The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.12 - Dec. (2012 vol.18)
pp: 2335-2344
Nathaniel Fout , University of California, Davis
Kwan-Liu Ma , University of California, Davis
ABSTRACT
In order to assess the reliability of volume rendering, it is necessary to consider the uncertainty associated with the volume data and how it is propagated through the volume rendering algorithm, as well as the contribution to uncertainty from the rendering algorithm itself. In this work, we show how to apply concepts from the field of reliable computing in order to build a framework for management of uncertainty in volume rendering, with the result being a self-validating computational model to compute a posteriori uncertainty bounds. We begin by adopting a coherent, unifying possibility-based representation of uncertainty that is able to capture the various forms of uncertainty that appear in visualization, including variability, imprecision, and fuzziness. Next, we extend the concept of the fuzzy transform in order to derive rules for accumulation and propagation of uncertainty. This representation and propagation of uncertainty together constitute an automated framework for management of uncertainty in visualization, which we then apply to volume rendering. The result, which we call fuzzy volume rendering, is an uncertainty-aware rendering algorithm able to produce more complete depictions of the volume data, thereby allowing more reliable conclusions and informed decisions. Finally, we compare approaches for self-validated computation in volume rendering, demonstrating that our chosen method has the ability to handle complex uncertainty while maintaining efficiency.
INDEX TERMS
Uncertainty, Rendering (computer graphics), Data visualization, Computational modeling, Transforms, Volume measurement, volume rendering, Uncertainty visualization, verifiable visualization
CITATION
Nathaniel Fout, Kwan-Liu Ma, "Fuzzy Volume Rendering", IEEE Transactions on Visualization & Computer Graphics, vol.18, no. 12, pp. 2335-2344, Dec. 2012, doi:10.1109/TVCG.2012.227
REFERENCES
[1] D. Aeschliman, W. Oberkampf, and F. Blottner., A proposed methodology for computational fluid dynamics code verification, calibration, and val-idation. In Int’ l. Congress on Instrumentation in Aerospace Simulation Facilities, pages 2701-2713, July 1995.
[2] M. V. A. Andrade,J. L. D. Comba,, and J. Stolfi., Affine arithmetic. In Int'l. Conf. on Interval and Computer-Algebraic Methods in Science and Engineering, pages 36-40, Mar. 1994.
[3] J. Baccou and E. Chojnacki., Combining probability and possibility to respect the real state of knowledge on uncertainties in the evaluation of safety margins. In ENBISIEMSE Conference Design and Analysis of Computer Experiments, Saint-Etienne (France), July1-3, 2009.
[4] C. Baudrit, D. Dubois, and D. Guyonnet, Joint propagation and ex-ploitation of probabilistic and possibilistic information in risk assessment IEEE Transactions on Fuzzy Systems, 14(5): 593-608, Oct. 2006.
[5] M. Berz and G. Hoffstatter, Computation and application of taylor poly-nomials with interval remainder bounds Reliable Computing, 4: 83-97, 1998.
[6] N. Boukhelifa and D. J. Duke., Uncertainty visualization: why might it fail? In Int'l Conf on Human Factors in Computing Systems, pages 4051-4056, New York, NY, USA, 2009. ACM.
[7] C. Correa, Y.-H. Chan, and K.-L. Ma., A framework for uncertainty-aware visual analytics. In IEEE Visual Analytics Science and Technology ‘09, pages 51-58, Oct. 2009.
[8] W. Dong and H. Shah, Vertex method for computing functions of fuzzy variables Fuzzy Sets and Systems, 24(1): 65-78, 1987.
[9] W. Dong, H. Shah, and F. Wong, Fuzzy computations in risk and decision analysis Civil Engineering and Environmental Systems, 2(4): 201-208, 1985.
[10] D. Dubois, L. Foulloy, G. Mauris,, and H. Prade., Probability-possibility transformations, triangular fuzzy sets, and probabilistic inequalities. Reliable Computing, pages 273-297, 2004.
[11] D. Dubois and H. Prade., Fuzzy sets and systems: theory and applications. Academic Press, 1 st edition, 1980.
[12] D. Dubois and H. Prade., Possibility theory: an approach to computerized processing of uncertainty. Plenum Press, 1st edition, 1988.
[13] A. Ferrero and S. Salicone, The random-fuzzy variables: a new approach to the expression of uncertainty in measurement IEEE Transactions on Instrumentation and Measurement, pages 1370-1377, 2004.
[14] M. Haidacher, D. Patel, S. Bruckner., A. Kanitsar, and M. Groller,Volume visualization based on statistical transfer-function spaces. In Pacific Visualization Symposium’ 10, PacVis ‘10, pages 17-24, March 2010.
