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October 2004 The Hough transform estimator
Alexander Goldenshluger, Assaf Zeevi
Ann. Statist. 32(5): 1908-1932 (October 2004). DOI: 10.1214/009053604000000760


This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that “best” fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the convergence rates are seen to be slower than those found in some standard regression methods, the Hough transform estimator is shown to be more robust as measured by its breakdown point. We next study the Hough transform in the context of the problem of detecting multiple lines. This is addressed via the framework of excess mass functionals and modality testing. Throughout, several numerical examples help illustrate various properties of the estimator. Relations between the Hough transform and more mainstream statistical paradigms and methods are discussed as well.


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Alexander Goldenshluger. Assaf Zeevi. "The Hough transform estimator." Ann. Statist. 32 (5) 1908 - 1932, October 2004.


Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62030
MathSciNet: MR2102497
Digital Object Identifier: 10.1214/009053604000000760

Primary: 62F12 , 62F35 , 68T45

Keywords: Breakdown point , Computer vision , cube-root asymptotics , Empirical processes , excess mass , Hough transform , multi-modality , robust regression

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 5 • October 2004
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