Probabilistic comparisons of morphological dilation and erosion with their equivalent linear shift-invariant systems in the case of a memoryless uniform source

This correspondence compares dilation and erosion with their spectrally equivalent affine-linear shift-invariant system in probabilistic characteristics in the case of a memoryless uniform source. The equivalent system, which is derived through spectral factorization, turns out to be of a finite-impulse-response filter and has a much smoother probability density than dilation.