A convex polygon is determined by its Hough transform

doi:10.1016/0167-8655(94)00102-9

Pattern Recognition Letters

Volume 16, Issue 3, March 1995, Pages 305-306

https://doi.org/10.1016/0167-8655(94)00102-9 Get rights and content

Abstract

A Hough transform maps a set of n collinear line elements in the plane into a spike of height n in a line parameter space (“Hough space”). Evidently, many different patterns of line elements can give rise to the same Hough transform, since collinear line elements can be located anywhere along a line. This note shows that if the line elements constitute the boundary of a convex polygon, the polygon is uniquely determined by the transform; but this is not true for arbitrary nonconvex polygons.

References (3)

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A survey of the Hough transforms
Computer Vision, Graphics, and Image Processing
(1988)

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^☆: The support of the Air Force Office of Scientific Research under Grants F49620-93-1-0039 and F49620-92-J-0332 in gratefully acknowledged, as is the help of Sandy German in preparing this paper. The authors also thank Mohamed Abdel-Mottaleb for suggesting the problem.

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A convex polygon is determined by its Hough transform☆

Abstract

Computer Vision, Graphics, and Image Processing