Abstract
Tensors are of great interest to many applications in engineering and in medical imaging, but a proper analysis and visualization remains challenging. Physics-based visualization of tensor fields has proven to show the main features of symmetric second-order tensor fields, while still displaying the most important information of the data, namely the main directions in medical diffusion tensor data using texture and additional attributes using color-coding, in a continuous representation. Nevertheless, its application and usability remains limited due to its computational expensive and sensitive nature.
We introduce a novel approach to compute a fabric-like texture pattern from tensor fields motivated by image-space line integral convolution (LIC). Although, our approach can be applied to arbitrary, non-selfintersecting surfaces, we are focusing on special surfaces following neural fibers in the brain.We employ a multipass rendering approach whose main focus lies on regaining three-dimensionality of the data under user interaction as well as being able to have a seamless transition between local and global structures including a proper visualization of degenerated points.
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References
Anwander, A., Schurade, R., Hlawitschka, M., Scheuermann, G., Knsche, T.: White matterimaging with virtual klingler dissection. NeuroImage 47(Supplement 1), S105 - S105 (2009).DOI 10.1016/S1053-8119(09)70916-4. Organization for Human Brain Mapping 2009 Annual Meeting
Blinn, J.F.: Models of light reflection for computer synthesized pictures. In: SIGGRAPH ’77:Proceedings of the 4th annual conference on Computer graphics and interactive techniques,192-198. ACM, New York, NY, USA (1977). DOI http://doi.acm.org/10.1145/563858.563893
Cabral, B., Leedom, L.C.: Imaging vector fields using line integral convolution. In: SIG-GRAPH ’93: Proceedings of the 20th annual conference on Computer graphics and interactivetechniques, 263-270. ACM, New York, NY, USA (1993). DOI http://doi.acm.org/10.1145/166117.166151
Chu, A., Chan, W.Y., Guo, J., Pang, W.M., Heng, P.A.: Perception-aware depth cueing forillustrative vascular visualization. In: BMEI ’08: Proceedings of the 2008 InternationalConference on BioMedical Engineering and Informatics, 341-346. IEEE Computer Society,Washington, DC, USA (2008). DOIhttp://dx.doi.org/10.1109/BMEI.2008.347
Delmarcelle, T., Hesselink, L.: Visualization of second order tensor fields and matrix data. In:VIS ’92: Proceedings of the 3rd conference on Visualization ’92, 316-323. IEEE ComputerSociety Press, Los Alamitos, CA, USA (1992)
Dick, C., Georgii, J., Burgkart, R., Westermann, R.: Stress tensor field visualization for implantplanning in orthopedics. IEEE Transactions on Visualization and Computer Graphics 15(6),1399-1406 (2009). DOI http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.184
Eichelbaum, S., Hlawitschka, M., Hamann, B., Scheuermann, G.: Fabric-like visualization oftensor field data on arbitrary surfaces in image space. Submitted to Dagstuhl Seminar 09302
Enders, F., Sauber, N., Merhof, D., Hastreiter, P., Nimsky, C., Stamminger, M.: Visualizationof white matter tracts with wrapped streamlines. In: C.T. Silva, E. Gr öller, H. Rushmeier (eds.)Proceedings of IEEE Visualization 2005, 51-58. IEEE Computer Society, IEEE ComputerSociety Press, Los Alamitos, CA, USA (2005)
Grabner, M., Laramee, R.S.: Image space advection on graphics hardware. In: SCCG ’05:Proceedings of the 21st spring conference on Computer graphics, 77-84. ACM, New York,NY, USA (2005). DOI http://doi.acm.org/10.1145/1090122.1090136
Hasan, K.M., Basser, P.J., Parker, D.L., Alexander, A.L.: Analytical computation of theeigenvalues and eigenvectors in DT-MRI. Journal of Magnetic Resonance 152(1), 41 - 47(2001). DOI 10.1006/jmre.2001.2400
Hesselink, L., Levy, Y., Lavin, Y.: The topology of symmetric, second-order 3d tensor fields.IEEE Transactions on Visualization and Computer Graphics 3(1), 1-11 (1997). DOI http://dx.doi.org/10.1109/2945.582332
Hlawitschka, M., Garth, C., Tricoche, X., Kindlmann, G., Scheuermann, G., Joy, K.I., Hamann,B.: Direct visualization of fiber information by coherence. International Journal of Computer AssistedRadiology and Surgery, CARS, CUARC.08 Special Issue (2009)
Hotz, I., Feng, L., Hagen, H., Hamann, B., Joy, K., Jeremic, B.: Physically based methods fortensor field visualization. In: VIS ’04: Proceedings of the conference on Visualization ’04,123-130. IEEE Computer Society, Washington, DC, USA (2004). DOI http://dx.doi.org/10.1109/VIS.2004.80
Hotz, I., Feng, Z.X., Hamann, B., Joy, K.I.: Tensor field visualization using a fabric-liketexture on arbitrary two-dimensional surfaces. In: T. M öller, B. Hamann, R.D. Russel (eds.)Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive DataExploration. Springer-Verlag Heidelberg, Germany (2009)
