The Hough transform estimator

Alexander Goldenshluger, Assaf Zeevi

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)1908-1932
Number of pages25
JournalAnnals of Statistics
Volume32
Issue number5
DOIs
StatePublished - Oct 2004
Externally publishedYes

Keywords

  • Breakdown point
  • Computer vision
  • Cube-root asymptotics
  • Empirical processes
  • Excess mass
  • Hough transform
  • Multi-modality
  • Robust regression

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