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

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