Abstract: Similar to the classic Hough transformation for analytic curves such as line
(segment), circle (arc), ellipse, parabola etc, a new cubic Bezier curve detection algorithm is
provided in this paper. A method of feature modeling for discrete Bezier curve and a new fast
Hough transformation for analytic curves using R-Function is presented. The algorithm set up
model of shape parameters from the target bitmap which will be detected. Then it detects the
position, size and direction of a same curve in complex images. The experimental results show
that the algorithm detects any cubic Bezier curve effectively. It has a better accuracy than the
generalized Hough transformation which is wildly used for detecting curves at present.

Key words: Hough transformation, Bezier curve, feature modeling, curve detection