American Institute of Mathematical Sciences

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

Edge detection by using rotational wavelets

Liming Zhang 1, , Tao Qian 1, and  Qingye Zeng 2,

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.
Keywords: edge detection, Radon measure, Morlet wavelet, Rotational wavelets.
Mathematics Subject Classification: 37C45.
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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