Abstract
Estimation of optical flow and physically motivated brightness changes can be formulated as parameter estimation in linear models. Accuracy of this estimation heavily depends on the filter families used to implement the models. In this paper we focus on models whose terms are all data dependent and therefore are best estimated via total-least-squares (TLS) or similar estimators. Using three different linear models we derive model dependent optimality criteria based on transfer functions of filter families with given fixed size. Using a simple optimization procedure, we demonstrate typical properties of optimal filter sets for optical flow, simultaneous estimation of optical flow and diffusion, as well as optical flow and exponential decay. Exemplarily we show their performance and state some useful choices.
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References
Badino, H.: A robust approach for ego-motion estimation using a mobile stereo platform. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds.) IWCM 2004. LNCS, vol. 3417, pp. 198–208. Springer, Heidelberg (2007)
Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12(1), 43–77 (1994)
Bruhn, A., Weickert, J., Schnörr, C.: Combining the advantages of local and global optic flow methods. In: Van Gool, L. (ed.) Pattern Recognition. LNCS, vol. 2449, pp. 454–462. Springer, Heidelberg (2002)
Elad, M., Teo, P., Hel-Or, Y.: Optimal filters for gradient-based motion estimation. In: ICCV’99 (1999)
Farid, H., Simoncelli, E.P.: Optimally rotation-equivariant directional derivative kernels. In: 7th Int’l Conf Computer Analysis of Images and Patterns, Kiel (1997)
Garbe, C.: Measuring Heat Exchange Processes at the Air-Water Interface from Thermographic Image Sequence Analysis. PhD thesis, Univ. Heidelberg (2001)
Haußecker, H., Fleet, D.J.: Computing optical flow with physical models of brightness variation. PAMI 23(6), 661–673 (2001)
Haußecker, H., Spies, H.: Motion. In: Jähne, B., Haußecker, H., Geißler, P. (eds.) Handbook of Computer Vision and Applications, Academic Press, London (1999)
Jähne, B.: Spatio-Temporal Image Processing. LNCS, vol. 751. Springer, Heidelberg (1993)
Jähne, B.: Digital Image Processing, 4th edn. Springer, Heidelberg (1997)
Jähne, B., Scharr, H., Körkel, S.: Principles of filter design. In: Handbook of Computer Vision and Applications, Academic Press, London (1999)
Kamgar-Parsi, B., Kamgar-Parsi, B., Rosenfeld, A.: Optimally isotropic laplacian operator. IEEE Trans. Img. Proc. 8(10) (1999)
Knutsson, H., Andersson, M.: Optimization of sequential filters. Technical Report LiTH-ISY-R-1797, CV Lab., Univ. Linköping (1995)
Knutsson, H., Andersson, M., Wiklund, J.: Multiple space filter design. In: Proc. SSAB Symposium on Image Analysis, Göteborg, Schweden (1998)
Knutsson, H., Andersson, M., Wiklund, J.: Advanced filter design. Proc. SCIA (1999)
Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs (1989)
Proakis, J.G., Manolakis, D.G.: Digital Signal Processing, Principles, Algorithms, and Applications. Macmillan, Basingstoke (1992)
Scharr, H.: Optimal Operators in Digital Image Processing. U. Heidelberg (2000)
Scharr, H.: Optimal filter families for extended optical flow. Report, Computational Nano-Vision Group, Santa Clara CA 95054, USA (2002)
Scharr, H., Körkel, S., Jähne, B.: Numerische Isotropieoptimierung von FIR-Filtern mittels Querglättung. In: DAGM’97, pp. 367–374 (1997)
Schnörr, C., Weickert, J.: Variational image motion computation: Theoretical framework, problems and perspectives. In: DAGM’2000, pp. 476–487 (2000)
Simoncelli, E.: Design of multidimensional derivative kernels. In: First IEEE Int’l Conf. on Image Processing, vol. I, Austin, Texas, pp. 790–793 (Nov. 1994)
van den Hengel, A., Chojnacki, W., Brooks, M.J.: Determining the Translational Speed of a Camera from Time-Varying Optical Flow. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds.) IWCM 2004. LNCS, vol. 3417, pp. 190–197. Springer, Heidelberg (2007)
Woelk, F., Koch, R.: Robust monocular detection of independent motion by a moving observer. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds.) IWCM 2004. LNCS, vol. 3417, pp. 209–222. Springer, Heidelberg (2007)
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Scharr, H. (2007). Optimal Filters for Extended Optical Flow. In: Jähne, B., Mester, R., Barth, E., Scharr, H. (eds) Complex Motion. IWCM 2004. Lecture Notes in Computer Science, vol 3417. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69866-1_2
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DOI: https://doi.org/10.1007/978-3-540-69866-1_2
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