Abstract—In order to study some statistical characteristics of matrix addition decomposition, the concept of function addition decomposition and its moments is defined. Theoretically, if the function can be decomposed into the addition of the function sequence, the sum of the moments of the function sequence can be found to be equal to the moments of the original function under certain conditions. Then the property of function decomposition is applied to matrix addition decomposition. If a matrix can be decomposed into the addition of matrix sequence, the sum of matrix sequence moments is equal to that of the original matrix. Finally, the normalized central moments and local normalized central moments of image are calculated. These normalized central moments have scaling and translation invariance, which shows that the function sequence moments can be used to extract local features of images.

Index Terms—Function addition decomposition, function sequence, function moments, matrix sequence, matrix addition decomposition.

Xueshang Nai and Xingyang Xu are with Shandong Vocational College of Foreign Affairs Translation, Shandong, Rushan City, Wei Hai City, Shandong, China (email: xsnai@163.com).
Yumin Tian is with Xidian University, No. 2 South Taibai Road, Xi’an, Shaanxi, China.

Cite: Xueshang Nai, Yumin Tian, Xingyang Xu, "Research on Function Addition Decomposition and Function Moments," International Journal of Applied Physics and Mathematics vol. 9, no. 4, pp. 158-166, 2019.