摘要
In this paper, it is argued that the mathematical morphological method seems to be morereasonable and powerful in studying vision problems than Marr ’s approach which uses deri-vatives of Gaussian-shaped filters in different sizes. To show the validity of this method,an application is given to form scale-space image of a 2-D shape employing morphologicalopening filtering. Proof is given to show that the morphological opening filter has the pro-perty of not introducing additional zero-crossings as one moves to coarser scale. This con-tradicts the conclusion by Poggio et al. that the Gaussian filter is the only filter with thisremarkable property. Besides, the opening filter is computationally simpler than theGaussian filter.
In this paper, it is argued that the mathematical morphological method seems to be morereasonable and powerful in studying vision problems than Marr 's approach which uses deri-vatives of Gaussian-shaped filters in different sizes. To show the validity of this method,an application is given to form scale-space image of a 2-D shape employing morphologicalopening filtering. Proof is given to show that the morphological opening filter has the pro-perty of not introducing additional zero-crossings as one moves to coarser scale. This con-tradicts the conclusion by Poggio et al. that the Gaussian filter is the only filter with thisremarkable property. Besides, the opening filter is computationally simpler than theGaussian filter.
