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GPU-Based Euclidean Distance Transforms and Their Application to Volume Rendering

  • Conference paper
Computer Vision, Imaging and Computer Graphics. Theory and Applications (VISIGRAPP 2009)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 68))

Abstract

We present discrete 2D and 3D distance transforms based on the vector propagation algorithm by Danielsson. Like other vector propagation algorithms, the proposed method is close to exact, i.e., the error can be strictly bounded from above and is significantly smaller than one pixel. Our contribution is that the algorithm runs entirely on consumer class graphics hardware, thereby achieving a throughput of up to 96 Mpixels/s. Therefore, the proposed method can be used in a wide range of applications that rely on both high speed and high quality. The usability of our approach is demonstrated in the context of hardware-accelerated volumetric isosurface raycasting.

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References

  1. Rosenfeld, A., Pfalz, J.: Sequential operations in digital picture processing. Journal of ACM 13, 471–494 (1966)

    Article  MATH  Google Scholar 

  2. Voronoi, G.: Nouvelles applications des paramètres continus à la théorie des formes quadratiques. deuxiéme mémoire: recherches sur les paralléloèdres primitifs. Reine Angewandte Mathematik 134, 198–287 (1908)

    Article  MATH  Google Scholar 

  3. Danielsson, P.: Euclidean distance mapping. Computer Graphics and Image Processing 14, 227–248 (1980)

    Article  Google Scholar 

  4. Schneider, J., Kraus, M., Westermann, R.: GPU-based real-time discrete euclidean distance transforms with precise error bounds. In: International Conference on Computer Vision Theory and Applications (VISAPP), pp. 435–442 (2009)

    Google Scholar 

  5. Jones, M., Bærentzen, J., Sramek, M.: 3D distance fields: a survey of techniques and applications. IEEE Trans. Visualization and Computer Graphics 12, 581–599 (2006)

    Article  Google Scholar 

  6. Cuisenaire, O.: Distance Transformation: Fast Algorithms and Applications to Medical Image Processing. Phd. thesis, Univ. Catholique de Louvain (1999)

    Google Scholar 

  7. Aurenhammer, F.: Voronoi diagrams–a fundamental geometric data structure. ACM Computing Surveys 23, 345–405 (1991)

    Article  Google Scholar 

  8. Okabe, A., Boots, B., Sugihara, K., Chiu, S.: Spatial Tesselations: Concepts and Applications of Voronoi Diagrams. John Wiley & Sons Ltd., Chichester (1999)

    Google Scholar 

  9. Mullikin, J.: The vector distance transform in two and three dimensions. CVGIP: Graphical Models and Image Processing 54, 526–535 (1992)

    Article  Google Scholar 

  10. Satherly, R., Jones, M.: Vector-city vector distance transform. Computer Vision and Image Understanding 82, 238–254 (2001)

    Article  Google Scholar 

  11. Tsitsiklis, N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Automatic Control 40, 1528–1538 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sethian, J.: A fast marching level set method for monotonically advancing fronts. Nat’l Academy of Sciences US-Paper Ed. 93, 1591–1595 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  13. Helmsen, J., Puckett, E., Colella, P., Dorr, M.: Two new methods for simulating photolithography development in 3D. In: SPIE, vol. 2726, pp. 253–261 (1996)

    Google Scholar 

  14. Telea, A., van Wijk., J.: An augmented fast marching method for computing skeletons and centerlines. In: Symp. on Visualization, pp. 251–260 (2002)

    Google Scholar 

  15. Butt, M., Maragos, P.: Optimum design of chamfer distance transforms. IEEE Trans. Image Processing 7, 1477–1484 (1998)

    Article  Google Scholar 

  16. Svensson, S., Borgefors, G.: Digital distance transforms in 3D images using information from neighborhoods up to 5×5×5. Computer Vision and Image Understanding 88, 24–53 (2002)

    Article  MATH  Google Scholar 

  17. Kulpa, Z., Kruse, B.: Methods of effective implementation of circular propagation in discrete images. Internal Report LiTH-ISY-I-0274, Dept. of Electrical Engineering, Linköping Univ., Sweden (1979)

