Multiscale Derivative Transform and Its Application to Image Watermarking

A transform that estimates the first and higher-order derivatives of images at multiple scales is proposed. The proposed transform, called Multi-Scale Derivative Transform (MSDT), is specially designed for image watermarking applications. To calculate the first and higher-order image derivatives, MSDT uses the detail wavelet coefficients of the image. Unlike traditional wavelet-based image derivative estimators that use only the horizontal and vertical wavelet coefficients, the proposed transform maps the diagonal as well as the horizontal and vertical wavelet coefficients to the horizontal and vertical derivatives of the image. The inverse transform is designed such that any change in the image derivative domain results in the minimum possible change in the wavelet coefficients. This renders a watermark, that is embedded in the derivative domain, less visible in the image domain. The application of this transform to image watermarking is discussed, and the results are compared with those obtained using traditional wavelet-based image derivative estimators.