摘要
自从Hong于1991年把奇异值(SV)代数引入图像识别中以来,奇异值作为良好的模式特征得到了广泛的研究和应用。Hong阐明了图像矩阵奇异值具有很多优良特性,也得出了图像矩阵奇异值具有旋转不变性这一结论。然而,在分析研究中发现,该结论的论证是建立在错误的前提基础上的。本文首先从空间解析几何与矩阵理论对此进行了详细分析,依据实例计算结果进一步引出了相反的结论。最后,提出了用图像矩阵的极变换来重建奇异值的旋转不变性,并给出了理论和实例证明。该研究结果保证了奇异值可作为通用图像特征用于目标识别。
Since Hong introduces the Singular Value (SV) algebra into Image Recognition in 1991, the SV vector as excellent pattern feature has been widely studied and applied. Hong’ article gives many excellent characteristics of the singular values extracted from an image matrix, and reaches the conclusion that the singular values are invariant to rotation. But, based on analysis and study, the authors find out that the argument for this conclusion begins with an incorrect premise. In this article, we, firstly, give detailed discussion on this point from both perspectives of Analytical Geometry and Matrix Theory, and, furthermore, come to inverse conclusion with instance calculation results. Then, a method is proposed to maintain the necessary rotation invariance by transforming image matrix to polar coordinate form followed by the proven of the effectiveness in theory and with numeric calculation results. The results of this study still hold the generality of singular value method for object recognition.
出处
《中国图象图形学报》
CSCD
北大核心
2005年第6期717-720,共4页
Journal of Image and Graphics
基金
国家"863"项目(863-2.5.1.25)
关键词
图像矩阵
奇异值
旋转不变性
极变换
image matrix, singular values, rotation invariance, polar transform
