提出了图形边界对偶点的概念，证明了对对称图形对偶点的存在性及其关于平移、缩放和旋转组合变换的不变性；结合Hough变换，建立了一种快速的图象检测方法，详细给出圆和椭圆检测的对偶点算法，并补充了文献[1]中公式的不足，实验结果表明，该对偶点法除保留了Hough变换法的容错性和鲁棒性外，还具有很快的计算速度，而且可以灵活地应用于解决一些较难的图象检测问题。

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.