Neville interpolation-based normal estimation

Displaying useful and meaningful information from 3D data is known as volume rendering. Ray casting is one of the most frequently used direct volume rendering methods. It consists of data preparation, sampling, classification, compositing, and shading steps. Normal values are needed for efficient shading. However, 3D volumetric data are discrete and cannot be used directly for shading. Hence, the estimation of normal values, at each voxel on the surface, is needed for realistic shading. In normal estimation, the use of small voxel neighborhoods results in the staircase effect. On the other hand, the use of larger voxel neighborhoods causes loss of details in the final image. In this work, an alternative normal estimation method that uses large voxel neighborhoods is proposed for providing smoother images without losing details.

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[1] Kaufman A. Volume visualization: principles and advances. ACM Comput Surv 1996; 28: 165-168.
[2] Meiβ ner M, Pfister H, Westermann R, Wittenbrink CM. Volume visualization and volume rendering techniques. In: EUROGRAPHICS 2000 Conference; 2125 August 2000; Interlaken, Switzerland. Geneva, Switzerland: Computer Graphics Forum. pp. 1-36.
[3] Kaufman A, Mueller K. Overview of volume rendering. In: Hansen CD, Johnson CR, editors. The Visualization Handbook. Oxford, UK: Academic Press, 2005. pp. 127-174.
[4] Zhang Q, Eagleson R, Peters TM. Volume visualization: a technical overview with a focus on medical applications. J Digit Imaging 2011; 24: 640-664.
[5] C¸ elebi OC, C¸ evik U. Accelerating volume rendering by ray leaping with back steps. Comput Methods Programs ¨ Biomed 2010; 97: 99-113.
[6] Li Z, Zhang J. Study on volume rendering of CT slices based on ray casting. In: 3rd IEEE International Conference on Computer Science and Information Technology; 911 July 2010; Chengdu, China. New York, NY, USA: IEEE. pp. 157-160.
[7] Levoy M. Efficient ray tracing of volume data. ACM T Graphic 1990; 9: 245-261.
[8] Ray H, Pfister H, Silver D, Cook TA. Ray casting architectures for volume visualization. IEEE T Vis Comput Gr 1999; 5: 210-223.
[9] Yagel R, Cohen D, Kaufman A. Normal estimation in 3D discrete space. Visual Comput 1992; 8: 278-291.
[10] Hoehne KH, Bernstein R. Shading 3D-images from CT using gray-level gradients. IEEE T Med Imaging 1986; 5: 45-47.
[11] Neumann L, Csebfalvi O, K¨onig A, Gr¨oller E. Gradient Estimation in Volume Data Using 4D Linear Regression. Report TR-186-2-00-03. Vienna, Austria: Institute of Computer Graphics, Vienna University of Technology, 2000.
[12] Brekelmans RCM, Driessen LT, Hamers HJM, Hertog D. Gradient estimation using Lagrange interpolation polynomials. J Opt Theory Appl 2008; 136: 341-357.
[13] Goldman R. Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modelling. San Francisco, CA, USA: Morgan Kaufman Publishers, 2002.