英语翻译define the widths of the Gaussian in the spatial domain

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.

确定宽度高斯在空间域的频率是复杂的血窦.一个众所周知的财产,这些职能是,它们实现的最低可能的联合决议在空间和频域[ 9 ] .加博尔职能形成一个完整的,但非正交基础上制定和任何特定的函数f （ x , Y ）的可扩展方面的这些基础functions.Such的扩大提供了本地化的频率描述,并已用于纹理分析[ 10 ] .地方频分析这种性质的,但不适合功能的代表性,因为它需要一个固定的窗宽的空间,因此频率带宽是恒定的线性规模.为了优化检测和定位功能,不同规模,不同的过滤器的支持,而不是一个固定的1顷需要.这意味着转变类似的小波分解,而不是当地傅里叶变换.我们现在考虑这样一个小波变换的基本小波是一个Gabor函数的形式
（ 2 ）
其中X是空间的宽高比, 0是首选方向.为了简化符号,我们放弃下标X和除非另有说明承担的X = 1 .对应的家庭是小波
（ 3 ）
在Gabor小波变换,然后确定
（ 4 ）
对于实际应用中,离散的参数是必要的.离散参数必须涵盖整个频谱的兴趣.让我们的方向范围[ 0 ]被离散成ñ间隔和规模q参数进行取样指数,因为.这样的结果是小波家庭
（ 5 ）
五结论
在本文中,我们有一个发展一个共同框架,侦查感知显着的特点,如边缘和纹理边界的图片.我们建议一个简单的模型的基础上注重功能检测在不同空间尺度和地方之间的互动功能.之间的互动频道是用于发电的最终抑制这方面发挥着重要作用边界的看法.有几个例子来说明性能的这种方法检测不同类型的边界
鸣谢
我们要感谢教授冯德Malsburg他的建议和鼓励的过程中这方面的工作.我们还要感谢约阿希姆Buhmann ,阿南德拉詹, Sundereshan Chandrashekar芬郑和宝贵的讨论.