Cube-based calculation of the symmetric transform of Boolean functions

The symmetric transform for Boolean functions is used to determine performances of stack filters in image processing. The standard symmetric transform starts from the function represented by a truth vector. This paper presents a cube-based method for calculation of the symmetric transform of Boolean functions. In the algorithm there are no matrix multiplications. Instead, there are only incrementation of coefficients. The proposed method is more efficient than the matrix method in both storage and execute time.