广义零阶矩

广义零阶矩(论文7000字)
摘要：图像矩是最常用的提取不变特征技术，然而高阶矩对噪声敏感，另一方面，作为最低阶矩的零阶矩只能用来规范化其它矩构造的量使之成为不变量，因而零阶矩无法直接用来构造不变量。本文从另外一个角度研究了零阶矩，在极坐标系中，零阶矩其实是一闭合曲线所围区域的面积，基于此本文将传统零阶矩推广为广义零阶矩，这种广义零阶矩定义为含有两个参数的闭合曲线所围区域的面积，参数只要满足条件，所提出的广义零阶矩即为仿射不变的。实验结果表明，由广义零阶矩提取的仿射不变特征比使用传统矩提取具有更强的抗噪性能。
关键词：仿射变换，广义零阶矩，不变量，特征提取，抗噪性。

The Generic Zero Order Moments
Abstract：Moment method is the widely used technique for the extraction of invariant features.But moments become very noise sensitive with increasing order. The zero order moment, which is the lowest order moment can only be used to normalize quantity derived by other moments for achieving invariance. In this paper, the zero order moment is studied from a different perspective. It is reviewed in polar coordinate system. Then, zero order moment is in fact the area of region enclosed by a closed curve. Generic zero order moment (GZOM), which is the generalization of traditional zero order moment, is defined as the area of region enclosed by closed curve with parameters. Conditions on these parameters have been developed such that affine invariants can be constructed by these GZOMs. Experiment results demonstrate that the affine invariants constructed by lower degree GZOMs have stronger robustness than using traditional moments.

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Key words：Affine transformation, generic zero - order moment, invariant, feature extraction, robustness.
目 录
1.引言    1
2.广义零阶矩    2
2.1.传统矩    2
2.2.广义零阶矩    2
2.3.广义零阶矩的性质    4
3.基于广义零阶矩的仿射不变量提取    4
3.1.仿射变换    4
3.2.广义零阶矩的仿射不变性    6
4.实验结果    8
4.1.仿射不变性的测试    9
4.2.抗噪性能的测试    10
4.3.目标识别    12
5.结论    14
参考文献    14
致谢    16

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