The Construction And Applications Of Wavelet-Based Edge Detector

Wavelet-Based edge detection has being surprisingly developed both in pure theory and application because wavelet transform has prominent abilities of multi-scale edge detection. Based on the development, this article's main contribution include research on wavelet theory, selection and construction of wavelet edge detector and wavelet-based adaptive edge detection for noisy aerial image.To begin with , an adaptive wavelet transform that maps integers to integers is presented in this paper. The wavelet transform that maps integers to integers is constructed generally by lifting schemes. Also basing on the adaptive lifting scheme with perfect reconstruction, we get the adaptive transform. Using lifting scheme presented by G. Piella, it is difficult to construct transform that maps integers to integers because of restrict on the sum of coefficients of update step. In order to get the transform, results is extended to more general cases. The adaptive transform treats edges and homogeneous regions in image differently , furthermore, if input signals are integers, the transform has no truncation error. These properties have important applications in compression of digital image.At the second place, feasibility of edge detection based on orthogonal wavelet is discussed in the article. It's theoretical key of edge detection based on orthogonal wavelet that approximate symmetrical or antisymmetrical orthogonal real wavelet can be constructed though Haar wavelet is the only symmetrical or antisymmetrical orthogonal real wavelet. With discrete exoression of canny's criteria, a new orthogonal wavelet edge detector can be derived via constrained optimization.On the part of construction of biorthogonal wavelet used for edge detection, also using the discrete expression of canny's criteria as restrictive condition, two biorthogonal wavelet edge detector are derived by lifting scheme and by system of equations, respectively. Furthermore, detection quality of these edge detectors derived in this paper are superior to the results derived by Hong-Yuan Mark Liao, etc both in experiments and theoretical analysis besides the criterion of good localization.At the end of this article, an algorithm used to detect aerial image's edge contaminated by addictive noise is discussed. Using statistical characteristic of contaminated aerial image's wavelet coefficients and multiresolution decomposition of wavelet transform, shrinkage factors is constructed and edge or noise is discriminated by it. Furthermore, through the maximum likelihood used for evaluating three parameters of wavelet coefficients' probability model, the adaptive algorithm is derived in the article. Results of the adaptive algorithm used for contaminated aerial image is satisfactory.