Abstract
In this paper, we analyse mathematical properties of spatial optical-flow computation algorithm. First by numerical analysis, we derive the convergence property on variational optical-flow computation method used for cardiac motion detection. From the convergence property of the algorithm, we clarify the condition for the scheduling of the regularisation parameters. This condition shows that for the accurate and stable computation with scheduling the regularisation coefficients, we are required to control the sampling interval for numerical computation.
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Zhou, Z., Synolakis, C.E., Leahy, R.M., Song, S.M.: Calculation of 3D internal displacement fields from 3D X-ray computer tomographic images. In: Proceedings of Royal Society: Mathematical and Physical Sciences, vol. 449, pp. 537–554 (1995)
Song, S.M., Leahy, R.M.: Computation of 3-D velocity fields from 3-D cine images of a human heart. IEEE Transactions on Medical Imaging 10, 295–306 (1991)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Springer, New York (2002)
Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–204 (1981)
Nagel, H.-H.: On the estimation of optical flow: Relations between different approaches and some new results. Artificial Intelligence 33, 299–324 (1987)
Barron, J.L., Fleet, D.J., Beauchemin, S.S.: Performance of optical flow techniques. International Journal of Computer Vision 12, 43–77 (1994)
Weickert, J., Schnörr, C.: Variational optic flow computation with a spatio-temporal smoothness constraint. Journal of Mathematical Imaging and Vision 14, 245–255 (2001)
Timoshenko, S.P.: History of Strength of Materials. Dover, Mineola, NY (1983)
Chang, H.-H.: Variational approach to cardiac motion estimation for small animals in tagged magnetic resonance imaging, 2006. IEEE Pacific-Rim Image and Video Technology, 363-372 (2006)
Chang, H.-H., Moura, J.M.F., Yijen, L., Wu, Y.L., Ho, C.: Early detection of rejection in cardiac MRI: A spectral graph approach. In: IEEE International Symposium on Biomedical Imaging, Arlington, pp. 113-116 (2006)
Grenander, U., Miller, M.: Computational anatomy: An emerging discipline. Quarterly of applied mathematics 4, 617–694 (1998)
Sorzano, C.Ó.S., Thévenaz, P., Unser, M.: Elastic registration of biological images using vector-spline regularization. IEEE Tr. Biomedical Engineering 52, 652–663 (2005)
Wahba, G., Wendelberger, J.: Some new mathematical methods for variational objective analysis using cross-validation. Monthly Weather Review 108, 36–57 (1980)
Amodei, L., Benbourhim, M.N.: A vector spline approximation. Journal of Approximation Theory 67, 51–79 (1991)
Benbourhim, M.N., Bouhamidi, A.: Approximation of vectors fields by thin plate splines with tension. Journal of Approximation Theory 136, 198–229 (2005)
Suter, D.: Motion estimation and vector spline. In: Proceedings of CVPR 1994, pp. 939–942 (1994)
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Kameda, Y., Imiya, A. (2007). Classification of Optical Flow by Constraints. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds) Computer Analysis of Images and Patterns. CAIP 2007. Lecture Notes in Computer Science, vol 4673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74272-2_8
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DOI: https://doi.org/10.1007/978-3-540-74272-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74271-5
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