Two-Dimensional Period Estimation by Ramanujan's Sum

Period estimation in one dimension (1-D) has been studied for years. However, 2-D period estimation is still a hard problem since it has three parameters to determine: length, width, and direction. Recently, a special kind of 2-D function called 2D-gcd-delta function is proposed. It has close relationship with Ramanujan's sum and the 2-D periodicity matrix. In this paper, we will describe how to use this function to decompose an image into subband signals. Each subband signal will have its own periodicity matrix so we also provide a simple algorithm to calculate the least common multiple (LCM) of those subband signal periodicity matrices. Concrete experiments are given to prove the robustness of the proposed 2-D period estimation method.