A Variational Approach to Joint Denoising, Edge Detection and Motion Estimation
The estimation of optical flow fields from image sequences is incorporated in a Mumford–Shah approach for image denoising and edge detection. Possibly noisy image sequences are considered as input and a piecewise smooth image intensity, a piecewise smooth motion field, and a joint discontinuity set are obtained as minimizers of the functional. The method simultaneously detects image edges and motion field discontinuities in a rigorous and robust way. It comes along with a natural multi–scale approximation that is closely related to the phase field approximation for edge detection by Ambrosio and Tortorelli. We present an implementation for 2D image sequences with finite elements in space and time. It leads to three linear systems of equations, which have to be iteratively in the minimization procedure. Numerical results underline the robustness of the presented approach and different applications are shown.
KeywordsOptical Flow Edge Detection Motion Estimation Image Denoising Variational Framework
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- 2.Nagel, H.H., Enkelmann, W.: An investigation of smoothness constraints for the estimation of dispalcement vector fields from image sequences. IEEE Trans. on PAMI 8(5), 565–593 (1986)Google Scholar
- 6.Schnörr, C.: Segmentation of visual motion by minimizing convex non-quadratic functionals. In: 12th ICPR (1994)Google Scholar
- 10.Memin, E., Perez, P.: A multigrid approach for hierarchical motion estimation. In: ICCV, pp. 933–938 (1998)Google Scholar
- 11.Paragios, N., Deriche, R.: Geodesic active contours and level sets for the detection and tracking of moving objects. IEEE Trans. on PAMI 22(3), 266–280 (2000)Google Scholar
- 12.Droske, M., Ring, W.: A Mumford-Shah level-set approach for geometric image registration. SIAM Appl. Math. (to appear, 2005)Google Scholar
- 13.Mumford-shah based registration. Computing and Visualization in Science (submitted, 2005)Google Scholar
- 14.Kapur, T., Yezzi, L., Zöllei, L.: A variational framework for joint segmentation and registration. IEEE CVPR, 44–51 (2001)Google Scholar
- 15.Unal, G., Slabaugch, G., Yezzi, A., Tyan, J.: Joint segmentation and non-rigid registration without shape priors (2004)Google Scholar
- 22.Amiaz, T., Kiryati, N.: Dense discontinuous optical flow via contour-based segmentation. In: Proc. ICIP 2005, vol. III, pp. 1264–1267 (2005)Google Scholar
- 24.Nir, T., Kimmel, R., Bruckstein, A.: Variational approach for joint optic-flow computation and video restoration. Technical report, Dep. of C. S. - Israel Inst. of Tech., Haifa, Israel (2005)Google Scholar
- 29.Group, C.V.R.: Optical flow datasets. Univ. of Otago, New Zealand (2005), http://www.cs.otago.ac.nz/research/vision