It is argued that the mathematical morphology method seems to be more reasonable and powerful in studying certain multiscaling vision problems than the approach that uses derivatives of Gaussian-shaped filters of different sizes. To show the validity of this method, the authors concentrated on an application that involves forming scale-space image of a 2-D shape using morphological opening filtering. A proof is given to show that morphological opening filtering has a property of not introducing additional zero-crossings as one moves to a coarser scale. This is a different result from the conclusion by A.L. Yuille and T.A. Poggio (ibid., vol.PAMI-8, Jan. 1986) that the Gaussian filter is the only filter with this property. In addition, opening filtering is computationaly simpler than the Gaussian filter.>

A novel smoothing filter is proposed for directional filtering, based on the optimal linear estimate and the multispike model. Because of differential operators being sensitive to noise in images, it is preferable to use bandpass filters that are insensitive to noise and have a good precision of line localization. Experiments are described that demonstrate that the images filtered are less noisy and have better precision than those filtered by the directional filter. The experimental results are very satisfactory with many images.>