On the extensive reconstruction of Hough transform

The authors introduce four conditions required by the family of extended Hough transform (EHT) functions, and a few basic examples such as the Hough-parabolic function are presented. Furthermore, two kinds of fast transform functions, the piecewise-linear and fast incremental Hough transforms (PLHT and FIHT), are proposed in order to show the practical usefulness of EHTs. After the definitions and basic properties such as computing cost reduction are briefly presented, it is shown that the line detector based on the EHT function can provide more flexible sensitivity for the angle of the line pattern segments