Vanishing points in point-to-line mappings and other line parameterizations

Some variants of the Hough transform can be used for detecting vanishing points and groups of concurrent lines. This article addresses a common misconception that in the polar line parameterization the vanishing point is represented by a line. The numerical error caused by this inaccuracy is then estimated.The article studies in detail point-to-line-mappings (PTLMs) – a class of line parameterizations which have the property that the vanishing point is represented by a line (and thus can be easily searched for). When a PTLM parameterization is used for the straight line detection by the Hough transform, a pair or a triplet of complementary PTLMs has to be used in order to obtain a limited Hough space. The complementary pairs and triplets of PTLMs are formalized and discussed in this article.

► Detection of lines and vanishing points by the Hough transform.
► Linearity and other properties of vanishing points’ images.
► Properties of point-to-line mappings.
► Shared properties of common PTLMs.
► Requirements for practically usefull PTLMs.