Design of Gaussian filters based on odd and even functions used for non-closed circular profile

In order to solve boundary effect for non-closed circular profile with conventional Gaussian filter, two modified Gaussian filters based on odd and even functions are put forward. By extending original profile data on the boundary effect area, the sampling information on the boundary effect area of non-closed circular profile can be used fully, and then open-loop Gaussian filter is used for filtering. The validity of two designed filters was tested by numerical simulation and experiment. The results demonstrate that the modified Gaussian filter based on even function is more effective to reduce boundary effect than that based on odd function.