Scale-space properties of the multiscale morphological dilation-erosion

A multiscale morphological dilation-erosion smoothing operation and its associated scale-space expansion for multidimensional signals are proposed. Properties of this smoothing operation are developed and, in particular a scale-space monotonic property for signal extrema is demonstrated. Scale-space fingerprints from this approach have advantages over Gaussian scale-space fingerprints in that: they are defined for negative values of the scale parameter; have monotonic properties in two and higher dimensions; do not cause features to be shifted by the smoothing; and allow efficient computation. The application of reduced multiscale dilation-erosion fingerprints to the surface matching of terrain is demonstrated.