Hough transform (HT) is a typical algorithm used for the detection of lines or line segments. The generalized HT can be used for detection of complex 2D polygons

but it needs voting in 3 or more dimensions. This results in the need of large memory space and long computing time. And some of its variations

in which the derivative/gradient information of the image is needed

are sensitive to noise in images

so that the robustness of the methods decreases. This paper presents a unified approach based on Hough Transform for quick detection of planar rectangles and circles. The presented approach introduces a geometrical invariant — the Shape Angle Dα

and makes good use of geometric properties of polygons for roughly classifying shapes of closed edges that are detected by Canny detector. It does not need any derivative/gradient information of images but simple computation and only 1D or 2D votes to improve the robustness and speed up the computation of the algorithm presented. Finally

it is shown by the experiments that this approach can be used for detecting various planar regular polygons

and it is not only quick but also accurate.