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Linear algorithms in sublinear time - a tutorial on statistical estimation

: Ullrich, Torsten; Fellner, Dieter W.


IEEE Computer Graphics and Applications 31 (2011), No.2, pp.58-66
ISSN: 0272-1716
ISSN: 1558-1756
Journal Article
Fraunhofer IGD ()
Fraunhofer Austria ()
computer graphic; algorithms; statistics; optimization; Forschungsgruppe Semantic Models, Immersive Systems (SMIS)

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.