[15] L. Hall, A. Bensaid, L. Clarke., R. Velthuizen, M. Silbiger,, and J. Bezdek., A comparison of neural network and fuzzy clustering techniques in segmenting magnetic resonance images of the brain. IEEE Trans. on Neural Networks, 3(5): 672-682, Sept. 1992.
[16] E. Hansen., A generalized interval arithmetic. In K. Nickel, editor, Interval Mathematics, 29 of Lecture Notes in Computer Science, pages 7-18. Springer Berlin / Heidelberg, 1975.
[17] C. Johnson, and A. Sanderson, A next step: Visualizing errors and uncertainty Computer Graphics and Applications, IEEE, 23(5): 6-10, Sep 2003.
[18] R. Kirby and C. Silva, The need for verifiable visualization Computer Graphics and Applications, IEEE, 28(5): 78-83, Sep 2008.
[19] G. Klir and B. Yuan., Fuzzy sets and juzzy logic: theory and applications. Prentice Hall, 1 st edition, 1995.
[20] J. Kniss,R. Van Uitert, A. Stephens, G.-S. Li, T. Tasdizen, and C. Hansen., Statistically quantitative volume visualization. In IEEE Visualization Con! ‘05, VIS ‘05, pages 287-294, Oct. 2005.
[21] J. Kronander, J. Unger, T. Mller,, and A. Ynnerman., Estimation and modeling of actual numerical errors in volume rendering. Computer Graphics Forum, 29(3): 893-902, 2010.
[22] C. Lundstrom, P. Ljung, A. Persson,, and A. Ynnerman., Uncertainty visualization in medical volume rendering using probabilistic animation. IEEE Trans. on Visualization and Computer Graphics, 13(6): 1648-1655, Nov. 2007.
[23] A. Mencattini, M. Salmeri, and R. Lojacono., Type-2 fuzzy sets for modeling uncertainty in measurement. In Proceedings of the 2006 IEEE International Workshop on Advanced Methods for Uncertainty Estimation in Measurement, pages 8-13, 2006.
[24] D. Michelucci and J.-M. Moreau, Lazy arithmetic IEEE Transactions on Computers, 46: 961-975, September 1997.
[25] N. Mohamed, M. Ahmed, and A. Farag., Modified fuzzy c-mean in medical image segmentation. In IEEE Int'l. Conf. on Acoustics, Speech, and Signal Processing ‘99, 6, pages 3429-3432, March 1999.
[26] R. Moore., Interval analysis. Prentice-Hall, 1st edition, 1966.
[27] K. Novins and J. Arvo., Controlled precision volume integration. In Volume Visualization Workshop ‘92, pages 83-89. ACM, 1992.
[28] J. V. d. Oliveira and W. Pedrycz, Advances in Fuzzy Clustering and its Applications. John Wiley & Sons, Inc., New York, NY, USA, 2007.
[29] A. T. Pang,C. M. Wittenbrink,, and S. K. Lodha., Approaches to uncertainty visualization The Visual Computer, 13: 370-390, 1997.
[30] T. Ross., Fuzzy logic with engineering applications. Wiley, 3rd edition, 2010.
[31] C. J. Roy and W. L. Oberkampf., A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing Computer Methods in Applied Mechanics and Engineering, 200(2528): 2131-2144, 2011.
[32] M. Skeels, B. Lee, G. Smith,, and G. Robertson., Revealing uncertainty for information visualization. In Proc. of Con! on Advanced Visual Interfaces, AVI ‘08, pages 376-379, New York, NY, USA, 2008. ACM.
[33] J. Smith and P. Gossett., A flexible sampling-rate conversion method. In IEEE Int'l. Conf. on Acoustics, Speech, and Signal Processing, 9 of ICASSP ‘84, pages 112-115, March 1984.
[34] A. Streit, B. Pham, and R. Brown, A spreadsheet approach to facilitate visualization of uncertainty in information IEEE Trans. on Visualization and Computer Graphics, 14: 61-72, January 2008.
[35] J. Thomson, B. Hetzlera, A. MacEachrenb., M. Gaheganb, and M. Pavel., A typology for visualizing uncertainty. In Proceedings of SPIE. Vol. SPIE-5669, pages 146-157, 2005.
[36] B. Widrow and I. Kollar., Quantization Noise. Cambridge University Press, 1st edition, 2008.
[37] L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning Information Science, 8: 199-249, 1975.
[38] Z. Zheng, W. Xu, and K. Mueller, VDVR: Verifiable volume visualization of projection-based data IEEE Trans. on Visualization and Computer Graphics, 16(6): 1515-1524, Nov.-Dec. 2010.
[39] Y. Zhou, T. Murata, and T. A. DeFanti., Modeling and performance analysis using extended fuzzy-timing Petri nets for networked virtual environments Trans. Sys. Man Cyber. Part B, 30(5): 737-756, Oct. 2000.
33 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool