The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.01 - Jan. (2014 vol.20)
pp: 140-154
Tiago Etiene , Sch. of Comput., Univ. of Utah, Salt Lake City, UT, USA
Daniel Jonsson , Campus Norrkoping, Linkopings Univ., Norrkoping, Sweden
Timo Ropinski , Campus Norrkoping, Linkopings Univ., Norrkoping, Sweden
Carlos Scheidegger , AT&T Labs.-Res., Florham Park, NJ, USA
Joao L. D. Comba , Univ. Fed. do Rio Grande do Sul, Porto Alegre, Brazil
Luis Gustavo Nonato , Depto Mat. Aplic. e Estatistica-ICMC/USP, Univ. de Sao Paulo, Sao Carlos, Brazil
Robert M. Kirby , Sch. of Comput., Univ. of Utah, Salt Lake City, UT, USA
Anders Ynnerman , Campus Norrkoping, Linkopings Univ., Norrkoping, Sweden
Claudio T. Silva , Center for Urban Sci. & Progress, New York Univ., Brooklyn, NY, USA
ABSTRACT
We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages.
INDEX TERMS
Rendering (computer graphics), Volume measurements, Error analysis, Testing,testing, Discretization errors, volume rendering, verifiable visualization, verification
CITATION
Tiago Etiene, Daniel Jonsson, Timo Ropinski, Carlos Scheidegger, Joao L. D. Comba, Luis Gustavo Nonato, Robert M. Kirby, Anders Ynnerman, Claudio T. Silva, "Verifying Volume Rendering Using Discretization Error Analysis", IEEE Transactions on Visualization & Computer Graphics, vol.20, no. 1, pp. 140-154, Jan. 2014, doi:10.1109/TVCG.2013.90
REFERENCES
[1] I. Babuska and J. Oden, "Verification and Validation in Computational Engineering and Science: Basic Concepts," Computer Methods in Applied Mechanics and Eng., vol. 193, no. 36-38 pp. 4057-4066, 2004.
[2] S. Bergner, T. Möller, D. Weiskopf, and D.J. Muraki, "A Spectral Analysis of Function Composition and Its Implications for Sampling in Direct Volume Visualization," IEEE Trans. Visualization and Computer Graphics, vol. 12, no. 5, pp. 1353-1360, Sept./Oct. 2006.
[3] E. Clarke, "The Birth of Model Checking," 25 Years of Model Checking, O. Grumberg and H. Veith, eds., pp. 1-26, Springer-Verlag, 2008.
[4] J. Duncan and N. Ayache, "Medical Image Analysis: Progress over Two Decades and the Challenges Ahead," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 1, pp. 85-106, Jan. 2000.
[5] J.-F. El Hajjar, S. Marchesin, J.-M. Dischler, and C. Mongenet, "Second Order Pre-Integrated Volume Rendering," Proc. IEEE Pacific Visualization Symp. (VIS '08), pp. 9-16, 2008.
[6] K. Engel, M. Hadwiger, J.M. Kniss, C. Rezk-Salama, and D. Weiskopf, Real-Time Volume Graphics. A.K. Peters, 2006.
[7] K. Engel, M. Kraus, and T. Ertl, "High-Quality Pre-Integrated Volume Rendering Using Hardware-Accelerated Pixel Shading," Proc. Graphics Hardware Workshop, pp. 9-16, 2001.
[8] T. Etiene, L.G. Nonato, C. Scheidegger, J. Tierny, T.J. Peters, V. Pascucci, R.M. Kirby, and C.T. Silva, "Topology Verification for Isosurface Extraction," IEEE Trans. Visualization and Computer Graphics, vol. 18, no. 6, pp. 952-965, June 2012.
[9] T. Etiene, C. Scheidegger, L.G. Nonato, R.M. Kirby, and C. Silva, "Verifiable Visualization for Isosurface Extraction," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 6, pp. 1227-1234, Nov./Dec. 2009.
[10] R.W. Floyd, "Assigning Meaning to Programs," Proc. Symp. Applied Math., vol. 19, pp. 19-32, 1967.
