Dynamic Scale-Space Paradigm
نویسنده
چکیده
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 paradigm. Dynamic here refers to a redistribution and recombination of this set and does not correspond to whether the images are static or spatio-temporal. The class of dynamic scale-space theories is constrained by exchange principles for the curvatures and derived equivalences over the image and by invariance conditions. In the context of these theories the concepts of a metric, connection, diiusion operator, curvatures and equivalences are the essential physical objects. Our dynamic scale-space paradigm extends existing scale-space theories 17] considerably. Firstly it delivers a mean to quantify the image formation in terms of curvatures and equivalences. Secondly, these curvatures and equivalences can be subjected to (categorical) ows on the basis of exchange principles for themselves. The latter principles strongly deviate from statistical annealing principles 6]. Furthermore, our paradigm allows a straightforward generalisation of mathematical morphological paradigms 18] in particular if gauge invariance is required.
منابع مشابه
Dynamic Scale - Space Paradigmversusmathematical Morphology ?
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...
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