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Normal estimation in 3 D discrete space

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Abstract

Three-dimensional voxel-based objects are inherently discrete and do not maintain any notion of a continuous surface or normal values, which are crucial for the simulation of light behavior. Thus, in volume rendering, the normal vector of the displayed surfaces must be estimated prior to rendering. We survey several methods for normal estimation and analyze their performance. One unique method, the context-sensitive approach, employs segmentation and segment-bounded operators that are based on object and slope discontinuities in order to achieve high fidelity normal estimation for rendering volumetric objects.

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References

  • Bergman L, Fuchs H, Grant E, Spach S (1986) Image rendering by adaptive refinement. Comput Graph 20(4):29–37

    Google Scholar 

  • Bright S, Laflin S (1986) Shading of solid voxel models. Comput Graph Forum 5(2):131–138

    Google Scholar 

  • Bryant J, Krumvieda C (1989) Display of discrete 3 D binary objects: I-shading. Computers and Graphics 13(4):441–444

    Google Scholar 

  • Chen L, Herman GT, Reynolds RA, Udupa JK (1985) Surface shading in the Cuberille environment. IEEE Comput Graph Appl 5(12):33–43

    Google Scholar 

  • Cohen D, Kaufman A (1990) Scan-conversion algorithms for linear and quadratic objects. In: Kaufman A (ed) Volume visualization. IEEE Computer Society Press, Los Alamitos, pp 280–301

    Google Scholar 

  • Cohen D, Kaufman A, Bakalash R, Bergman S (1990) Real-time discrete shading. The Visual Computer 6(1):16–27

    Google Scholar 

  • Goldwasser SM (1986) Rapid techniques for the display and manipulation of 3-D biomedical data. Proc NCGA Conf II:115–149

    Google Scholar 

  • Goldwasser SM, Reynolds RA, Talton DA, Walsh ES (1989) High performance graphics processors for medical imaging applications. In: Dew PM, Earnshaw RA, Heywood TR (eds) Parallel processing for computer vision and display. Addison Wesley, Reading, pp 461–470

    Google Scholar 

  • Gordon D, Reynolds RA (1985) Image space shading of 3-dimensional objects. Comput Graph and Image Proc 29(3):361–376

    Google Scholar 

  • Grimson WEL (1981) From images to surfaces: a computational study of human early visual system (chap 9). MIT Press, Cambridge

    Google Scholar 

  • Grimson WEL, Pavlidis T (1985) Discontinuity detection for visual surface reconstruction. Comput Vision, Graph and Image Proc 30:316–330

    Google Scholar 

  • Hoehne KH, Bernstein R (1986) Shading 3 D-images from CT using gray-level gradients. IEEE Trans Med Imaging MI 5(1):45–47

    Google Scholar 

  • Hoehne KH, Bomans M, Pommert A, Riemer M, Schiers C, Tiede U, Wiebecke G (1990) 3 D-visualization of tomographic volume data using the generalized voxel model. The Visual Computer 6(1):28–37

    Google Scholar 

  • Horn BKP (1982) Hill shading and the reflection map. Geo-Processing 2:65–146

    Google Scholar 

  • Kaufman A (1987) Efficient algorithms for 3 D scan-conversion of parametric curves, surfaces, and volumes. Comput Graph 21(4):171–179

    MathSciNet  Google Scholar 

  • Kaufman A (1992) Thevoxblt engine: a voxel frame buffer processor. In: Kuijk AAM, Strasser W (eds) Advances in computer graphics hardware III. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Kaufman A, Yagel R, Cohen D (1990) Intermixing surface and volume rendering. In: Hoehne KH, Fuchs H, Pizer SM (eds) 3 D imaging in medicine. Algorithms, systems, applications. Springer, Berlin Heidelberg New York, pp 217–227

    Google Scholar 

  • Magnusson M, Lenz R, Danielsson PE (1988) Evaluation of methods for shaded display of CT volumes. Proc 9th Int Conf Pattern Recognition II:1287–1294

    Google Scholar 

  • Pavlidis T (1982) Algorithms for graphics and image processing. Computer Science Press, Rockville

    Google Scholar 

  • Pommert A, Tiede U, Wiebecke G, Hoehne KH (1990) Surface shading in tomographic volume visualization: a comparative study. Proc 1st Conf Visualization in Biomedical Computing, pp 19–26

  • Potmesil M, Chakravarty I (1982) Synthetic image generation with a lens and aperture camera model. ACM Trans Graph 1:85–108

    Google Scholar 

  • Rosenfeld A, Kak AC (1982) Digital picture processing. Academic Press, Boston, MA

    Google Scholar 

  • Saito T, Takahashi T (1990) Comprehensive rendering of 3 D shapes. Comput Graph 24(4):197–206

    Google Scholar 

  • Schlusselberg DS, Smith K, Woodward DJ (1986) Three-dimensional display of medical image volumes. Proc NCGA Conf III:114–123

    Google Scholar 

  • Tam YW, Davis WA (1988) Display of 3 D medical images. Proc Graphics Interface, pp 78–86

  • Tiede U, Hoehne KH, Bomans M, Pommert A, Riemer M, Wiebecke G (1990) Investigation of medical 3 D-rendering algorithms. IEEE Comput Graph Appl 10(3):41–53

    Google Scholar 

  • Torrance KE, Sparrow EM (1967) Theory for off-specular reflection from roughened surfaces. J Optical Soc Am 57:1105–1114

    Google Scholar 

  • Udupa JK, Hung HM (1990) Surface versus volume rendering: a comparative assessment. Proc 1st Conf Visualization in Biomedical Computing. pp 83–91

  • Webber RE (1990) Ray tracing voxel based data via biquadratic local surface interpolation. The Visual Computer 6(1):8–15

    Google Scholar 

  • Yagel R, Cohen D, Kaufman A (1992) Discrete ray tracing. To appear in IEEE Comput Graph Appl

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Yagel, R., Cohen, D. & Kaufman, A. Normal estimation in 3 D discrete space. The Visual Computer 8, 278–291 (1992). https://doi.org/10.1007/BF01897115

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