The scaling of physical, biological, ecological, and social phenomena is a major focus of efforts to develop simple representations of complex systems. Much of the attention has been on discovering universal scaling laws that emerge from simple physical and geometric processes. However, there are regular patterns of departures both from those scaling laws and from continuous distributions of at...

Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simpliication of the set of construction rules is proposed by applying a dynamic scale-space theory. Dynamic he...

4 Colour connected filters 11 4.1 Colour area morphology scale-spaces . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1.1 Colour Extrema . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.1.2 Distance metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4.2 Convex Colour Sieve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.3 Vecto...

In this paper, we propose a robust fully non-supervised method dedicated to the segmentation of the brain in T1-weighted MR images. The first step consists in the analysis of the scale-space of the histogram first and second derivative. We show first that the crossings in scale-space of trajectories of extrema of different derivative orders follow regular topological properties. These propertie...

This work presents some new results on the morphological scale-space theory and their use in image segmenta-tion. Basically, we introduce an idempotent smoothing operation based on the recently proposed multiscale-morphological-dilation-erosion method, and analyse some of its features concerned mainly with monotonic-ity and the way the image extrema merge in a multi-scale simpliication process.

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...