本文从信号处理与分析的实际需要出发，对二进小波的构造问题进行了研究，成功地构造出了适合作边缘检测和描述的两类具有零对称性的二进小波：一类是以零点为对称点的对称二进小波，另一类是以零点为反对称点的反对称二进小波，这些结果丰富了二进小波的理论，并为利用二进小波进行边缘检测打下了坚实的基础，还从计算理论和算法两个方面讨论了这两类二进小波在边缘检测，分类及刻画中的应用。理论分析和实验结果都表明，基于二进小波变换的边缘检测，分类与描述算法，具有计算复杂度低，速度快，抗噪声能力强等优点。

In this paper we construct two types of dyadic wavelets suiting for edge detection and description: one is zero-symmetrical,the other is zero -antisymmetrical. These results have enriched the theory of dyadic wavelet and laid a solid foundation for properly applying dyadic wavelet to edge detection and description. Then the application of dyadic wavelet to edge detection, classification and description are studied from computation theory and algorithm aspects. Experimental results are also given to show the effectiveness.