Relative Phase In Texture Retrieval

This paper studies the structures of complex wavelet transforms in the implementation of relative phase (RP). The RP feature is a new kind of multiscale feature to exploit the phase information from2-D complex wavelet coefficients for image modeling. For many image processing tasks, a rich, reliable and precise representation of the location of features is essential. Compared with conventional real-valued wavelets, complex wavelets which are able to provide both magnitude and phase information have shown a consistently representation to the structures of images. The magnitudes of complex wavelet coefficients indicate the amplitude of features while the phases indicate the locations of these features. Then we develop two new complex wavelet transforms based on the discrete shearlet transform, named as dual tree shearlets and p-shearlets respectively. The contents of the study include three parts that are as follows in detail.In part one, we focuses on the study of RP. The RP is an efficient approach to exploit the phase information of complex wavelet coefficients. However, the RP original generated from the pyramidal dual tree directional filter bank has three defaults. Firstly, its texture retrieval performance does not simultaneous improve in general as the scale and direction increasing. Secondly, for the reason that the directional subbands in PDTDFB are not uniform downsampled along row and column, they cannot ensure the unbiased reference direction for the features of original image, thus the RP model is not accurate enough. Thirdly, its number of directions is not optimal. Then we describe three properties of the desired transform for RP.Part two is about the structure of new complex wavelet transform. We construct the dual tree shearlets by combing the dual tree complex wavelet transform (DTCWT) and shearlets. The transform is based on the discrete shearlet transform, but a dual tree Laplacian pyramid is adopted to create a real-imaginary pair structure for deriving phase information under multiscale framework. The new multiscale and multi-direction transform has the properties of uniform downsampled subbands; higher directional sensitivity and the2-D Hilbert transform relationship between two channels as the DTCWT. Part three continues with the constructing of new complex wavelet transform with another method. The p-shearlets first project a real signal into an analytic signal and then the discrete shearlet transform is applied on it. For real-valued two-dimensional images, we filter the columns or rows of it with a projecting filter. By this operator, we eliminate the redundant information carried by negative half-plane of the Fourier transform and obtain a complex-valued spatial image. Applied the discrete shearlet transform on real part and imaginary part of it respectively, we achieved the p-shearlets coefficients in each directional subband. In above two transforms subbands the RP model is accuracy enough in multiscale and multi-direction.We present the numerical experiments to demonstrate that the RP of our proposed methods outperforms that of the PDTDFB in texture retrieval application both in terms of performance and computational efficiency. The results does conform our previous suspicions on the formal RP. Comparing with the RP defined in PDFTFB, our work exploits the multiscale characteristic, with uniform downsampled subbands, flexible directional sensitivity. Thus the dual tree shearlets and p-shearlets do have advantages and provides a more appropriate representation for the implementation of RP.