The Bispectrum as a Source of Phase-Sensitive Invariants for Fourier Descriptors: A Group-Theoretic Approach
The Bispectrum as a Source of Phase-Sensitive Invariants for Fourier Descriptors: A Group-Theoretic Approach
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DOI：
10.1007/s10851-012-0330-6
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发表时间：
2012-11-01
影响因子：
2
通讯作者：
Kakarala, Ramakrishna
中科院分区：
文献类型：
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作者：
Kakarala, Ramakrishna
本文发展了双谱背后的理论，双谱的概念在统计信号处理中得到了很好的确立，但直到最近才扩展到计算机视觉中，作为频域不变量的来源。最近关于在视觉中使用双谱的论文显示了将双谱应用于三维形状的球谐模型时的良好结果，特别是通过改善对先前提出的幅度不变量的区分，以及通过在人体活动检测中检测中性姿势。向量球谐函数的双谱也被表示出来，它已用于医学成像中的三维解剖建模。在这本杂志上发表的一篇论文中，Smach等人。使用对偶理论建立二阶不变量的完备性，如这里所示，它与双谱相同。本文统一了前人的工作，导出了所有紧群的双谱公式。它还提供了从SO(3)上的双谱值恢复函数的构造性算法。主要的理论结果表明，对于紧群的齐性空间，包括球面S(2)这样的重要区域，双谱是不变量的完全来源。
This paper develops the theory behind the bispectrum, a concept that is well established in statistical signal processing but not, until recently, extended to computer vision as a source of frequency-domain invariants. Recent papers on using the bispectrum in vision show good results when the bispectrum is applied to spherical harmonic models of three-dimensional (3-D) shapes, in particular by improving discrimination over previously-proposed magnitude invariants, and also by allowing detection of neutral pose in human activity detection. The bispectrum has also been formulated for vector spherical harmonics, which have been used in medical imaging for 3-D anatomical modeling. In a paper published in this journal, Smach et al. use duality theory to establish the completeness of second-order invariants which, as shown here, are the same as the bispectrum. This paper unifies earlier works of various researchers by deriving the bispectrum formula for all compact groups. It also provides a constructive algorithm for recovering functions from their bispectral values on SO(3). The main theoretical result shows that the bispectrum serves as a complete source of invariants for homogeneous spaces of compact groups, including such important domains as the sphere S (2).