Image blur from camera shake is a common cause for poor image quality in digital photography, prompting a significant recent interest in image deblurring. The vast majority of work on blind deblurring splits the problem into two subsequent steps: First, the blur process (i.e., blur kernel) is estimated, then the image is restored given the estimated kernel using a non-blind deblurring algorithm. Recent work in non-blind deblurring has shown that discriminative approaches can have clear image quality and runtime benefits over typical generative formulations. In this paper, we propose a cascade for blind deblurring that alternates between kernel estimation and discriminative deblurring using regression tree fields (RTFs). We further contribute a new dataset of realistic image blur kernels from human camera shake, which we use to train the discriminative component. Extensive qualitative and quantitative experiments show a clear gain in image quality by interleaving kernel estimation and discriminative deblurring in an iterative cascade.

We address the problem of estimating and removing localized image blur, as it for example arises from moving objects in a scene, or when the depth of field is insufficient to sharply render all objects of interest. Unlike the case of camera shake, such blur changes abruptly at the object boundaries. To cope with this, we propose an automated sharp image recovery method that simultaneously determines blurred regions and estimates their responsible blur kernels. To address a wide range of different scenarios, our model is not restricted to a discrete set of candidate blurs, but allows for arbitrary, non-parametric blur kernels. Moreover, our approach does not require specialized hardware, an alpha matte, or user annotation of the blurred region. Unlike previous methods, we show that localized blur estimation can be accomplished by incorporating a pixel-wise latent variable to indicate the active blur kernel. Furthermore, we generalize the marginal likelihood technique of blind deblurring to the case of localized blur. Specifically, we integrate out the latent image derivatives to permit marginal density estimates of both blur kernels and their regions of influence. We obtain sharp images in applications to both object motion blur and defocus blur removal. Quantitative results on two novel datasets as well as qualitative results comparing to a range of specialized methods demonstrate the versatility and effectiveness of our non-parametric approach.

Spatially-discrete Markov random fields (MRFs) and spatially-continuous variational approaches are ubiquitous in low-level vision, including image restoration, segmentation, optical flow, and stereo. Even though both families of approaches are fairly similar on an intuitive level, they are frequently seen as being technically rather distinct since they operate on different domains. In this paper we explore their connections and develop a direct, rigorous link with a particular emphasis on first-order regularizers. By representing spatially-continuous functions as linear combinations of finite elements with local support and performing explicit integration of the variational objective, we derive MRF potentials that make the resulting MRF energy equivalent to the variational energy functional. In contrast to previous attempts, we provide an explicit connection for modern non-quadratic regularizers and also integrate the data term. The established connection opens certain classes of MRFs to spatially-continuous interpretations and variational formulations to a broad range of probabilistic learning and inference algorithms.

Conventional non-blind image deblurring algorithms involve natural image priors and maximum a-posteriori (MAP) estimation. As a consequence of MAP estimation, separate pre-processing steps such as noise estimation and training of the regularization parameter are necessary to avoid user interaction. Moreover, MAP estimates involving standard natural image priors have been found lacking in terms of restoration performance. To address these issues we introduce an integrated Bayesian framework that unifies non-blind deblurring and noise estimation, thus freeing the user of tediously pre-determining a noise level. A sampling-based technique allows to integrate out the unknown noise level and to perform deblurring using the Bayesian minimum mean squared error estimate (MMSE), which requires no regularization parameter and yields higher performance than MAP estimates when combined with a learned high-order image prior. A quantitative evaluation demonstrates state-of-the-art results for both non-blind deblurring and noise estimation.