# American Institute of Mathematical Sciences

September  2007, 6(3): 899-915. doi: 10.3934/cpaa.2007.6.899

## Edge detection by using rotational wavelets

 1 Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira, Taipa, Macau, Macau 2 Department of Image Engineering, Chinese Academy of Sciences, Beijing 100101, China

Received  February 2006 Revised  March 2007 Published  June 2007

Based on a mathematical model involving Radon measure explicit computations on convolution integrals defining continuous (integral) wavelet transformations are carried out. The study shows that the truncated Morlet wavelet significantly depends on a rotation parameter and thus lay a foundation of edge detection in pattern recognition and image processing using rotational (directional) wavelets. Experiments and algorithms are developed based on the theory. The theory is further generalized to the $n$-dimensional cases and to a large class of rotational wavelets.
Citation: Liming Zhang, Tao Qian, Qingye Zeng. Edge detection by using rotational wavelets. Communications on Pure & Applied Analysis, 2007, 6 (3) : 899-915. doi: 10.3934/cpaa.2007.6.899
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