A Bi-Scale-Space for the Analysis of Blobs

We present a scale-space with separate scales in the greyscale and spatial dimensions, using ideas from mathematical morphology. Dynamics are used for greyscale (luminance) filtering and openings or closings with scaled disks for spatial scaling. Dynamics cater naturally for the inclusion relationships between regions and give a very good measure of the salience (scale) of a region in greyscale terms however dynamics lack any notion of spatial extent or scale. In contrast, spatial closings or openings with scaled flat disks provide a natural measure of size or spatial scale without regard to greyscale variation. The two techniques together both monotonic with respect to scale provide a full basis for analysis of the image. We show the strict monotonicity properties of these operations, that is, the strict reduction of number and size of regions with increasing scales, and we give an example of use in the classification of textures.