematics and Stochastic Analysis, Article ID 93502, 1–18 (2006)Google Scholar