A LOCALLY SUPPORTED WAVELET WITH INFINITELY HIGH REGULARITY AND FAST ALGORITHM FOR EDGE DETECTION
Li Cui · Chinese Journal of Computers · 1999
According to I.Daubechies' theory,the regularity of orthonormal wavelet bases with compact support increases linearly with the support width.By relaxing the orthogonality,much more freedom on the choice of wavelet function is gained.In this paper,an infinitely differentiable wavelet with a local support is proposed.Its properties are different from those of orthonormal wavelet bases.The wavelet is derived from the first or second order derivatives of a radial function.It is then proven that the wavelet is a two dimensional dyadic one.Consequently,an arbitrary square integrable function can be reconstructed from its dyadic wavelet transformation,and the reconstruction is stable.Different from tensor product multidimensional wavelets,this wavelet is inseparable.As an example of application,an algorithm is developed for detecting edges in image by finding the local maxima of its wavelet transform modulus.The computation of the wavelet transform in image processing depends only on the wavelet functional values at a few integer points. For a N×N image,the computational complexity of the detection scheme is O(N 2) ,which is significantly better than the order O(N 2 log N ) by using Mallat's fast wavelet algorithm. Numerical experiments indicate that the wavelet transform given here can be used in computer vision and real time processing, such as edge detection, feature extraction, and texture analysis.