A fast Algorithm of Gaussian filtering for three-dimensional Surface Topography

摘要

The 2D Gaussian filter was realized in approximation method. A fast algorithm of 2D Gaussian filtering is presented to determine the reference surface for 3D surface topography. The 2D Gaussian filter can be separated into two 1D Gaussian filters, an x-direction Gaussian filter and a y-direction Gaussian filter. A 1D Gaussian filter can be implemented approximately by the cascaded moving average filters. More cascaded moving average filters result in higher filtering accuracy. A recursive algorithm for 2D Gaussian filtering is deduced from a moving average algorithm. This algorithm requires only some simple mathematical operations such as addition, subtraction and a small number of multiplications, so that it has considerable computational efficiency which is very important for 3D surface topography measurement.