Abstract: Deterministic hierarchical approaches in image analysiscomprise two major sub-classes: the multiresolutionapproach and the scale-space representation. Bothapproaches require either a coarse-to-fine explorationof the hierarchical structure, or a careful selectionof a single analysis parameter, but neither one takesfull advantage of the hierarchical structure (the endresult is obtained at only one analysis level). Toovercome this limitation, we propose an explicithierarchical-based model in which any image primitiveis expressed as a finite sum of mobile wavelets (MW),which are defined as wavelets whose dilation,translation and amplitude parameters are allowed tovary. This description derives from an adaptivediscretization of the continuous, inverse wavelettransform. First, the MW-based representation is usedwithin the framework of active contour modeling. Theprimitive corresponds to a deformable, parametrizedcurve expressed as a sum of MWs. The initial curve isrefined by updating the three parameters of each MW inorder to minimize the intensity gradient along theactive contour. Surface reconstruction is alsoaddressed by the MW approach. In this case, theprimitive, the intensity function, is expressed as asum of MW whose associated parameters are estimatedfrom the noisy data by minimizing a regularizing energyfunctional. !37
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