While using conventional two-dimensional wavelet transform for texture analysis and classification the image decomposition is carried out with separable filtering along the abscissa and ordinate using the same pyramidal algorithm as in the one-dimensional case. This process is simple and can be implemented easily in practical applications, however, it is rotation-sensitive and some information may be lost since the decomposition is performed only in low frequency channels. In this paper the quincunx transform using nonseparable sampling and filters is substituted for conventional dyadic transform. Since the energy of natural textures is mainly concentrated in the mid-frequencies, this transform can preserve more of the original signal energy and can provide more reliable description of the texture. At the same time, the tree-structured wavelet transform or wavelet packets is applied instead of using the pyramid-structured one. With this transform, we are able to zoom into any desired frequency channels for further decomposition and a series of subimages with the largest energy can be obtained for an image. In comparison with conventional wavelet transform, it can be concluded that this transform can still reach higher classification accuracy especially for the characterization of noisy data.
The problem of electromagnetic wave scattering from randomly rough surfaces has been studied using both low- and high-frequency approximations. It has been recognized that scattering at small incident angles seemed to follow the high-frequency solution based on the Kirchhoff approximation (KA), and at large incident angles the small perturbation method (SPM) appears to explain the measurements better. However, for very rough surfaces with large rms height and rms slopes around unity or more, both of them failed to give satisfactory results. In this paper the integral equation model (IEM) is introduced to solve the electromagnetic scattering from very rough surfaces. It can be shown that the IEM not only can describe the single scattering but can interpret the multiple scattering well. In addition, the upward and downward multiple scattered wave are identified when taking multiple scattering into consideration, therefore it is possible to assign the correct shadowing effect to multiple scattering calculation. By numerical calculation the phenomenon of backscattering enhancement can be observed and the results are in good agreement with experimental data.
A numerical study of scattering from 2D ocean-like surfaces is presented in this paper. Fist a new model for generating 2D fractal rough sea surface is introduced. This model incorprates the spectrum into fractal mode,, thus it can apply to any forms of sea spectrum. In this paper the Semi- Empirical Sea-Spectrum proposed by AK Fung is chosen for its simplicity. Afterwards, an improved composite surface model is developed to calculate the scattering coefficient. In this mode,, we calculate the value of slopes at each point of the large-scale roughness using numerical method, therefore avoid assuming the probability density distribution of slopes in the conventional composite surface mode. Afterwards, the ray-tracing method is adopted to predict the intensity of light scattered from rough sea surface, which helps to probe the sea surface's microstructure. Moreover, we make a study of the shadowing of each point on the surface by tracing the incident and scattered wave, and can get the ratio of the number of points unshadowed to the total number, i.e. the shadowing function. Finally an analysis of the amplitude characteristics and fractal characteristic of the scattered wave from sea surfaces is made, which are of great significance for distinguishing and detecting targets on the sea.
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