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Hierarchical SegmentationDuring resolution reduction by diffusion, local signal variations smooth out as ''time'' t proceeds. Extrema disappear one after the other (only rarely a new on in created, see [6]), and finally only the strongest signal variations survive. Thus a hierarchical ordering of extrema is induced by the diffusion process. The images f(x,y;t) obtained from the original
data f(x,y;t) obey further a concept of causality
[3]: every value From Thom's theory it follows that every such event has qualitatively the same generic form [3]. Since f(x,y;t) is a one-parameter family of functions in t, the only possible way to change is given by the so-called fold catastrophe, generically described through the function
In figure 2 the contour sheets
of this function are displayed near a critical value
Figure 2: The change of the topology of contour sheets near a critical
value For Between critical values, all surfaces are similar and can be continuously
deformed into each other. We thus have an onion-like, hierarchical structure
of contour sheets, changing topology only at a few critical values Several schemes have been proposed for exploiting the structure of scale
space [3, 6,
7]. Most approaches need a very dense
sampling of scale space and are therefore computationally expensive. Furthermore,
the connection with biological vision systems is not clear. We propose
here a single and simple neuronal mechanism for utilizing scale space:
the tracing and merging of contour sheets in scale space by neuronal oscillators.
Within this ansatz, neurons distributed over scale space at discrete points
Comments are welcome! © 1997 by Rolf Henkel - all rights reserved. |