Bayesian entropy estimation: Applications in robust image filtering

In this paper, a joint video fusion and super-resolution algorithm is proposed. The method addresses the problem of generating a high-resolution (HR) image from infrared (IR) and visible (VI) low-resolution (LR) images, in a Bayesian framework. In order to preserve better the discontinuities, a Generalized Gaussian Markov Random Field (MRF) is used to formulate the prior. Experimental results demonstrate that information from both visible and infrared bands is recovered from the LR frames in an effective way.

The objective of fMRI data analysis is to detect the region of the brain that gets activated in response to a specific stimulus presented to the subject. We develop a new algorithm for activation detection in event-related fMRI data. We utilize a forward model for fMRI data acquisition which explicitly incorporates physiological noise, scanner noise and the spatial blurring introduced by the scanner. After slice-by-slice image restoration procedure that independently restores each data slice corresponding to each time index, we estimate the parameters of the hemodynamic response function (HRF) model for each pixel of the restored data. In order to enforce spatial regularity in our estimates, we model the prior distribution of the HRF parameters as a generalized Gaussian Markov random field (GGMRF) model. We develop an algorithm to compute the maximum a posteriori (MAP) estimates of the parameters. We then threshold the amplitude parameters to obtain the final activation map. We illustrate our algorithm by comparing it with the widely used general linear model (GLM) method. In synthetic data experiments, under the same probability of false alarm, the probability of correct detection for our method is up to 15% higher than GLM. In real data experiments, through anatomical analysis and benchmark testing using block paradigm results, we demonstrate that our algorithm produces fewer false alarms than GLM.

We propose using the generalized Gaussian Markov random field (GGMRF) image model with MAP estimation to solve the problem of restoration for a blurred and noise corrupted image. The restoration algorithm is adapted to specific characteristics of the true image by estimating the GGMRF shape parameter used in computing the MAP estimation. This shape parameter, p, is estimated based on the sample kurtosis of the image. It is shown that higher quality restorations are obtained when the estimated p value is used, rather than some arbitrary choice as other investigators have used.

This paper proposes a new-wavelet-based synthetic aperture radar (SAR) image despeckling algorithm using the sequential Monte Carlo method. A model-based Bayesian approach is proposed. This paper presents two methods for SAR image despeckling. The first method, called WGGPF, models a prior with Generalized Gaussian (GG) probability density function (pdf) and the second method, called WGMPF, models prior with a Generalized Gaussian Markov random field (GGMRF). The likelihood pdf is modeled using a Gaussian pdf. The GGMRF model is used because it enables texture parameter estimation. The prior is modeled using GG pdf, when texture parameters are not needed. A particle filter is used for drawing particles from the prior for different shape parameters of GG pdf. When the GGMRF prior is used, the particles are drawn from prior in order to estimate noise-free wavelet coefficients and for those coefficients the texture parameter is changed in order to obtain the best textural parameters. The texture parameters are changed for a predefined set of shape parameters of GGMRF. The particles with the highest weights represents the final noise-free estimate with corresponding textural parameters. The despeckling algorithms are compared with the state-of-the-art methods using synthetic and real SAR data. The experimental results show that the proposed despeckling algorithms efficiently remove noise and proposed methods are comparable with the state-of-the-art methods regarding objective measurements. The proposed WGMPF preserves textures of the real, high-resolution SAR images well.

In this paper, we present a Bayesian-based superresolution algorithm that uses approximations of symmetric alpha-stable (SαS) Markov random fields as prior. The approximated SαS prior is used to perform maximum a posteriori (MAP) estimation for the high-resolution (HR) image reconstruction process. Compared with other state-of-the-art prior models, the proposed prior can better capture the heavy tails of the distribution of the HR image. Thus, the edges of the reconstructed HR image are preserved better in our method. As the corresponding energy function is nonconvex, the graduated nonconvexity method is used to solve the MAP estimation. Experiments confirm the better fit achieved by the proposed model to the actual data distribution and the consequent improvement in terms of visual quality over previously proposed super-resolution algorithms.

A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.

This paper presents a new two-step pseudo maximum a posteriori (MAP) segmentation method for the Markov random field (MRF)-modeled image because the exact MAP estimation is hard to implement due to intractable complexity. The expectation maximization (EM) and Markov Chain Monte Carlo (MCMC) methods are adopted to estimate the parameters for the MRF model due to their comparatively good performance. Although the image segmentation algorithms via graph cuts have become very popular nowadays, our proposed algorithm still performs significantly better in automatic identification and segmentation of fuzzy images than them, which is shown by the quantitative results on synthesized images. In practical applications, the proposed two-step pseudo MAP method is superior in segmenting the fuzzy laser images reflected from the weld pool surfaces during the P-GMAW welding process.

