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References

  1. L. Alvarez, P.L. Lions, and J.M. Morel. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal., 29:845–866, 1992.

    Article  MathSciNet  Google Scholar 

  2. E. Angelini, A. Laine, S. Takuma, and S. Homma. Directional representations of 4D echocardiography for temporal quantification of LV volume. In Proc. MICCAI’99, pages 430–440, Cambridge, 1999.

    Google Scholar 

  3. M. Bertram. Fairing scalar fields by variational modeling of contours. In Proc. IEEE Visualiszation 2003, pages 387–392, Seattle, Washington, 2003.

    Google Scholar 

  4. U. Clarenz, U. Diewald, and M. Rumpf. Anisotropic geometric diffusion in surface processing. In Proc. IEEE Visualization 2000, pages 397–405, Salt Lake City, Utah, 2000.

    Google Scholar 

  5. M. Desbrun, M. Meyer, P. Schröder, and A. Barr. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proc. SIGGRAPH 1999, pages 317–324, 1999.

    Google Scholar 

  6. M. Desbrun, M. Meyer, P. Schröder, and A. Barr. Anisotropic feature-preserving denoising of height fields and bivariate data. In Proc. Graphics Interface 2000, pp. 145–152, 2000.

    Google Scholar 

  7. Josiah W. Gibbs. Fourier series. Nature, 59, 1899.

    Google Scholar 

  8. I. Guskov and Z. Wood. Topological noise removal. In Proc. Graphics Interface 2001, pp. 19–26, 2001.

    Google Scholar 

  9. M. Hilton, T. Ogden, D. Hattery, G. F. Eden, and B. Jawerth. Wavelet denoising of functional MRI data. In A. Aldroubi and M. Unser, editors,Wavelets in Biology and Medicine, pp. 93–112. CRC Press, 1996.

    Google Scholar 

  10. D. T. Kuan, A. A. Sawchuk, T. C. Strand, and P. Chavel. Adaptive noise smoothing filter for images with signal-dependent noise. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-7:165–177, 1985.

    Google Scholar 

  11. J. S. Lee. Digital image enhancement and noise filtering by use of local statistics. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-2:165–168, 1980.

    Google Scholar 

  12. Steve Marschner and Richard Lobb. An evaluation of reconstruction filters for volume rendering. In R. D. Bergeron and Arie Kaufman, editors, Proc. IEEE Visualization’ 94, pp. 100–107. IEEE Computer Society Press, October 1994.

    Google Scholar 

  13. Torsten Möller, Raghu Machiraju, Klaus Mueller, and Roni Yagel. A comparison of normal estimation schemes. In Proc. IEEE Visualization’ 97, pp. 19–26, Phoenix, AZ, November 1997.

    Google Scholar 

  14. Torsten Möller, Raghu Machiraju, Klaus Mueller, and Roni Yagel. Evaluation and design of filters using a Taylor series expansion. IEEE Transactions on Visualization and Computer Graphics, 3(2):184–199, April–June 1997. ISSN 1077-2626.

    Google Scholar 

  15. Torsten Möller, Klaus Mueller, Yair Kurzion, Raghu Machiraju, and Roni Yagel. Design of accurate and smooth filters for function and derivative reconstruction. In Proc. IEEE Symposium on Volume Visualization, pp. 143–151, October 1998.

    Google Scholar 

  16. H. P. Moreton and C. H. Sequin. Functional optimization for fair surface design. In Proc. SIGGRAPH’ 92, pp. 167–176, 1992.

    Google Scholar 

  17. L. Neumann, B. Csébfalvi, A. König, and E. Gröller. Gradient estimation in volume data using 4D linear regression. Computer Graphics Forum, 19(3):C351–C357, 2000.

    Article  Google Scholar 

  18. Y. Ohtake, A. G. Belyaev, and I. A. Bogaevski. Polyhedral surface smoothing with simultaneous mesh regularization. In Proc. Geometric Modeling and Processing 2000, pp. 229–237, Hong Kong, 2000.

    Google Scholar 

  19. J. Peng, V. Strela, and D. Zorin. A simple algorithm for surface denoising. In Proc. IEEE Visualiszation 2001, pp. 107–112, San Diego, California, 2001.

    Google Scholar 

  20. Pietro Perona and Jitendra Malik. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639, July 1990.

    Article  Google Scholar 

  21. M. P. Persoon, I. W. O. Serlie, F. H. Post, and F. M. Vos. Visualization of noisy and biased volume data using first and second order derivative techniques. In Proc. IEEE Visualiszation 2003, pp. 379–385, Seattle, Washington, 2003.

    Google Scholar 

  22. David Rodgman and Min Chen. Refraction in discrete raytracing. In Klaus Mueller and Arie Kaufman, editors, Proc. Volume Graphics 2001, New York, 2001. Springer. ISBN 3-211-83737-X.

    Google Scholar 

  23. C. Rössl, F. Zeilfelder, G. Nürnberger, and H.-P. Seidel. Visualization of volume data with quadratic super splines. In Proc. IEEE Visualiszation 2003, pp. 393–400, Seattle, Washington, 2003.

    Google Scholar 

  24. G. Sapiro. Geometric Partial Differential Equations and Image Analysis. Cambridge University Press, 2001.

    Google Scholar 

  25. T. Tasdizen, R. Whitaker, P. Burchard, and S. Osher. Geometric surface smoothing via anisotropic diffusion of normals. In Proc. IEEE Visualiszation 2002, pp. 125–132, Boston, Massachusetts, 2002.

    Google Scholar 

  26. Thomas Theußl. Sampling and Reconstruction in Volume Visualization. PhD thesis, Vienna University of Technology, 2000.

    Google Scholar 

  27. Joachim Weickert. A review of nonlinear diffusion filtering. In Scale-Space Theories in Computer Vision, pp. 3–28, 1997.

    Google Scholar 

  28. Joachim Weickert. Anisotropic Diffusion in Image Processing. ECMI Series, Teubner, Stuttgart, 1998.

    Google Scholar 

  29. W. Welch and A. Witkin. Free-form shape design using triangulated surfaces. In Proc. SIGGRAPH’ 94, pp. 247–256, 1994.

    Google Scholar 

  30. R. T. Whitaker. Volumetric deformable models: active blobs. In R. A. Robb, editor, Proc. Visualization in Biomedical Computing, SPIE, 1994.

    Google Scholar 

  31. Andrew S. Winter and Min Chen. vlib: A volume graphics API. In Proc. Volume Graphics 2001, pp. 133–147, New York, 2001. Springer.

    Google Scholar 

  32. Roni Yagel, Daniel Cohen, and Arie Kaufman. Normal estimation in 3D discrete space. The Visual Computer, pp. 278–291, 1992.

    Google Scholar 

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Rodgman, D., Chen, M. (2006). Volume Denoising for Visualizing Refraction. In: Bonneau, GP., Ertl, T., Nielson, G.M. (eds) Scientific Visualization: The Visual Extraction of Knowledge from Data. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-30790-7_11

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