Mobile wavelet method: application to active contour modeling and surface reconstruction

Deterministic hierarchical approaches in image analysis comprise two major sub-classes: the multiresolution approach and the scale-space representation. Both approaches require either a coarse-to-fine exploration of the hierarchical structure, or a careful selection of a single analysis parameter, but neither one takes full advantage of the hierarchical structure (the end result is obtained at only one analysis level). To overcome this limitation, we propose an explicit hierarchical-based model in which any image primitive is expressed as a finite sum of mobile wavelets (MW), which are defined as wavelets whose dilation, translation and amplitude parameters are allowed to vary. This description derives from an adaptive discretization of the continuous, inverse wavelet transform. First, the MW-based representation is used within the framework of active contour modeling. The primitive corresponds to a deformable, parametrized curve expressed as a sum of MWs. The initial curve is refined by updating the three parameters of each MW in order to minimize the intensity gradient along the active contour. Surface reconstruction is also addressed by the MW approach. In this case, the primitive, the intensity function, is expressed as a sum of MW whose associated parameters are estimated from the noisy data by minimizing a regularizing energy functional.