Often, moving object detection in a video sequence has been achieved a variant of temporal segmentation methods. For slow moving video objects, a temporal segmentation method fails to detect the objects. In this paper, we propose a Markov random Field (MRF) model based scheme to detect slow movements in a video sequence. The proposed scheme is a combination of a proposed spatio-temporal segmentation scheme and temporal segmentation method. A compound MRF model is used in spatio-temporal framework. In this framework, the a priori distribution is MRF and this takes care of spatial distribution of current frame, temporal frames and the Change Detection Masks (CDM) of the temporal frames. The spatio-temporal segmentation problem is formulated as a pixel labeling problem in Maximum a posteriori (MAP) framework. The MAP estimates are obtained using a hybrid algorithm. These estimated labels are used to obtain the Video Object Plane (VOP) and hence the detection of objects. The results are compared with joint segmentation scheme (JSEG). Results presented demonstrate that the proposed scheme with CDM model could detect slow moving video objects.

Image segmentation is the process of partitioning a digital image into a set of homogeneous regions (according to some homogeneity criterion) to facilitate a subsequent higher-level analysis. In this context, the present paper proposes an unsupervised and graph-based method of image segmentation, which is driven by an application goal, namely, the generation of image segments associated with a user-defined and application-specific goal. A graph, together with a random grid of source elements, is defined on top of the input image. From each source satisfying a goal-driven predicate, called seed, a propagation algorithm assigns a cost to each pixel on the basis of similarity and topological connectivity, measuring the degree of association with the reference seed. Then, the set of most significant regions is automatically extracted and used to estimate a statistical model for each region. Finally, the segmentation problem is expressed in a Bayesian framework in terms of probabilistic Markov random field (MRF) graphical modeling. An ad hoc energy function is defined based on parametric models, a seed-specific spatial feature, a background-specific potential, and local-contextual information. This energy function is minimized through graph cuts and, more specifically, the alpha-beta swap algorithm, yielding the final goal-driven segmentation based on the maximum a posteriori (MAP) decision rule. The proposed method does not require deep a priori knowledge (e.g., labelled datasets), as it only requires the choice of a goal-driven predicate and a suited parametric model for the data. In the experimental validation with both magnetic resonance (MR) and synthetic aperture radar (SAR) images, the method demonstrates robustness, versatility, and applicability to different domains, thus allowing for further analyses guided by the generated products.

In this article, we analyse right censored survival data by modelling their common hazard function nonparametrically. The hazard rate is assumed to be a stochastic process, with sample paths taking the form of step functions. This process jumps at times that form a time-homogeneous Poisson process, and a class of Markov random fields is used to model the values of these sample paths. Features of the posterior distribution, such as the mean hazard rate and survival probabilities, are evaluated using the Metropolis--Hastings--Green algorithm. We illustrate our methodology by simulation examples.

This paper presents a Markov random field (MRF) model for object recognition in high level vision. The labeling state of a scene in terms of a model object is considered as an MRF or couples MRFs. Within the Bayesian framework the optimal solution is defined as the maximum a posteriori (MAP) estimate of the MRF. The posterior distribution is derived based on sound mathematical principles from theories of MRF and probability, which is in contrast to heuristic formulations. An experimental result is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper proposes a stochastic approach to estimate the occlusion and disparity fields of stereoscopic images. The fields are estimated by the Bayesian maximum a posteriori (MAP) framework and Markov random field (MRF) models. The occlusion field model is based on the stochastic observation that the probability distribution in MAP estimator is relatively unstable and uniform at occluded regions. The occlusion is explicitly modelled as MRF, and is estimated in an energy optimization method called stochastic diffusion. The detected occluded region is compensated for the re-estimated disparity field in the same stochastic diffusion and the dynamic programming approach. Experimental results show good occlusion detection and disparity estimation. These results show the novel stochastic approach is suitable for occlusion detection and disparity estimation.

