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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
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