Singularity detection for regularity scalable image coding

Abstract

Scalability has been one of the important design criteria of modern image and video codec. The features such as resolution and SNR scalable coding provided in the EZW of MPEG-4 and the EBCOT in JPEG2000 are typical examples. However, the quality levels provided by the above two scalabilities do not correlate with visual perception, which means they do not particularly emphasize the display of some important features such as edges, boundaries, textures and surfaces of an image. So various feature-based progressive or scalable wavelet image coding algorithms were proposed. Nevertheless, their implementation cannot simultaneously satisfy some practical concerns such as coding efficiency and implementation complexity. In this thesis, a new scalable coding technique, namely, regularity scalable image coding, is proposed. We refer to a coding system that generates compressed bitstream in the order of the regularity of the image concerned. This algorithm can be fully embedded into any existing wavelet codec and avoid the problems that the other feature-based scalable coders encounter. From fluid dynamics in physics to pattern recognition or computer vision in engineering, it is known that regularity (or singularity) of signals or images can be estimated from the interscale evolution of their wavelet transform. However, our regularity scalable coding algorithm is embedded into a wavelet codec, where the separable wavelet transform with decimation is applied. Therefore, the first objective of our work is to investigate the approach for estimating Lipschitz regularity from the separable wavelet transform. To avoid the error and ambiguities when tracing the modulus maxima at coarser scales, we study the existing interscale evolution of the magnitude sums over the 'cone of influence'. Since it cannot be applied here directly to estimate the Lipschitz regularity, we determine the magnitude sums over the decimated 'cone of influence', which was not developed before. The PSNR and subjective quality results show that the coding efficiency is higher than applying resolution scalability alone. Multiwavelet transform has been applied to image compression and denoising in the past few years. Multiwavelet transform is a generalization of the traditional single wavelet with higher multiplicity. It offers simultaneous orthogonality, symmetry and short supports, which are not possible with single wavelet transform. Due to the shorter support and higher vanishing moments of the multifilters, it generally outperforms the single wavelet transform. As the second part of our work, the singularity detection is further extended to multiwavelet systems. Again we investigate the relationship between the interscale evolution of the multiwavelet coefficients and Lipschitz regularity. The shorter supports of the multifilters introduce smaller size of 'cone of influence', which can be more clearly determined at lower scales. Hence improved results for singularity detection can be achieved. We also perform thresholding according to the interscale difference of the magnitude sum, which is complementary to the interscale ratio, in the denoising algorithm. The MSE and subjective quality results depict the performances from our theory. Singularity detection by the Lipschitz regularity condition plays an important role in the above signal processing applications, because it fully represents the characteristics of the features of a signal or an image. We believe that it can be further applied to more signal processing applications.