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Morphological image sequence processing

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Computing and Visualization in Science

Abstract

We present a morphological multi-scale method for image sequence processing, which results in a truly coupled spatio-temporal anisotropic diffusion. The aim of the method is not to smooth the level-sets of single frames but to denoise the whole sequence while retaining geometric features such as spatial edges and highly accelerated motions. This is obtained by an anisotropic spatio-temporal level-set evolution, where the additional artificial time variable serves as the multi-scale parameter. The diffusion tensor of the evolution depends on the morphology of the sequence, given by spatial curvatures of the level-sets and the curvature of trajectories (=acceleration) in sequence-time. We discuss different regularization techniques and describe an operator splitting technique for solving the problem. Finally we compare the new method with existing multi-scale image sequence processing methodologies.

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References

  1. Alvarez, L., Guichard, F., Lions, P.L., Morel, J.M.: Axioms and fundamental equations of image processing. Arch. Ration. Mech. Anal. 123(3), 199–257 (1993)

    Article  Google Scholar 

  2. Alvarez, L., Weickert, J., Sánchez, J.: A scale-space approach to nonlocal optival flow calculations. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds.), Scale-Space Theories in Computer Vision. Second International Conference, Scale-Space 1999, Corfu, Greece, September 1999, Lecture Notes in Computer Science 1682, pp. 235–246, Springer, 1999

  3. Alvarez, L., Weickert, J., Sánchez, J.: Reliable estimation of dense optimal flow fields with large displacements. Int. J. of Computer Vision 39(1), 41–56 (2000)

    Article  Google Scholar 

  4. Angenent, S.B., Gurtin, M.E.: Multiphase thermomechanics with interfacial structure 2, evolution of an is othermal interface. Arch. Rational Mech. Anal. 108, 323–391 (1989)

    Article  MathSciNet  Google Scholar 

  5. Bänsch, E., Mikula, K.: A coarsening finite element strategy in image selective smoothing. Comput. Visual. Sci. 1, 53–63 (1997)

    Article  Google Scholar 

  6. Bellettini, G., Paolini, M.: Anisotropic motion by mean curvature in the context of finsler geometry. Hokkaido Math. J. 25, 537–566 (1996)

    Article  MathSciNet  Google Scholar 

  7. Catté, F., Lions, P.-L., Morel, J.-M., Coll, T.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)

    Article  MathSciNet  Google Scholar 

  8. Chen, Y.-G., Giga, Y., Goto, S.: Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Diff. Geom. 33(3), 749–786 (1991)

    Google Scholar 

  9. Christensen, G.E., Joshi, S.C., Miller, M.I.: Volumetric transformations of brain anatomy. IEEE Trans. Medical Imaging 16(6), 864–877 (1997)

    Article  Google Scholar 

  10. Christensen, G.E., Rabbitt, R.D., Miller, M.I.: Deformable templates using large deformation kinematics. IEEE Trans. Medical Imaging 5(10), 1435–1447 (1996)

    Google Scholar 

  11. Davatzikos, C.A., Bryan, R.N., Prince, J.L.: Image registration based on boundary mapping. IEEE Trans. Medical Imaging 15(1), 112–115 (1996)

    Article  Google Scholar 

  12. Deriche, R., Kornprobst, P., Aubert, G.: Optical–flow estimation while preserving its discontinuities: A variational approach. In Proc. Second Asian Conf. Computer Vision (ACCV ’95, Singapore, December 5–8, 1995), Vol. 2, pp. 290–295, 1995

  13. Evans, L., Spruck, J.: Motion of level sets by mean curvature I. J. Diff. Geom. 33(3), 635–681 (1991)

    Google Scholar 

  14. Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly Appl. Math. LVI, 617–694 (1998)

  15. Guichard, F.: Axiomatisation des analyses multi-échelles dímages et de films. PhD thesis, University Paris IX Dauphine, 1994

  16. Guichard, F.: A morphological, affine, and galilean invariant scale–space for movies. IEEE Trans. on Image Processing 7(3), 444–456 (1998)

    Article  Google Scholar 

  17. Joshi, S.C., Miller, M.I.: Landmark matching via large deformation diffeomorphisms. IEEE Trans. Medical Imaging 9(8), 1357–1370 (2000)

    Google Scholar 

  18. Kačur, J., Mikula, K.: Solution of nonlinear diffusion appearing in image smoothing and edge detection. Appl. Numer. Math. 17(1), 47–59 (1995)