    Google Scholar 

  18. Maurer, C., Qi, R., Raghavan, V.: A linear time algorithm for computing exact euclidean distance transforms of binary images in arbitrary dimensions. IEEE Trans. Pattern Analysis and Machine Intelligence 25, 265–270 (2003)

    Article  Google Scholar 

  19. Denny, M.: Algorithmic Geometry via Graphics Hardware. Phd. thesis, Universität des Saarlandes, Saarbrücken, Germany (2003)

    Google Scholar 

  20. Fortune, S.: A sweepline algorithm for Voronoi diagrams. In: ACM Symp. Computational Geometry, pp. 313–322 (1986)

    Google Scholar 

  21. Hoff, K.E., Culver, T., Keyser, J., Lin, M., Manocha, D.: Fast computation of generalized Voronoi diagrams using graphics hardware. ACM Trans. on Graphics 18, 277–286 (1999)

    Google Scholar 

  22. Mauch, S.: Efficient algorithms for solving static Hamilton-Jacobi equations. PhD thesis, California Institute of Technology, Pasadena, CA (2003)

    Google Scholar 

  23. Sigg, C., Peikert, R., Gross, M.: Signed distance transform using graphics hardware. In: IEEE Visualization, pp. 83–90 (2003)

    Google Scholar 

  24. Sud, A., Otaduy, M., Manocha, D.: DiFi: Fast 3D distance field computation using graphics hardware. EG Computer Graphics Forum 23, 557–566 (2004)

    Article  Google Scholar 

  25. Strzodka, R., Telea, A.: Generalized distance transforms and skeletons in graphics hardware. In: Joint EG/IEEE TVCG Symp. Visualization, pp. 221–230 (2004)

    Google Scholar 

  26. Rong, G., Tan, T.S.: Jump flooding in gpu with applications to Voronoi diagram and distance transform. In: ACM Symp. Interactive 3D Graphics and Games, pp. 109–116 (2006)

    Google Scholar 

  27. Cuntz, N., Kolb, A.: Fast hierarchical 3D distance transformations on the GPU. In: Proceedings Eurographics Short Papers, pp. 93–96 (2007)

    Google Scholar 

  28. Jähne, B.: Digital Image Processing: Concepts, Algorithms and Scientific Applicartions, 5th edn. Springer, Heidelberg (2002)

    Google Scholar 

  29. Krüger, J., Westermann, R.: Acceleration Techniques for GPU-based Volume Rendering. In: Proceedings IEEE Visualization (2003)

    Google Scholar 

  30. Miller, G.: Efficient algorithms for local and global accessibility shading. In: Proceedings of ACM SIGGRAPH, pp. 319–326 (1994)

    Google Scholar 

  31. US National Library of Medicine: The Visible Human Project®, http://www.nlm.nih.gov/research/visible

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Authors and Affiliations

  1. Computer Graphics & Visualization Group, Technische Universität München, Boltzmannstraße 3, D-85748, Garching bei München, Germany

    Jens Schneider, Martin Kraus & Rüdiger Westermann

Authors
  1. Jens Schneider
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  2. Martin Kraus
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  3. Rüdiger Westermann
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Editor information

Editors and Affiliations

  1. INSTICC, Avenida D. Manuel I, 2910, Setúbal, Portugal

    AlpeshKumar Ranchordas

  2. Departamento de Engenharia Informática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal,

    João Madeiras Pereira

  3. Institute for Systems and Robotics, Department of Electrical and Computer Engineering Polo II, University of Coimbra, 3030-290, Coimbra, Portugal

    Hélder J. Araújo

  4. Departamento de Engenharia Mecânica e Gestão Industrial, Rua Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal

    João Manuel R. S. Tavares

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© 2010 Springer-Verlag Berlin Heidelberg

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Schneider, J., Kraus, M., Westermann, R. (2010). GPU-Based Euclidean Distance Transforms and Their Application to Volume Rendering. In: Ranchordas, A., Pereira, J.M., Araújo, H.J., Tavares, J.M.R.S. (eds) Computer Vision, Imaging and Computer Graphics. Theory and Applications. VISIGRAPP 2009. Communications in Computer and Information Science, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11840-1_16

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  • DOI: https://doi.org/10.1007/978-3-642-11840-1_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11839-5

  • Online ISBN: 978-3-642-11840-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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