Gaussian积分 e(ikx)*e(-k‘x^2/2)积分区间无穷,积分变量x,k k'参数

问一句英语翻译：the data from two-class categories with a Gaussian distribution are shown in Fig.1

请帮忙查这篇文章的EI检索号,The Rao Test of Weak Signal in non-Gaussian Clutter.

图像处理英文文献中的一句话,
The difference of Gaussian function is obtained by subtracting image B from A,resulting in a ratio of sqrt(2) between the two Gaussians.请大家帮我翻译一下这句摘自一篇关于图像处理的句子吧.

英语翻译
define the widths of the Gaussian in the spatial domain is the frequency of the complex sinusoid.A well known property of these functions is that they achieve the minimum possible joint resolution in space and frequency domains [9].Gabor functions form a complete but non-orthogonal basis set and any given function f(x,y) can be expanded in terms of these basis functions.Such an expansion provides a localized frequency description and has been used in texture analysis [l0].Local frequency analysis of this nature,however,is not suitable for feature representation as it requires a fixed window width in space and consequently the frequency bandwidth is constant on a linear scale.In order to optimally detect and localize features at various scales,filters with varying support rather than a fixed one are required.This would suggest a transformation similar to wavelet decomposition rather than a local Fourier transform.We now consider such a wavelet transform where the basic wavelet is a Gabor function of the form
(2)
where X is the spatial aspect ratio,0 is the preferred orientation.To simplify the notation,we drop the subscript X and unless otherwise stated assume that X = 1.The corresponding family of wavelets is
(3)
The Gabor wavelet transform is then defined by
(4)
For practical applications,discretization of the parameters is necessary.The discretized parameters must cover the entire frequency spectrum of interest.Let the orientation range [0,] be discretized into N intervals and the scale parameter Q be sampled exponentially as ,.This results in the wavelet family
(5)
5 Conclusions
In this paper we have a developed a common framework for detecting perceptually significant features such as edges and texture boundaries in images.We have suggested a simple model based on detecting oriented features at different spatial scales and on local interactions between features.Interactions between frequency channels is used in generating end-inhibition which plays an important role in boundary perception.Several examples are provided to illustrate the performance of this approach in detecting different types of boundaries
Acknowledgements
We wish to thank Professor von der Malsburg for his suggestions and encouragement during the course of this work.We also would like to thank Joachim Buhmann,Anand Rangarajan,Sundereshan Chandrashekar and Qinfen Zheng for valuable discussions.
急需这篇文章的中文翻译,有些地方没翻译清楚没关系只要读的通畅.