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3. ˜ w(k) ˆ ˆ d ˜ − dh (k) ˜ (k) ˆ |d| |dˆh | → min (37) As spatial smoothing in a Laplacian does not occur in 2d but in 3d and higher dimensions, we not only state 2d filters (Tab. 4) but also 3d filter families. The 1d filters of the 5 × 5 × 5 family are shown in Fig. 5 in order to visualize symmetries. For the 2d filters we observe that spatial and temporal derivatives and smoothers no longer use the same coefficients, but the larger the filters get the less severe the differences are. Similar to the approach in [2, 8] we also test the performance of the 3d filter sets on sinusoidal plaid test sequences.
0235] Optimal Filters for Extended Optical Flow 29 (Fig. 2), leading to severely improved accuracy in optical flow estimation (Tab. 1 and Tab. 2). Thus optimized filter families are a key ingredient for highly accurate motion and brightness estimations by extended optical flow. References 1. H. Badino. A robust approach for ego-motion estimation using a mobile stereo platform. In this volume, 2004. 2. L. J. S. Beauchemin. Performance of optical flow techniques. International Journal of Computer Vision, 12(1):43–77, 1994.
IEEE Trans. Img. , 8(10), Oct. 1999. 13. H. Knutsson and M. Andersson. Optimization of sequential filters. , Univ. Linköping, 1995. 14. H. Knutsson, M. Andersson, and J. Wiklund. Multiple space filter design. In Proc. SSAB Symposium on Image Analysis, Göteborg, Schweden, 1998. 15. H. Knutsson, M. Andersson, and J. Wiklund. Advanced filter design. In Proc. SCIA, 1999. 16. A. V. Oppenheim and R. W. Schafer. Discrete-Time Signal Processing. Prentice Hall, 1989. 17. J. G. Proakis and D. G. Manolakis.