Complex NSST Based On Projection And Its Applications In Image Analysis

Multiscale and multidirectional transform has been widely used in the field of image processing.The earlier multiscale geometric analysis have devoted to studying higher directionality,anisotropy and the optimal sparse representation of multidimensional images.Shearlet is a multiscale multidirectional transform method developed in recent years,inheriting the advantages of previous multiscale geometric analysis methods.Complex wavelets transform can obtain the phase information of the subband coefficients compared with the real-valued wavelets transform,which improves the accuracy of the representation of images.Relative phase is an effective expansion of the phase information in complex wavelets transform,which indicates the phase difference between adjacent subbands.This paper studies the complex multiscale and multidirectional analysis in complex wavelets transform and the applications of its relative phase and magnitude in image analysis.The main contents of this paper are as follows:Firstly,we propose a complex wavelets transform based on projection,complex NSST is developed based on Non-subsampled Shearlet Transform and projection.Projection is adopted to create an analytic signal(image),the real part and imaginary part of analytic signal can form a precise Hilbert pair.NSST is developed based on the multiscale and multidirectional transform and the desampling operation which can realize the translation invariance.Secondly,by studying the shortcomings of dual-tree complex wavelet(DTCWT)and pyramidal dual-tree directional filter bank(PDTDFB),we find that precise relative phase can be achieved from the complex wavelets transform which satisfies following three conditions: 1)precise Hilbert relationship between real and imaginary parts of complex wavelet coefficients;2)squared subbands of complex wavelets which ensure unbiased reference directions and 3)arbitrary direction selectivity which decomposes a signal with optimal basis.Thirdly,we obtain relative phase information from complex NSST,the availability and accuracy are verified by its use in texture retrieval.Complex NSST inherits the arbitrary direction selectivity of Shearlet transform,and the reference directions of the subband coefficients are unbiased,and the projection operation guarantees the precise Hilbert transform relationship.Thus these conditions guarantee that we can obtain precise relative phase information.Lastly,we combine the magnitude and relative phase in complex NSST into a new feature,and the availability and accuracy are verified by its use in text localization.The magnitude and phase in complex wavelet coefficients are extremely important features in image processing,thus the combination of magnitude and relative phase can accurately characterize the structure of images.The higher retrieval rates in texture retrieval verify the accuracy of relative phase in complex NSST,and the combination of magnitude and relative phase can locate correct text regions in text localization which verifies the rationality and accuracy of the combined feature in complex NSST.