Abstract: In order to reduce the image reconstruction error, a new moment based on fitting Kronecker Dirac function in discrete space is proposed. This moment overcomes the shortcomings of traditional non-orthogonal moments that are difficult to reconstruct and the defects of discrete moments that are used to reconstruct and require resampling. It is named the moment based on Legendre polynomials. The newly proposed moment has good properties in moments error calculation, rotation invariance and so on, especially in the field of large-size images where the current mainstream image moments are not satisfactory. In addition, the ground-breaking anti-noise performance of image moments is explored. By compared with three kinds of moments of current mainstream：Zernike moment, Polar-Fourier moment and Polar Harmonic Transform（PHT） moment, the results show that the rotation invariant performance of the proposed moment is superior. More importantly, the performance of reducing image reconstruction error and improving the noise stability can be improved by at least 22%.

Key words: image moment, rotation invariant moment, image reconstruction, noise resistance, Legendre polynomials, Kronecker Dirac function

摘要： 针对传统非正交矩很难进行图像重建的缺点，以及离散矩用于重建需要重复采样的缺陷，以降低图像重建误差为目标，提出了一种以在离散坐标空间内拟合克罗内克狄拉克函数为核心思想的新形式矩的定义——基于勒让德多项式的矩，并对其性质进行了阐述。这种矩在函数空间非正交却拥有优秀的重建效果，且其在矩计算误差、旋转不变性等多个维度较目前主流矩都具有更优秀性能，特别是在目前主流图像矩表现不尽如人意的大尺寸图像领域。此外，突破性地发掘图像矩的抗噪音性能并加入性能对比。通过与目前主流的三种矩：Zernike矩、Polar-Fourier矩以及Polar Harmonic Transform（PHT）矩的对比实验，证明利用这种基于新思想的矩提取图像特征可以具有更小的信息冗余度及多个维度的鲁棒性，其在旋转不变性、减小图像重建误差以及提高抗噪稳定性方面的性能表现至少可以提高22%。

关键词: 图像矩, 旋转不变矩, 图像重建, 抗噪音, 勒让德多项式, 克罗内克狄拉克函数