Bayesian Structure Learning for Markov Random Fields with a Spike and Slab Prior

In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive cross-validation to find the optimal regularization parameter. Moreover, the model's predictive performance may degrade dramatically with a suboptimal value of the regularization parameter (which is sometimes desirable to induce sparseness). We propose a fully Bayesian approach based on a "spike and slab" prior (similar to L0 regularization) that does not suffer from these shortcomings. We develop an approximate MCMC method combining Langevin dynamics and reversible jump MCMC to conduct inference in this model. Experiments show that the proposed model learns a good combination of the structure and parameter values without the need for separate hyper-parameter tuning. Moreover, the model's predictive performance is much more robust than L1-based methods with hyper-parameter settings that induce highly sparse model structures.Comment: Accepted in the Conference on Uncertainty in Artificial Intelligence (UAI), 201

Markov Random Fields on Triangle Meshes

In this paper we propose a novel anisotropic smoothing scheme based on Markov Random Fields (MRF). Our scheme is formulated as two coupled processes. A vertex process is used to smooth the mesh by displacing the vertices according to a MRF smoothness prior, while an independent edge process labels mesh edges according to a feature detecting prior. Since we should not smooth across a sharp feature, we use edge labels to control the vertex process. In a Bayesian framework, MRF priors are combined with the likelihood function related to the mesh formation method. The output of our algorithm is a piecewise smooth mesh with explicit labelling of edges belonging to the sharp features

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus

A Stochastic Modeling Approach to Region-and Edge-Based Image Segmentation

The purpose of image segmentation is to isolate objects in a scene from the background. This is a very important step in any computer vision system since various tasks, such as shape analysis and object recognition, require accurate image segmentation. Image segmentation can also produce tremendous data reduction. Edge-based and region-based segmentation have been examined and two new algorithms based on recent results in random field theory have been developed. The edge-based segmentation algorithm uses the pixel gray level intensity information to allocate object boundaries in two stages: edge enhancement, followed by edge linking. Edge enhancement is accomplished by maximum energy filters used in one-dimensional bandlimited signal analysis. The issue of optimum filter spatial support is analyzed for ideal edge models. Edge linking is performed by quantitative sequential search using the Stack algorithm. Two probabilistic search metrics are introduced and their optimality is proven and demonstrated on test as well as real scenes. Compared to other methods, this algorithm is shown to produce more accurate allocation of object boundaries. Region-based segmentation was modeled as a MAP estimation problem in which the actual (unknown) objects were estimated from the observed (known) image by a recursive classification algorithms. The observed image was modeled by an Autoregressive (AR) model whose parameters were estimated locally, and a Gibbs-Markov random field (GMRF) model was used to model the unknown scene. A computational study was conducted on images having various types of texture images. The issues of parameter estimation, neighborhood selection, and model orders were examined. It is concluded that the MAP approach for region segmentation generally works well on images having a large content of microtextures which can be properly modeled by both AR and GMRF models. On these texture images, second order AR and GMRF models were shown to be adequate