Quantitative magnetic resonance image analysis via the EM algorithm with stochastic variation

Quantitative Magnetic Resonance Imaging (qMRI) provides researchers insight into pathological and physiological alterations of living tissue, with the help of which researchers hope to predict (local) therapeutic efficacy early and determine optimal treatment schedule. However, the analysis of qMRI has been limited to ad-hoc heuristic methods. Our research provides a powerful statistical framework for image analysis and sheds light on future localized adaptive treatment regimes tailored to the individual's response. We assume in an imperfect world we only observe a blurred and noisy version of the underlying pathological/physiological changes via qMRI, due to measurement errors or unpredictable influences. We use a hidden Markov random field to model the spatial dependence in the data and develop a maximum likelihood approach via the Expectation--Maximization algorithm with stochastic variation. An important improvement over previous work is the assessment of variability in parameter estimation, which is the valid basis for statistical inference. More importantly, we focus on the expected changes rather than image segmentation. Our research has shown that the approach is powerful in both simulation studies and on a real dataset, while quite robust in the presence of some model assumption violations.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS157 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives

We present a new parallel algorithm for probabilistic graphical model optimization. The algorithm relies on data-parallel primitives (DPPs), which provide portable performance over hardware architecture. We evaluate results on CPUs and GPUs for an image segmentation problem. Compared to a serial baseline, we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare our performance to a reference, OpenMP-based algorithm, and find speedups of up to 7X (CPU).Comment: LDAV 2018, October 201

Neighbourhood-consensus message passing and its potentials in image processing applications

In this paper, a novel algorithm for inference in Markov Random Fields (MRFs) is presented. Its goal is to find approximate maximum a posteriori estimates in a simple manner by combining neighbourhood influence of iterated conditional modes (ICM) and message passing of loopy belief propagation (LBP). We call the proposed method neighbourhood-consensus message passing because a single joint message is sent from the specified neighbourhood to the central node. The message, as a function of beliefs, represents the agreement of all nodes within the neighbourhood regarding the labels of the central node. This way we are able to overcome the disadvantages of reference algorithms, ICM and LBP. On one hand, more information is propagated in comparison with ICM, while on the other hand, the huge amount of pairwise interactions is avoided in comparison with LBP by working with neighbourhoods. The idea is related to the previously developed iterated conditional expectations algorithm. Here we revisit it and redefine it in a message passing framework in a more general form. The results on three different benchmarks demonstrate that the proposed technique can perform well both for binary and multi-label MRFs without any limitations on the model definition. Furthermore, it manifests improved performance over related techniques either in terms of quality and/or speed

Accuracy of MAP segmentation with hidden Potts and Markov mesh prior models via Path Constrained Viterbi Training, Iterated Conditional Modes and Graph Cut based algorithms

In this paper, we study statistical classification accuracy of two different Markov field environments for pixelwise image segmentation, considering the labels of the image as hidden states and solving the estimation of such labels as a solution of the MAP equation. The emission distribution is assumed the same in all models, and the difference lays in the Markovian prior hypothesis made over the labeling random field. The a priori labeling knowledge will be modeled with a) a second order anisotropic Markov Mesh and b) a classical isotropic Potts model. Under such models, we will consider three different segmentation procedures, 2D Path Constrained Viterbi training for the Hidden Markov Mesh, a Graph Cut based segmentation for the first order isotropic Potts model, and ICM (Iterated Conditional Modes) for the second order isotropic Potts model. We provide a unified view of all three methods, and investigate goodness of fit for classification, studying the influence of parameter estimation, computational gain, and extent of automation in the statistical measures Overall Accuracy, Relative Improvement and Kappa coefficient, allowing robust and accurate statistical analysis on synthetic and real-life experimental data coming from the field of Dental Diagnostic Radiography. All algorithms, using the learned parameters, generate good segmentations with little interaction when the images have a clear multimodal histogram. Suboptimal learning proves to be frail in the case of non-distinctive modes, which limits the complexity of usable models, and hence the achievable error rate as well. All Matlab code written is provided in a toolbox available for download from our website, following the Reproducible Research Paradigm