On Dimensionality in Multiscale Morphological Scale-Space with Elliptic Poweroid Structuring Functions

\Dimensionality" has recently been shown to be an important property in image measurement and image processing operators. It is often thought that morphological operations on an image with \volumic" (non-at) structuring elements lead to the breakdown of dimensionality. After a brief review of a new morphological scale-space, we show here that any dimensional functional of the scale-space image is also a dimensional functional of the underlying image if multiscale structuring functions from the \elliptic poweroid" family, which are in general volumic, are used to construct the scale-space. Further, from a large class of structuring functions, the elliptic poweroids are the only functions that preserve dimensionality.