[11] A. Globus and S. Uselton, "Evaluation of Visualization Software," SIGGRAPH Computer Graphics, vol. 29, no. 2, pp. 41-44, 1995.
[12] P. Godefroid, A. Kiezun, and M.Y. Levin, "Grammar-Based Whitebox Fuzzing," SIGPLAN Notices, vol. 43, no. 6, pp. 206-215, 2008.
[13] W.E. Howden, "Applicability of Software Validation Techniques to Scientific Programs," ACM Trans. Programming Languages and Systems, vol. 2, pp. 307-320, July 1980.
[14] IEEE, IEEE Standard Glossary of Software Engineering Terminology, IEEE Std 610.12-1990, p. 1, 1990.
[15] C. Johnson, "Top Scientific Visualization Research Problems," IEEE Computer Graphics and Applications, vol. 24, no. 4, pp. 13-17, July 2004.
[16] C.R. Johnson and A.R. Sanderson, "A Next Step: Visualizing Errors and Uncertainty," IEEE Computer Graphics and Applications, vol. 23, no. 5, pp. 6-10, Sept. 2003.
[17] G. Kindlmann http:/teem.sourceforge.net,, Apr. 2013.
[18] R. Kirby and C. Silva, "The Need for Verifiable Visualization," IEEE Computer Graphics and Applications, vol. 28, no. 5, pp. 78-83, Sept. 2008.
[19] P. Knupp and K. Salari, Verification of Computer Codes in Computational Science and Engineering. Chapman and Hall/CRC, 2002.
[20] J. Kronander, J. Unger, T. Möller, and A. Ynnerman, "Estimation and Modeling of Actual Numerical Errors in Volume Rendering," Computer Graphics Forum, vol. 29, no. 3, pp. 893-902, 2010.
[21] J. Krüger and R. Westermann, "Acceleration Techniques for GPU-Based Volume Rendering," Proc. IEEE Visualization '03, pp. 38-43, 2003.
[22] H. Kye, B. Shin, and Y. Shin, "Interactive Classification for Pre-Integrated Volume Rendering of High-Precision Volume Data," Graphical Models, vol. 70, no. 6, pp. 125-132, 2008.
[23] J. Lee and T. Newman, "New Method for Opacity Correction in Oversampled Volume Ray Casting," J. WSCG, vol. 15, pp. 1-8, 2007.
[24] P. Ljung, C. Lundström, and A. Ynnerman, "Multiresolution Interblock Interpolation in Direct Volume Rendering," Proc. Eurographics Conf. Visualization (EuroVis), pp. 259-266, 2006.
[25] N. Max, "Optical Models for Direct Volume Rendering," IEEE Trans. Visualization and Computer Graphics, vol. 1, no. 2, pp. 99-108, June 1995.
[26] M. Meissner, J. Huang, D. Bartz, K. Mueller, and R. Crawfis, "A Practical Evaluation of Popular Volume Rendering Algorithms," Proc. IEEE Symp. Vol. Visualization, pp. 81-90, Oct. 2000.
[27] J. Meyer-Spradow, T. Ropinski, J. Mensmann, and K.H. Hinrichs, "Voreen: A Rapid-Prototyping Environment for Ray-Casting-Based Volume Visualizations," IEEE Computer Graphics and Applications, vol. 29, no. 6, pp. 6-13, Nov./Dec. 2009.
[28] T. Möller, R. Machiraju, K. Mueller, and R. Yagel, "Classification and Local Error Estimation of Interpolation and Derivative Filters for Volume Rendering," Proc. IEEE Symp. Vol. Visualization, pp. 71-78, Oct. 1996.
[29] T. Möller, R. Machiraju, K. Mueller, and R. Yagel, "Evaluation and Design of Filters Using a Taylor Series Expansion," IEEE Trans. Visualization and Computer Graphics, vol. 3, no. 2, pp. 184-199, Apr.-June 1997.
