A convex polygon is determined by its Hough transform

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.

[1]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

[2]  V. Arnold Mathematical Methods of Classical Mechanics , 1974 .

[3]  Friedrich M. Wahl,et al.  Polyhedral object recognition using Hough-space features , 1988, Pattern Recognit..