This paper proposes a novel technique to reduce noise while preserving edge sharpness during image filtering. This method is based on the image multiresolution decomposition by a discrete wavelet transform, given a proper wavelet basis. In the transform space, edges are implicitly located and preserved, at the same time that image noise is filtered out. At each resolution level, geometric continuity is used to preserve edges that are not isolated. Finally, we compare consecutive levels to preserve edges having continuity along scales. As a result, the proposed technique produces a filtered version of the original image, where homogeneous regions appear separated by well-defined edges. Possible applications include image presegmentation and image denoising.