    MathSciNet  Google Scholar 

  19. Kriva, Z., Mikula, K.: An adaptive finite volume scheme for solving nonlinear diffusion equations in image processing. J. Vis. Comm. and Image Repres. 13, 22–35 (2002)

    Article  Google Scholar 

  20. Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multi–modal volume registration by maximization of mutual information. IEEE Trans. Medical Imaging 16(7), 187–198 (1997)

    Article  Google Scholar 

  21. Mikula, K., Preusser, T., Rumpf, M., Sgallari, F.: On anisotropic geometric diffusion in 3D image processing and image sequence analysis. In Trends in Nonlinear Analysis, pp. 305–319, Springer, 2002

  22. Mikula, K., Ramarosy, N.: Semi–implicit finite volume scheme for solving nonlinear diffusion equations in image processing. Numerische Mathematik, 2001

  23. Nagel, H.H., Enkelmann, W.: An investigation of smoothness constraints for the estimation of displacement vector fields from images sequences. IEEE Trans. Pattern Anal. Mach. Intell. 8, 565–593 (1986)

    Article  Google Scholar 

  24. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. In IEEE Computer Society Workshop on Computer Vision, 1987

  25. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)

    Article  Google Scholar 

  26. Preusser, T., Rumpf, M.: Anisotropic nonlinear diffusion in flow visualization. In Proceedings Visualization 1999, pp. 325–332, 1999

  27. Preusser, T., Rumpf, M.: An adaptive finite element method for large scale image processing. J. Vis. Comm. and Image Repres. 11, 183–195 (2000)

    Article  Google Scholar 

  28. Preusser, T., Rumpf, M.: A level set method for anisotropic diffusion in 3D image processing. SIAM J. Appl. Math. 62(5), 1772–1793 (2001)

    MathSciNet  Google Scholar 

  29. Preusser, T., Rumpf, M.: Extracting motion velocities from 3D image sequences and coupled spatio-temporal smoothing. In Proceedings Visual Data Analysis, pp. 181–192, 2003

  30. Radmoser, E., Scherzer, O., Weickert, J.: Scale-space properties of regularization methods. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds.), Scale-Space Theories in Computer Vision. Second International Conference, Scale-Space ’99, Corfu, Greece, September 1999, Lecture Notes in Computer Science 1682, pp. 211–220, Springer, 1999

  31. Sapiro, G.: Vector (self) snakes: A geometric framework for color, texture, and multiscale image segmentation. In Proc. IEEE International Conference on Image Processing, Lausanne, September 1996

  32. Sarti, A., Mikula, K., Sgallari, F.: Nonlinear multiscale analysis of 3D echocardiography sequences. IEEE Trans. Medical Imaging 18(6), 453–466 (1999)

    Article  Google Scholar 

  33. Sethian, J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999

  34. Taylor, J.E., Cahn, J.W., Handwerker, C.A.: Geometric models of crystal growth. Acta metall. mater. 40, 1443–1474 (1992)

    Article  Google Scholar 

  35. Thirion, J.P.: Image matching as a diffusion process: An analogy with maxwell’s demon. Medical Imag. Analysis 2, pp. 243–260, 1998

  36. Thomée, V.: Galerkin – Finite Element Methods for Parabolic Problems. Springer, 1984

  37. Weickert, J.: Anisotropic diffusion filters for image processing based quality control. In: Fasano, A., Primicerio, M. (eds.), Proc. Seventh European Conf. on Mathematics in Industry, pp. 355–362, Teubner, 1994

  38. Weickert, J.: Anisotropic diffusion in image processing. Teubner, 1998

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Authors and Affiliations

  1. Department of Mathematics, Slovak University of Technology, Bratislava, Slovakia

    Karol Mikula

  2. Fakulty 4, Institute for Mathematics, Duisburg University, 47057, Duisburg, Germany

    Tobias Preusser & Martin Rumpf

Authors
  1. Karol Mikula
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  2. Tobias Preusser
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  3. Martin Rumpf
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Correspondence to Karol Mikula.

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J. Kačur

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Mikula, K., Preusser, T. & Rumpf, M. Morphological image sequence processing. Comput. Visual Sci. 6, 197–209 (2004). https://doi.org/10.1007/s00791-004-0129-0

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