Abstract
In this paper we investigate systematic sampling in the image- synthesis context. Systematic sampling has been widely used in stereology to improve the efficiency of different probes in experimental design. These designs are theoretically based on estimators of 1-dimensional and 2-dimensional integrals. For the particular case of the characteristic function, the variance of these estimators has been shown to be asymptotically N − − 3/2, which improves on the O(N − − 1) behaviour of independent estimators using uniform sampling. Thus, when no a priori knowledge of the integrand function is available, like in several image synthesis techniques, systematic sampling efficiently reduces the computational cost.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Baddeley, A., Vedel Jensen, E.B.: Stereology for Statisticians. Chapman & Hall/CRC (2005)
Barabesi, L.: A Monte Carlo integration approach to Horvitz-Thompson estimation in replicated environment designs. METRON – International Journal of Statistics, LXI(3), 355–374 (2003)
Cruz-Orive, L.M.: On the precision of systematic sampling: a review of Matheron’s transitive methods. Journal of Microscopy 153(Pt3), 315–333 (1989)
Cruz-Orive, L.M.: Systematic sampling in stereology. In: Proceedings 49th Session Bull. Intern. Statis. Instit., Florence, vol. 55, pp. 451–468 (1993)
Purgathofer, W.: A statistical method for adaptive stochastic sampling. Computers & Graphics 11(2), 157–162 (1987)
Sobol, I.M.: Monte Carlo numerical methods. Science, Moscou (1973) (in Russian)
Keller, A., Heidrich, W.: Interleaved Sampling. In: Eurographics Workshop on Rendering 2001 (2001)
Kollig, T., Keller, A.: Efficient Multidimensional Sampling. Computer Graphics Forum 21(3), 557–563 (2002)
Krishnaiah, P.R., Rao, C.R.: Handbook of statistics, vol. 6. Elsevier, Amsterdam (1988)
Cochran, W.G.: Sampling Techniques. John Wiley and sons, New York (1997)
Iones, A., Krupkin, A., Sbert, M., Zhukov, S.: Fast realistic lighting for video games. IEEE Computer Graphics & Applications (2003)
Mendez, A., Sbert, M.: Comparing Hemisphere Sampling Techniques for Obscurance Computation. In: 3IA 2004, Limoges, France (2004)
Sbert, M.: The Use of Global Random Directions to Compute Radiosity. Global Monte Carlo Techniques, PhD dissertation, Universitat Politècnica de Catalunya (1997)
Szirmay-Kalos, L.: Photorealistic Image Synthesis Using Ray-bundles, D.Sc. dissertation, Hungarian Academy of Sciences (2000)
Gual–Arnau, X., Cruz-Orive, L.M.: Systematic sampling on the circle and the sphere. Advances in Applied Probability (SGSA) 32, 628–647 (2000)
Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and its Applications. Wiley, Chichester (1987)
Purgathofer, W., Tobler, R.F., Geiler, M.: Forced Random Dithering: Improved Threshold Matrices for Ordered Dithering. In: Proceedings of the First IEEE International Conference on Image Processing, Austin, Texas (1994)
Purgathofer, W., Tobler, R.F., Geiler, M.: Improved Threshold Matrices for Ordered Dithering. In: Graphics Gems V. Academic Press, London (1995)
Shirley, P.: Discrepancy as a Quality Measure for Sample Distributions. In: Proceedings of Eurographics 1991 (1991)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sbert, M., Rigau, J., Feixas, M., Neumann, L. (2006). Systematic Sampling in Image-Synthesis. In: Gavrilova, M., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751540_48
Download citation
DOI: https://doi.org/10.1007/11751540_48
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34070-6
Online ISBN: 978-3-540-34071-3
eBook Packages: Computer ScienceComputer Science (R0)