Research On Shearlet-based Image Multiscale Geometric Analysis And Its Applications

As a multi-dimensional analysis method which developed from the computational analysis fields and others, the Multiscale Geometric Analysis (MGA) methods were proposed to approximate and describe the multi-dimensional geometric image features like edges and textures effectively in order to represent, analyze and process the multi-dimensional image data in an efficient way. As a result, MGA overcome the drawback that Wavelet transform cannot capture the multi-dimensional singularities, and acquire extensive applications in image processing. Therefore, it is significant to research further MGA theory and its applications. In this dissertation, the author mainly focuses on the research of Shearlet transform and the key techniques of its theory and applications in image processing. The major research achievements and innovations are as follows:(1) Firstly an in-depth research of MGA theory and its typical tools is given. And in Chapter 2, we provide Shearlet transform with a detailed analysis to the fundamental principles, implementation scheme, merits and demerits, which can be thought as the foundation of latter image processing applications.(2) In Chapter 3, a new algorithm of Discrete Median Shearlet Transform (DMST) based on the FIR-median hybrid filters is put forward here to overcome the drawbacks of traditional discrete Shearlet transform such as the poor sparse property of the coe-fficients and the ambiguity of captured structural details. DMST adopted the nonlinear pyramid to realize multiscale decomposition of the source image, which enhances the coefficients sparsity and improves capturing structural details ability and the sustained ability.(3) A comparative analysis of edges detection based on MGA is given firstly in Chapter 4. By contrast, we propose a novel fused edge detector which fuses DMST and a small-scaled isotropic Gaussian kernel to obtain edge maps of images. The DMST-based edge strength map is noise-robust and has good edge resolution, but poor in edges localization and suffering some edge stretch effect, while the gradient-based edge strength map from a small-scaled isotropic Gaussian kernel is good at edge localized but poor in noise-robust. Because they are complementary in specific properties, we fused the both into a noise-robust edge strength map of high quality. Finally we test and verify the proposed detector by a serial of experiments.(4) Considering that a tractable statistical model is essential to successfully solve the complicated image processing task, we model DMST coefficients using the Hidden Markov Tree (HMT) model in Chapter 5. We start at the in-depth study on the statistical properties of DMST coefficients. And then the study shows the non-Gaussian marginal distribution with zero-mean and intense interlocation, interscale and interdirection dependencies of DMST coefficients. And the study reveals that conditioned on the magnitudes of their generalized neighborhood coefficients, DMST coefficients approxi-mately obeys Gaussian distribution. Based on these findings, we model DMST coeffi-cients using HMT and obtain the DMST-HMT. In the end we show experimental results in texture retrieval applications with this model and have considerable improvements in performance for various oriented textures.