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

摘要

In this paper, we study statistical classification accuracy of two differentMarkov field environments for pixelwise image segmentation, considering thelabels of the image as hidden states and solving the estimation of such labelsas a solution of the MAP equation. The emission distribution is assumed thesame in all models, and the difference lays in the Markovian prior hypothesismade over the labeling random field. The a priori labeling knowledge will bemodeled with a) a second order anisotropic Markov Mesh and b) a classicalisotropic Potts model. Under such models, we will consider three differentsegmentation procedures, 2D Path Constrained Viterbi training for the HiddenMarkov Mesh, a Graph Cut based segmentation for the first order isotropic Pottsmodel, and ICM (Iterated Conditional Modes) for the second order isotropicPotts model. We provide a unified view of all three methods, and investigate goodness offit for classification, studying the influence of parameter estimation,computational gain, and extent of automation in the statistical measuresOverall Accuracy, Relative Improvement and Kappa coefficient, allowing robustand accurate statistical analysis on synthetic and real-life experimental datacoming from the field of Dental Diagnostic Radiography. All algorithms, usingthe learned parameters, generate good segmentations with little interactionwhen the images have a clear multimodal histogram. Suboptimal learning provesto be frail in the case of non-distinctive modes, which limits the complexityof usable models, and hence the achievable error rate as well. All Matlab code written is provided in a toolbox available for download fromour website, following the Reproducible Research Paradigm.