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中文摘要：
该文定义了一类以Franklin函数为核的正交矩,称之为Franklin矩.Franklin函数是一类完备正交一次样条函数系.传统的Legendre矩、Zernike矩等多项式矩,由于涉及高次多项式的计算,往往会导致计算不稳定,特征空间维数扩展受到制约.Franklin函数是正交的,相应的矩函数可以使得图像分解后的信息具有独立性,没有信息的冗余.而且,Franklin函数仅由一次分段多项式组成,在计算过程中,避免了高次多项式的计算,兼具复杂度低、数值稳定的优点.通过对图像的重构实验表明,Franklin矩比传统正交多项式矩具有更好的特征表达能力.
英文摘要：
A set of novel orthogonal moments named as Franklin moments is proposed in this paper. The kernel functions of Franklin moments are Franklin functions which composed of a class of complete orthogonal splines function system of degree one. For digital images, the traditional polynomial moments such as Legendre moments and Zernike Moments could cause numerical approximation error because of the calculation for high order polynomials. In contrast, Franklin function system is composed of a series of orthogonal piecewise polynomials of degree one. There-fore, it provides possibility of avoiding calculating high order polynomials, and thus the exact values of Franklin moments can be obtained directly with smaller calculation effort. Experimental results show that images reconstructed from Franklin moments have lower error than that of the conventional orthogonal polynomial moments.
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