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

提出了一种基于区间算术(IA)和二进小波变换(DYWT)、双树复离散小波变换(DT-CDWT)等平移不变小波的数字图像盲水印新方法。我们的方法生成的水印图像具有更好的质量，并且对以下类型的攻击具有鲁棒性：标记、剪切、图像压缩、旋转、调整大小等。我们还证明了利用基于IA的DYWT(IDYWT)得到的高频分量包含低频分量。基于这一特性，我们提出了一种新的基于IDYWT的数字图像水印认证方法。该方法是一种基于内容的水印方法，因为它从宿主图像生成水印，并通过比较使用测试图像构造的两种类型的水印来认证测试图像。我们的方法生成高质量的水印图像，并可以定位被篡改的区域。

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.