This paper has presented two image processing applications, compression and watermarking, by exploiting the localization property of wavelet transform. The first application proposes a simple region-based and scalable image compression algorithm. We locate the wavelet coefficients in the region of interest in each subband, and these groups of wavelet coefficients are used to adjust the resolution of the interested region. A watermarking method is described in the second application of this paper. The scheme examines the variations of the local Hölder regularity of the image and calculates the similarity of the correct watermark before and after modifications. Experimental results show that the proposed approach is quite effective in authenticating the origin of an image.