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Image representation by level crossings of the wavelet transform

Images are decomposed by the visual systems into several spatially oriented frequency channels. Such a decomposition presented in the context of multiresolution analysis, provides a powerful tool for image processing. This study is devoted to multiresolution representation by partial information of the wavelet transform. A theorem defining the conditions necessary for the zero crossing representation to be stable and complete, is presented. This theorem is based on the properties of the multiresolution theory, using orthonormal wavelet functions. An iterative fast reconstruction algorithm, which is easy to implement, is presented and illustrated by examples.