Wavelet-based gradient transform and its applications

A wavelet-based image gradient transform is proposed. The proposed transform, called multi-scale gradient transform (MSGT), obtains the first order derivative of an image in terms of the wavelet detail coefficients. While traditional methods estimate the image gradients at each wavelet scale in terms of the horizontal and vertical wavelet coefficients only, the proposed transform obtains the gradients in terms of the diagonal, as well as the horizontal and vertical wavelet coefficients. The proposed MSGT is designed to be invertible, non-redundant and computationally efficient. We demonstrate the potential applications of the proposed transform in texture feature extraction, multi-scale edge detection, image quality assessment and image watermarking.