Simultaneous estimation of super-resolved scene and depth map from low resolution defocused observations

This paper presents a novel technique to simultaneously estimate the depth map and the focused image of a scene, both at a super-resolution, from its defocused observations. Super-resolution refers to the generation of high spatial resolution images from a sequence of low resolution images. Hitherto, the super-resolution technique has been restricted mostly to the intensity domain. In this paper, we extend the scope of super-resolution imaging to acquire depth estimates at high spatial resolution simultaneously. Given a sequence of low resolution, blurred, and noisy observations of a static scene, the problem is to generate a dense depth map at a resolution higher than one that can be generated from the observations as well as to estimate the true high resolution focused image. Both the depth and the image are modeled as separate Markov random fields (MRF) and a maximum a posteriori estimation method is used to recover the high resolution fields. Since there is no relative motion between the scene and the camera, as is the case with most of the super-resolution and structure recovery techniques, we do away with the correspondence problem

Filter-Based Probabilistic Markov Random Field Image Priors: Learning, Evaluation, and Image Analysis

Markov random fields (MRF) based on linear filter responses are one of the most popular forms for modeling image priors due to their rigorous probabilistic interpretations and versatility in various applications. In this dissertation, we propose an application-independent method to quantitatively evaluate MRF image priors using model samples. To this end, we developed an efficient auxiliary-variable Gibbs samplers for a general class of MRFs with flexible potentials. We found that the popular pairwise and high-order MRF priors capture image statistics quite roughly and exhibit poor generative properties. We further developed new learning strategies and obtained high-order MRFs that well capture the statistics of the inbuilt features, thus being real maximum-entropy models, and other important statistical properties of natural images, outlining the capabilities of MRFs. We suggest a multi-modal extension of MRF potentials which not only allows to train more expressive priors, but also helps to reveal more insights of MRF variants, based on which we are able to train compact, fully-convolutional restricted Boltzmann machines (RBM) that can model visual repetitive textures even better than more complex and deep models. The learned high-order MRFs allow us to develop new methods for various real-world image analysis problems. For denoising of natural images and deconvolution of microscopy images, the MRF priors are employed in a pure generative setting. We propose efficient sampling-based methods to infer Bayesian minimum mean squared error (MMSE) estimates, which substantially outperform maximum a-posteriori (MAP) estimates and can compete with state-of-the-art discriminative methods. For non-rigid registration of live cell nuclei in time-lapse microscopy images, we propose a global optical flow-based method. The statistics of noise in fluorescence microscopy images are studied to derive an adaptive weighting scheme for increasing model robustness. High-order MRFs are also employed to train image filters for extracting important features of cell nuclei and the deformation of nuclei are then estimated in the learned feature spaces. The developed method outperforms previous approaches in terms of both registration accuracy and computational efficiency

Machine Learning for Fluid Mechanics

The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the underlying fluid mechanics. Moreover, machine learning algorithms can augment domain knowledge and automate tasks related to flow control and optimization. This article presents an overview of past history, current developments, and emerging opportunities of machine learning for fluid mechanics. It outlines fundamental machine learning methodologies and discusses their uses for understanding, modeling, optimizing, and controlling fluid flows. The strengths and limitations of these methods are addressed from the perspective of scientific inquiry that considers data as an inherent part of modeling, experimentation, and simulation. Machine learning provides a powerful information processing framework that can enrich, and possibly even transform, current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202

Image Restoration Using Joint Statistical Modeling in Space-Transform Domain

This paper presents a novel strategy for high-fidelity image restoration by characterizing both local smoothness and nonlocal self-similarity of natural images in a unified statistical manner. The main contributions are three-folds. First, from the perspective of image statistics, a joint statistical modeling (JSM) in an adaptive hybrid space-transform domain is established, which offers a powerful mechanism of combining local smoothness and nonlocal self-similarity simultaneously to ensure a more reliable and robust estimation. Second, a new form of minimization functional for solving image inverse problem is formulated using JSM under regularization-based framework. Finally, in order to make JSM tractable and robust, a new Split-Bregman based algorithm is developed to efficiently solve the above severely underdetermined inverse problem associated with theoretical proof of convergence. Extensive experiments on image inpainting, image deblurring and mixed Gaussian plus salt-and-pepper noise removal applications verify the effectiveness of the proposed algorithm.Comment: 14 pages, 18 figures, 7 Tables, to be published in IEEE Transactions on Circuits System and Video Technology (TCSVT). High resolution pdf version and Code can be found at: http://idm.pku.edu.cn/staff/zhangjian/IRJSM

Depth Estimation Through a Generative Model of Light Field Synthesis

Light field photography captures rich structural information that may facilitate a number of traditional image processing and computer vision tasks. A crucial ingredient in such endeavors is accurate depth recovery. We present a novel framework that allows the recovery of a high quality continuous depth map from light field data. To this end we propose a generative model of a light field that is fully parametrized by its corresponding depth map. The model allows for the integration of powerful regularization techniques such as a non-local means prior, facilitating accurate depth map estimation.Comment: German Conference on Pattern Recognition (GCPR) 201