The Community for Technology Leaders
RSS Icon
Issue No.02 - March/April (2011 vol.31)
pp: 58-66
Torsten Ullrich , Fraunhofer Austria Research
Dieter W. Fellner , Fraunhofer IGD
This tutorial presents probability theory techniques for boosting linear algorithms. The approach is based on statistics and uses educated guesses instead of comprehensive calculations. Because estimates can be calculated in sublinear time, many algorithms can benefit from statistical estimation. Several examples show how to significantly boost linear algorithms without negative effects on their results. These examples involve a Ransac algorithm, an image-processing algorithm, and a geometrical reconstruction. The approach exploits that, in many cases, the amount of information in a dataset increases asymptotically sublinearly if its size or sampling density increases. Conversely, an algorithm with expected sublinear running time can extract the most information.
computations on discrete structures, geometrical problems and computations, statistical computing, computer graphics, graphics and multimedia
Torsten Ullrich, Dieter W. Fellner, "Linear Algorithms in Sublinear Timeā??a Tutorial on Statistical Estimation", IEEE Computer Graphics and Applications, vol.31, no. 2, pp. 58-66, March/April 2011, doi:10.1109/MCG.2010.21
1. A. Czumaj et al., eds., Sublinear Algorithms, Schloss Dagstuhl—Leibniz-Zentrum für Informatik, 2008.
2. P.K. Agarwal, S. Har-Peled, and K.R. Varadarajan, "Geometric Approximations via Coresets," Combinatorial and Computational Geometry, MSRI Publications, 2005, pp. 1–30.
3. E. Weisstein ed., MathWorld—a Wolfram Web Resource, Wolfram Research, 2009.
4. H. Bandemer and A. Bellmann eds., Statistische Versuchsplanung [Statistical Test Planning], Teubner Verlag, 1979.
5. M.A. Fischler, and R.C. Bolles, "Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography," Comm. ACM, vol. 24, no. 6, 1981, pp. 381–395.
6. M. Hudec and C. Neumann eds., Stichproben und Umfragen, [Random Samples and Polls], Institut für Statistik der Universität Wien, 2002.
7. O. Chum and J. Matas, "Randomized Ransac with Td,d Test," Image and Vision Computing, vol. 22, no. 10, 2004, pp. 837–842.
8. C.V. Stewart, "Robust Parameter Estimation in Computer Vision," SIAM Rev., vol. 41, no. 3, 1999, pp. 513–537.
9. R. Storn and K. Price, "Differential Evolution: A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces," J. Global Optimization, vol. 11, no. 4, 1997, pp. 341–359.
10. T. Ullrich, V. Settgast, and D.W. Fellner, "Semantic Fitting and Reconstruction," J. Computing and Cultural Heritage, vol. 1, no. 2, 2008, pp. 1201–1220.
398 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool