| Summary: | Multi-order image derivatives are used in many image processing and computer vision applications, such as edge detection, feature extraction, image enhancement, segmentation, matching, watermarking and quality assessment. In some applications, the image derivatives are modified and then inverse-transformed to the image domain. For example, one approach for image denoising is to keep the significant image derivatives and shrink the non-significant derivatives. The denoised image
is then reconstructed from the modified derivatives. The main challenge here is how to inverse-transform the derivatives to the image domain. This thesis proposes different algorithms to estimate the image derivatives and apply them to image denosing , watermarking and quality assessment. For noisy color images, we present a method that yields accurate and robust estimates of the gradient magnitude and direction. This method obtains the gradient at a certain direction by applying a prefilter and a postfilter in the perpendicular direction. Simulation results show that the proposed method outperforms state-of-the-art methods. We also present a multi-scale derivative transform, MSDT, that obtains the
gradient at a given image scale using the detail horizontal, vertical and diagonal wavelet coefficients of the image at that scale. The inverse transform is designed such that any change in the image derivative results in the minimum possible change in the image. The MSDT transform is used to derive a novel multi-scale image watermarking method. This method embeds the watermark bits in the angles of the significant gradient vectors, at different image scales. Experimental results show that the proposed method outperforms other watermarking methods in terms
of robustness to attacks, imperceptibility of the watermark and watermark capacity.The MSDT is then used to obtain a semi-blind method for video quality assessment. The method embeds pseudo-random binary watermarks in the derivative
vectors of the original undistorted video. The quality of the distorted video is estimated based on the similarity between the embedded and the extracted watermarks. The simulation results on video distorted by compression/decompression show that the proposed method can accurately estimate the quality of a video and its frames for a wide range of compression ratios.
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