Iwakiri, Y., Omori, Y., Kanko, T.: Practical texture mapping on free-form surfaces. In: PG ’00:Proceedings of the 8th Pacific Conference on Computer Graphics and Applications, 97. IEEEComputer Society, Washington, DC, USA (2000)
Kindlmann, G.: Superquadric tensor glyphs. In: Proceedings of IEEE TCVG/EG Symposiumon Visualization 2004, 147-154 (2004)
Kindlmann, G., Tricoche, X., Westin, C.F.: Anisotropy creases delineate white matter structurein diffusion tensor MRI. In: Ninth International Conference on Medical Image Computingand Computer-Assisted Intervention (MICCAI’06), Lecture Notes in Computer Science 4190,126-133. Copenhagen, Denmark (2006)
Knoll, A., Hijazi, Y., Hansen, C., Wald, I., Hagen, H.: Interactive ray tracing of arbitraryimplicits with simd interval arithmetic. In: RT ’07: Proceedings of the 2007 IEEE Symposiumon Interactive Ray Tracing, 11-18. IEEE Computer Society, Washington, DC, USA (2007).DOI http://dx.doi.org/10.1109/RT.2007.4342585
Laramee, R.S., Jobard, B., Hauser, H.: Image space based visualization of unsteady flow onsurfaces. In: VIS ’03: Proceedings of the 14th IEEE Visualization 2003 (VIS’03), 18. IEEEComputer Society, Washington, DC, USA (2003). DOI http://dx.doi.org/10.1109/VISUAL.2003.1250364
Laramee, R.S., van Wijk, J.J., Jobard, B., Hauser, H.: Isa and ibfvs: Image space-basedvisualization of flow on surfaces. IEEE Transactions on Visualization and Computer Graphics10,637-648 (2004). DOI http://doi.ieeecomputersociety.org/10.1109/TVCG.2004.47
Purnomo, B., Cohen, J.D., Kumar, S.: Seamless texture atlases. In: SGP ’04: Proceedings ofthe 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, 65-74. ACM,New York, NY, USA (2004). DOI http://doi.acm.org/10.1145/1057432.1057441
Schultz, T., Seidel, H.P.: Estimating crossing fibers: A tensor decomposition approach. IEEETransactions on Visualization and Computer Graphics 14(6), 1635-1642 (2008). DOI http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.128
Tricoche, X.: Vector and tensor field topology simplification, tracking, and visualization. Ph.D.thesis, University of Kaiserslautern, Germany (2002)
Tricoche, X., Scheuermann, G., Hagen, H.: Tensor topology tracking: A visualization methodfor time-dependent 2D symmetric tensor fields. In: Eurographics 2001 Proceedings, ComputerGraphics Forum 20(3), 461-470. The Eurographics Association, Saarbr ücken, Germany(2001). DOI http://dx.doi.org/10.1111/1467-8659.00539
Turing, A.: The chemical basis of morphogenesis. Philosophical Transactions of the RoyalSociety of London 237(641), 37 - 72 (1952)
Turk, G.: Generating textures on arbitrary surfaces using reaction-diffusion. In: SIGGRAPH’91: Proceedings of the 18th annual conference on Computer graphics and interactivetechniques, 289-298. ACM, New York, NY, USA (1991). DOI http://doi.acm.org/10.1145/122718.122749
Weiskopf, D., Ertl, T.: A hybrid physical/device-space approach for spatio-temporally coherentinteractive texture advection on curved surfaces. In: GI ’04: Proceedings of Graphics Interface2004,263-270. Canadian Human-Computer Communications Society, School of ComputerScience, University of Waterloo, Waterloo, Ontario, Canada (2004)
van Wijk, J.J.: Image based flow visualization. In: SIGGRAPH ’02: Proceedings of the 29thannual conference on Computer graphics and interactive techniques, 745-754. ACM, NewYork, NY, USA (2002). DOI http://doi.acm.org/10.1145/566570.566646
van Wijk, J.J.: Image based flow visualization for curved surfaces. In: VIS ’03: Proceedingsof the 14th IEEE Visualization 2003 (VIS’03), 17. IEEE Computer Society, Washington, DC,USA (2003). DOI http://dx.doi.org/10.1109/VISUAL.2003.1250363
Zhang, E., Yeh, H., Lin, Z., Laramee, R.S.: Asymmetric tensor analysis for flow visualization.IEEE Transactions on Visualization and Computer Graphics 15, 106-122 (2009). DOI http://doi.ieeecomputersociety.org/10.1109/TVCG.2008.68
Zheng, X., Pang, A.: Hyperlic. In: VIS ’03: Proceedings of the 14th IEEE Visualization 2003(VIS’03), 33. IEEE Computer Society, Washington, DC, USA (2003). DOI http://dx.doi.org/10.1109/VISUAL.2003.1250379
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Eichelbaum, S., Hlawitschka, M., Hamann, B., Scheuermann, G. (2012). Image-Space Tensor Field Visualization Using a LIC-like Method. In: Linsen, L., Hagen, H., Hamann, B., Hege, HC. (eds) Visualization in Medicine and Life Sciences II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21608-4_11
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DOI: https://doi.org/10.1007/978-3-642-21608-4_11
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