The Hough transform is useful for detecting or locating translated two dimensional shapes. However

a weakness of the Hough transform is its storage requirements and hence the acutely increased computational complexity resulting from the increased dimension of the parameter space of the shapes. Significant improvement in speed and storage are needed for efficient use of the Hough transform. The size of the parameter space must be reduced significantly to save storage and to minimise the associated search task. In this paper

the concept of boundary dual points of shapes is present and the existence of dual points of symmetric shapes as well as their invariant under translation

scale and rotation are proved. A quick algorithm of the image detection specially for circles and ellipses is presented by combining the dual points with the Hough transform. And the shortcoming of the formula in Ref. is replenished. The experiment examples indicate that this algorithm is easy in use and insensitive for noise and occlusion as the Hough transform and has high calculation speed. It can be flexibly used for some difficult shape detection problems.