Key points are not available for this paper at this time.
Decomposition by extrema is put into the context of linear vision systems and scale-space. It is proved that discrete one-dimensional, M- and N-sieves neither introduce new edges as the scale increases nor create new extrema. They share this property with diffusion based filters. They are robust and preserve edges of large scale features.
Bangham et al. (Wed,) studied this question.