[30] K. Moreland and E. Angel, "A Fast High Accuracy Volume Renderer for Unstructured Data," Proc. IEEE Symp. Vol. Visualization and Graphics, pp. 9-16, 2004.
[31] K. Novins and J. Arvo, "Controlled Precision Volume Integration," Proc. ACM Workshop Vol. Visualization, pp. 83-89, 1992.
[32] A. Pommert and K.H. Höhne, "Evaluation of Image Quality in Medical Volume Visualization: The State of the Art," Proc. Fifth Int'l Conf. Medical Image Computing and Computer-Assisted Intervention-Part II (MICCAI '02), pp. 598-605, 2002.
[33] A. Pommert and K.H. Höhne, "Validation of Medical Volume Visualization: A Literature Review," Int'l Congress Series, vol. 1256, pp. 571-576, 2003.
[34] T. Riley, A. Goucher, R. Tim, and G. Adam, Beautiful Testing: Leading Professionals Reveal How They Improve Software, first ed. O'Reilly Media, Inc., 2009.
[35] P.J. Roache, Verification and Validation in Computational Science and Engineering. Hermosa Publishers, 1998.
[36] S. Röttger, S. Guthe, D. Weiskopf, T. Ertl, and W. Strasser, "Smart Hardware-Accelerated Volume Rendering," Proc. Joint Eurographics - IEEE TCVG Symp. Visualization (VISSYM), pp. 231-238, May 2003.
[37] S. Röttger, M. Kraus, and T. Ertl, "Hardware-Accelerated Volume and Isosurface Rendering Based on Cell-Projection," Proc. IEEE Conf. Visualization, pp. 109-116, Oct. 2000.
[38] C.J. Roy, "Review of Code and Solution Verification Procedures for Computational Simulation," J. Computational Physics, vol. 205, no. 1, pp. 131-156, 2005.
[39] W. Schroeder, K. Martin, and W. Lorensen, Visualization Toolkit, An Object-Oriented Approach to 3D Graphics, second ed. Prentice-Hall, 1998.
[40] M. Smelyanskiy, D. Holmes, J. Chhugani, A. Larson, D.M. Carmean, D. Hanson, P. Dubey, K. Augustine, D. Kim, A. Kyker, V.W. Lee, A.D. Nguyen, L. Seiler, and R. Robb, "Mapping High-Fidelity Volume Rendering for Medical Imaging to CPU, GPU and Many-Core Architectures," IEEE Trans. Visualization and Computer Graphics, vol. 15, no. 6, pp. 1563-1570, Nov. 2009.
[41] M. Unser, "Splines: A Perfect Fit for Signal and Image Processing," IEEE Signal Processing Magazine, vol. 16, no. 6, pp. 22-38, Nov. 1999.
[42] A. Usman, T. Möller, and L. Condat, "Gradient Estimation Revitalized," IEEE Trans. Visualization and Computer Graphics, vol. 16, no. 6, pp. 1495-1504, Nov. 2010.
[43] L. Westover, "Interactive Volume Rendering," Proc. Chapel Hill Workshop ACM Vol. Visualization, pp. 9-16, 1989.
[44] P.L. Williams and N. Max, "A Volume Density Optical Model," Proc. ACM Workshop Vol. Visualization, pp. 61-68, 1992.
[45] P.L. Williams, N.L. Max, and C.M. Stein, "A High Accuracy Volume Renderer for Unstructured Data," IEEE Trans. Visualization and Computer Graphics, vol. 4, no. 1 pp. 37-54, Jan. 1998.
[46] J. Yang, P. Twohey, D. Engler, and M. Musuvathi, "Using Model Checking to Find Serious File System Errors," ACM Trans. Computer Systems, vol. 24, no. 4, pp. 393-423, Nov. 2006.
[47] Z. Zheng, W. Xu, and K. Mueller, "VDVR: Verifiable Volume Visualization of Projection-Based Data," IEEE Trans. Visualization and Computer Graphics, vol. 65, no. 6, pp. 1515-1524, Nov./Dec. 2010.
90 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool