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Edge Detection Using Discrete Complex Wavelet Transform
H. Rabbani, M. Vafadoost, and S. Kasaie

Department of Medical Physics and Biomedical Engineering, Isfahan University of Medical Sciences
Faculty of Biomedical Engineering, Amirkabir University of Technology
Department of Computer Engineering, Sharif University of Technology

Abstract: Analysis and interpretation of medical images are of clinical importance for medical diagnosis and treatment while they also have technical implications for computer vision and pattern recognition. In this context, one of the most fundamental
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issues is the detection of object boundaries, which is often useful for further processes such as organ/tissue recognition, image registration, motion analysis, measurement of anatomical and physiological parameters, etc. Although one of the best methods of edge detection is based on wavelet transform, the standard wavelet transform has its own shortcomings such as lack of shift invariant and lack of directional selectivity in sub-bands in multidimensional applications. The discrete complex wavelet transform, which is based on complex mother wavelet, not only overcomes these shortcomings but has acceptable redundancy and complexity as well. It is especially useful for multidimensional situations and for high accuracy applications such as medical image processing. In this paper, the shortcomings of ordinary wavelet transform are initially investigated and comparisons are made between the standard wavelet and the complex wavelet. Then, the discrete complex wavelet domain is applied for image enhancement and edge detection of noisy images. The simulation results show that our method exhibits a better performance, especially in noisy cases, as compared with the standard wavelet and spatial methods.

Keywords: Image processing, Edge detection, Complex wavelet transform, Noise reduction.

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