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.
Similar content being viewed by others
References
Bergman L, Fuchs H, Grant E, Spach S (1986) Image rendering by adaptive refinement. Comput Graph 20(4):29–37
Bright S, Laflin S (1986) Shading of solid voxel models. Comput Graph Forum 5(2):131–138
Bryant J, Krumvieda C (1989) Display of discrete 3 D binary objects: I-shading. Computers and Graphics 13(4):441–444
Chen L, Herman GT, Reynolds RA, Udupa JK (1985) Surface shading in the Cuberille environment. IEEE Comput Graph Appl 5(12):33–43
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
Cohen D, Kaufman A, Bakalash R, Bergman S (1990) Real-time discrete shading. The Visual Computer 6(1):16–27
Goldwasser SM (1986) Rapid techniques for the display and manipulation of 3-D biomedical data. Proc NCGA Conf II:115–149
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
Gordon D, Reynolds RA (1985) Image space shading of 3-dimensional objects. Comput Graph and Image Proc 29(3):361–376
Grimson WEL (1981) From images to surfaces: a computational study of human early visual system (chap 9). MIT Press, Cambridge
Grimson WEL, Pavlidis T (1985) Discontinuity detection for visual surface reconstruction. Comput Vision, Graph and Image Proc 30:316–330
Hoehne KH, Bernstein R (1986) Shading 3 D-images from CT using gray-level gradients. IEEE Trans Med Imaging MI 5(1):45–47
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
Horn BKP (1982) Hill shading and the reflection map. Geo-Processing 2:65–146
Kaufman A (1987) Efficient algorithms for 3 D scan-conversion of parametric curves, surfaces, and volumes. Comput Graph 21(4):171–179
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
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
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
Pavlidis T (1982) Algorithms for graphics and image processing. Computer Science Press, Rockville
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
Rosenfeld A, Kak AC (1982) Digital picture processing. Academic Press, Boston, MA
Saito T, Takahashi T (1990) Comprehensive rendering of 3 D shapes. Comput Graph 24(4):197–206
Schlusselberg DS, Smith K, Woodward DJ (1986) Three-dimensional display of medical image volumes. Proc NCGA Conf III:114–123
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
Torrance KE, Sparrow EM (1967) Theory for off-specular reflection from roughened surfaces. J Optical Soc Am 57:1105–1114
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
Yagel R, Cohen D, Kaufman A (1992) Discrete ray tracing. To appear in IEEE Comput Graph Appl
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1007/BF01897115