We have proposed a unifying discrete regularization approach to achieve high quality partially-blurred image partition, identification and blind restoration. This approach integrates and shares the advantages from both spectral graph theory and regularization theory for solving ill-posed inverse problems. Different from existing off-line and supervised labeling methods, this approach allows on-line unsupervised learning and labeling so that we can achieve a meaningful task-driven segmentation. Perceptual blind image restoration can be achieved in a different identified layer via optimal scale control. This approach has robust performance on different types of partially-blurred natural images. The integrated approach also demonstrates that the mutual support between natural prior knowledge and low-level image processing has great potential to improve the results in early vision.
we have introduced a new approach to enable variational Bayesian ensemble learning for restor-ing real nonstationary blurred images. The experiments suggest that the approach enables an efficient trade-off between intractable inferences and tractable solution for difficult inverse problems. In particular, the approach makes effective use of the natural image statistics prior through the learning scheme. By alternating the radius of the natural image statistics, we are able change the approach to restore more types of blurred images including nonuniform blurred images. A thorough evaluation has shown that the proposed approach has more flexibilities for identifying and restoring blurred images in real environments. The new approach outperforms state-of-the art methods on challenging real blurred data, underlining the effectiveness of the approach.
6 Nonuniform Blurred Image Identification, Segmentation and Restoration
Wir m¨ussen wissen, Wir werden wissen. - David Hilbert
7.1 Summary
In this thesis, we have proposed three main approaches for blur identification, image restoration and partially-blurred identification, segmentation and restoration in an integrated Bayesian estimation and regularization framework based on continuous Hilbert, bounded variation spaces and discrete graph spaces.
The observation and experiments have guided us to seek alternative approaches of scoring can-didate statistical learning based optimization methods. Furthermore, convex optimization cri-teria are employed to achieve existing, unique, stable solution for blind image reconstruction or restoration and segmentation. These approaches are an integration of statistics and regulariza-tion, and transductive inference of regularization on discrete graph spaces. The soundness of these approaches is demonstrated by numerical experiments. The main contributions of this the-sis to the computer vision, image processing and pattern recognition community are summarized in the following.
The first part of our work focuses on the strategy of global nonparametric estimation to local parametric optimization for high-accuracy blur identification. The nonparametric estimation used to adapt adaptation of the parametric methods to the data when the parametric structural assumption is not fulfilled. This approach is based on statistical learning priors and determin-istic regularization for blur identification and image restoration for stationary-blurred images.
The proposed double regularized Bayesian estimation is strictly convex so that the approach can achieve the global convergence. The accurate initial value can also speedup the conver-gence for the estimation of point spread function and image restoration. An early work of this approach has been published in [295], [289]. Simultaneously, a family of variational function-als like Mumford-Shah, and total variation have been investigated and implemented for image restoration and segmentation, published in [294], [293], [291] and natural image statistics and variational Bayesian learning in [287], [298].
The second part of this work focuses on high-fidelity and perceptual image restoration. Vari-ational regularization in the BV space has been extended in a Bayesian framework to achieve simultaneously blur identification and image restoration. Based on a family of general and more general linear-growth functional in the BV space, we propose a Bayesian based double variational blind image restoration functional which can be optimal controlled via self-adjusting diffusion operators, self-adaptive regularization parameters, and the optimal time of stopping the process. The underlying mathematic principles and practical roles are embodied in an en-ergy optimization approach. Related works have been published in [294], [290], [292], [296] and the submitted journal paper [297].
7 Summary and Future Work
The third part of this work focuses on partially-blurred image segmentation, identification and restoration [292],[299]. The original idea of this work is to find underlying mathematic rela-tionship between regularization theory and spectral graph theory, since these two theories can be individually used for image segmentation based on the same strategy of global optimization.
Moreover, both theory based approaches can use Laplacian for controlling and smoothing the convergence results. The proposed discrete regularization approach integrates spectral graph theory and regularization theory in graph spaces based on the underlying mathematic connec-tions and generalization. First, this novel approach can efficiently utilize, covert, and store the high-level knowledge to guide low-level image segmentation and restoration. Second, the seg-mentation is also optimized by modifying weight affinity function. Furthermore, the flexibility and generality make this approach easily extendable to solve many related image processing and vision tasks. Several related papers have been submitted recently.
In this thesis, we have introduced several new approaches for low-level vision problems based on an integrated statistical learning, Bayesian estimation and regularization framework. These ex-periments suggest that our strategy and our suggested approaches enables efficient and tractable solutions for difficult inverse problems. In particular, these approaches makes effective use of the natural image statistics based generative and discriminative prior information through their re-lated learning scheme. By alternating the radius of the image statistics and learning in Bayesian estimation, we are able change our approaches to solve other inverse problems in pattern recog-nition and computer vision. These approaches outperforms state-of-the art methods on chal-lenging real vision problems, underlining the effectiveness of our strategy and these introduced approaches.