Self-similarity is a prominent characteristic of natural images that can play a major role when it comes to their denoising, restoration or compression. In this paper, we propose a novel probabilistic model that is based on the concept of image patch similarity and applied to the problem of Single Image Super Resolution. Based on this model, we derive a Variational Bayes algorithm, which super resolves low-resolution images, where the assumed distribution for the quantified similarity between two image patches is heavy-tailed. Moreover, we prove mathematically that the proposed algorithm is both an extended and superior version of the probabilistic Non-Local Means (NLM). Its prime advantage remains though, which is that it requires no training. A comparison of the proposed approach with state-of-the-art methods, using various quantitative metrics shows that it is almost on par, for images depicting rural themes and in terms of the Structural Similarity Index (SSIM) with the best performing methods that rely on trained deep learning models. On the other hand, it is clearly inferior to them, for urban themed images and in terms of all metrics, especially for the Mean-Squared-Error (MSE). In addition, qualitative evaluation of the proposed approach is performed using the Perceptual Index metric, which has been introduced to better mimic the human perception of the image quality. This evaluation favors our approach when compared to the best performing method that requires no training, even if they perform equally in qualitative terms, reinforcing the argument that MSE is not always an accurate metric for image quality.

In this paper, we deal with object tracking in stereo video sequences. We introduce a Bayesian framework for utilizing the results of any conventional single channel object tracker, in order to accomplish the refinement of the tracking accuracy in the left/right video channel. In this Bayesian framework, a variational Bayesian algorithm is employed to this end, where a priori information about the object displacement (movement) over time is incorporated by means of a prior distribution. This a priori information is obtained in a pre-processing step, in which the object displacement over time is estimated. Experiments demonstrate the efficiency of the proposed post-processing methodology in terms of tracking accuracy.

In this paper we propose a Bayesian framework for accurate object tracking in stereoscopic sequences. Object detection and forward tracking are first combined according to predefined rules to get a first set of tracked regions candidates. Backward tracking is then applied to provide another set of possible object localizations. Moreover, this strategy is applied herein in stereoscopic video. We introduce a Bayesian inference algorithm which is used to merge the information of both forward and backward tracking in order to refine the tracked region localization results. Experiments, performed on face tracking, show that the proposed method provides higher tracking accuracy than a forward tracker.

In this paper, a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted total variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.

Image priors based on products have been recognized to offer many advantages because they allow simultaneous enforcement of multiple constraints. However, they are inconvenient for Bayesian inference because it is hard to find their normalization constant in closed form. In this paper, a new Bayesian algorithm is proposed for the image restoration problem that bypasses this difficulty. An image prior is defined by imposing Student-t densities on the outputs of local convolutional filters. A variational methodology, with a constrained expectation step, is used to infer the restored image. Numerical experiments are shown that compare this methodology to previous ones and demonstrate its advantages.

In this paper we present new detectors for additive watermarks when the power of the watermark is unknown. These detectors are based on modeling the image using student-t statistics. As a result, due to the generative properties of the student-t density function, such models are spatially adaptive and the Expectation-Maximization algorithm can be used to obtain maximum likelihood estimates of their parameters. Using these image models detectors based on the generalized likelihood ratio and Rao tests are derived for this problem. Numerical experiments are presented that demonstrate the properties of these detectors and compared them with previously proposed detectors.

In this paper, we propose a maximum a posteriori ramework for the super-resolution problem, i.e., reconstructing high-resolution images from shifted, rotated, low-resolution degraded observations. The main contributions of this work are two; first, the use of a new locally adaptive edge preserving prior for the super-resolution problem. Second an efficient two-step reconstruction methodology that includes first an initial registration using only the low-resolution degraded observations. This is followed by a fast iterative algorithm implemented in the discrete Fourier transform domain in which the restoration, interpolation and the registration subtasks of this problem are preformed simultaneously. We present examples with both synthetic and real data that demonstrate the advantages of the proposed framework.

In this paper, we propose a class of image restoration algorithms based on the Bayesian approach and a new hierarchical spatially adaptive image prior. The proposed prior has the following two desirable features. First, it models the local image discontinuities in different directions with a model which is continuous valued. Thus, it preserves edges and generalizes the on/off (binary) line process idea used in previous image priors within the context of Markov random fields (MRFs). Second, it is Gaussian in nature and provides estimates that are easy to compute. Using this new hierarchical prior, two restoration algorithms are derived. The first is based on the maximum a posteriori principle and the second on the Bayesian methodology. Numerical experiments are presented that compare the proposed algorithms among themselves and with previous stationary and non stationary MRF-based with line process algorithms. These experiments demonstrate the advantages of the proposed prior.

In this paper we propose a new hierarchical non stationary image prior for image restoration. This prior captures the directional edges using a continuous model and regularizes accordingly the restored images. In addition, the corresponding generative graphical model does not contain cycles, thus learning this model is easy and fast. Based on this prior image model, a maximum a posteriori (MAP) estimation algorithm is derived. Numerical experiments are provided that demonstrate the advantages of the proposed non stationary model as compared with algorithms that use stationary models.