Mathematics in image processing combining wavelet analysis and numerical method with guaranteed accuracy

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We propose new blind digital image watermarking methods based on interval arithmetic (IA) and shift-invariant wavelets such as the dyadic wavelet transform (DYWT) and the dual-tree complex discrete wavelet transform (DT-CDWT). Our method produces watermarked images that have better quality and are robust with respect to attacks on the following types: marking, clipping, image compressions, rotation, resizing and so on. We also prove that high-frequency components obtained using the DYWT based on IA (IDYWT) contain low-frequency components. Based on this property,We develop new digital image watermarking methods for authentication based on the IDYWT. This method is a kind of content-based watermarking, because it generates a watermark from the host image and authenticates the test image by comparing two types of watermarks constructed using the test image. Our method produces high-quality watermarked images and can locate the areas that have been tampered with.