图像处理中一些实际函数的不确定度分析

J. Bloom, T. Reed
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引用次数: 13

摘要

在图像处理和压缩中,使用在空间和空间频率上都是局部的分析函数可以获得许多好处。通常假设这些好处在某种程度上与所使用的函数的关节局部性成正比。在不确定性原理的限制下,在不同的局部函数族中,这个联合局部性可能有很大的变化。虽然没有普遍接受的适合于视觉应用的关节局部性度量,但Gabor的关节不确定性经常被引用来证明一组函数的使用是合理的。结果表明,复Gabor函数优化了该度量。然而,关于受限实数函数中哪一类具有最低的联合不确定性,存在一些争论。本文研究了三种实函数族,并直接评价了联合不确定度的Gabor度量。与以前试图证明任何一个函数的最优性不同,这种分析为比较这些实际函数提供了明确的数值基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An uncertainty analysis of some real functions for image processing applications
There are many benefits to be gained in image processing and compression by the use of analyzing functions which are local in both space and spatial frequency. It is often assumed that these benefits are in some way proportional to the degree of joint locality of the functions being used. Within the limits imposed by the uncertainty principle, there can be great variation in this joint locality across different local function families. While there is no generally accepted joint locality metric appropriate for visual applications, Gabor's joint uncertainty is often cited to justify the use of a set of functions. It has been shown that complex Gabor functions optimize this metric. There is some debate however regarding which, of the restricted class of real functions, has the lowest joint uncertainty. In this paper we examine three families of real functions and directly evaluate the Gabor metric for joint uncertainty. In contrast to previous attempts to prove the optimality of any one function, this analysis provides an explicit numerical basis for comparison of these real functions.
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