Image classification of remote sensing data is an important topic and long-term tasks in applications [1]. Markov random field (MRF) has more advantages in processing contextual information [2]. Bayesian approach enables the incorporation of prior model and likelihood distribution, this paper has formulated a Bayesian-MRF classification model based on MAP-ICM framework. It uses Potts model in label field and assume Gaussian distribution in observation field. According to maximum a posteriori (MAP) criterion, each new classified label can be obtained by the minimum of energy using Iterated Conditional Modes (ICM) algorithm. Finally, classification tasks are carried out by Bayesian-MRF classification model. Experimental results show that: (1) Clique potential parameters affect classification greatly. When it is 0.5, the classification accuracy reaches maximum with the best classification result for study area of Dali Erhai Lake basin using landsat TM data. (2) Bayesian MRF model have obvious advantages in classification for neighbourhood pixels so that it can separate Shadow class from Water class because the Shadow in mountain areas is very similar to Water in spectrum. In this case study, the best classification accuracy reaches 95.8%. The approaches and results will have important reference value for applications such as land use/cover classification, environment/ecological monitoring etc.

A well known problem associated with super-resolution of imagery is the introduction of oscillatory artifacts into the super-resolved object estimate. In this paper, we derive a Maximum A-Posteriori (MAP) object estimator subject to a constraint on the norm of the first differences of adjacent object pixels. The posterior density is derived from a Poisson observation model and a Poisson prior for the object. It is shown that this optimization problem is identical to a MAP estimator with a Markov Random Field (MRF) prior using zero- and first-order neighborhood cliques. While most MRF priors used for image restoration neglect the singleton clique, our model incorporates this additional a-priori object knowledge into the estimator. An iterative solution to the optimization problem is developed using the Picard iteration technique. Results are presented which demonstrate substantial artifact reduction while achieving the bandwidth extension necessary to accomplish super-resolution. Test cases include extended objects and natural scenes.© (1993) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

One popular method of assessing brain functional connectivity (FC) is through seed-based correlation (SCA) analysis. One drawback of this method is when the seed location is varied slightly, the FC can vary dramatically. We propose a method superior to SCA, robust to variations in seed location, which confers a probabilistic interpretation. We introduce a probabilistic method which generates a cloud of highly connected voxels to determine a stable set of voxels connected to the seed location (SC-SCA). This cloud can generate a correlation map or a probabilistic map. The method is applied to the default mode network (DMN) based on a posterior cingulate cortex (PCC) seed, and the auditory network (AN) as validation on a smaller network. A Bayesian interpretation is demonstrated through performing a maximum a posteriori (MAP) estimation on the DMN. The advantages of the method are tested by performing stability analyses on its influential parameters. The method is extended to region-based SC-SCA, and then comparisons are made based on seed-based vs region-based versions of the methods SC-SCA vs traditional SCA. The statistical significance between the methods is assessed via a bootstrap method using the difference in medians of the standard deviation of the voxels for 16 subjects. The proposed method, SC-SCA, is able to identify a set of regions - the DMN - that are known to be associated with and have high correlation with the PCC, and the method is also extensible to smaller networks as shown by its performance on the AN. Based on the certainty of the a priori distribution for MAP analysis, the method is able to identify regions with high probability of belonging to the DMN. The stability analyses demonstrated that substantial deviations from the initial seed locations in the sagittal, posterior transverse, and axial directions by ±10mm do not cause substantial variation in the correlation network produced. Qualitative inspection of the average correlation maps garnered from the four methods showed that SC-SCA shows a larger amount of detail in FC connectivity as compared to SCA. Seed-based methods show higher detail and contrast in the maps in comparison with region-based methods. Quantitatively, the statistical tests between seed-based vs region-based and SC-SCA vs SCA revealed that there is no significant difference between the following methods: region-based SCA or region-based SC-SCA, and seed-based SC-SCA or region-based SC-SCA. However, there are statistically significant differences and advantages conferred between the following methods: seed-based SC-SCA over seed-based SCA, region-based SC-SCA over seed-based SCA, region-based SCA over seed-based SCA, and region-based SCA over seed-based SC-SCA. Finally, seed-based SC-SCA outperforms sphere-based SCA. The proposed method offers several advantages over traditional SCA: robust single-seed FC estimation, novel Bayesian estimation capabilities, enhanced detail of brain structures, robustness to initial seed location, and enhanced consistency in the correlation maps generated. Region-based SC-SCA is equivalent or superior to all investigated methods, where seed-based SCA is inferior to all methods. The method confers improved single-seed SCA with the additional benefit of Bayesian estimation.