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

On segmentation with Markovian models

This paper addresses the image modeling problem under the assumption that images can be represented by 2d order, hidden Markov random fields models. The modeling applications we have in mind com- prise pixelwise segmentation of gray-level images coming from the field of Oral Radiographic Differential Diagnosis. Segmentation is achieved by approximations to the solution of the maximum a posteriori equation (MAP) when the emission distribution is assumed the same in all models and the difference lays in the Neighborhood Markovian hypothesis made over the labeling random field. For two algorithms, 2d path-constrained Viterbi training and Potts-ICM we investigate goodness of fit by study- ing statistical complexity, computational gain, extent of automation, and rate of classification measured with kappa statistic. All code written is provided in a Matlab toolbox available for download from our website, following the Reproducible Research Paradigm.Sociedad Argentina de Informática e Investigación Operativ

On segmentation with Markovian models

This paper addresses the image modeling problem under the assumption that images can be represented by 2d order, hidden Markov random fields models. The modeling applications we have in mind com- prise pixelwise segmentation of gray-level images coming from the field of Oral Radiographic Differential Diagnosis. Segmentation is achieved by approximations to the solution of the maximum a posteriori equation (MAP) when the emission distribution is assumed the same in all models and the difference lays in the Neighborhood Markovian hypothesis made over the labeling random field. For two algorithms, 2d path-constrained Viterbi training and Potts-ICM we investigate goodness of fit by study- ing statistical complexity, computational gain, extent of automation, and rate of classification measured with kappa statistic. All code written is provided in a Matlab toolbox available for download from our website, following the Reproducible Research Paradigm.Sociedad Argentina de Informática e Investigación Operativ

Hidden Markov Models for Analysis of Multimodal Biomedical Images

Modern advances in imaging technology have enabled the collection of huge amounts of multimodal imagery of complex biological systems. The extraction of information from this data and subsequent analysis are essential in understanding the architecture and dynamics of these systems. Due to the sheer volume of the data, manual annotation and analysis is usually infeasible, and robust automated techniques are the need of the hour. In this dissertation, we present three hidden Markov model (HMM)-based methods for automated analysis of multimodal biomedical images. First, we outline a novel approach to simultaneously classify and segment multiple cells of different classes in multi-biomarker images. A 2D HMM is set up on the superpixel lattice obtained from the input image. Parameters ensuring spatial consistency of labels and high confidence in local class selection are embedded in the HMM framework, and learnt with the objective of maximizing discrimination between classes. Optimal labels are inferred using the HMM, and are aggregated to obtain global multiple object segmentation. We then address the problem of automated spatial alignment of images from different modalities. We propose a probabilistic framework, constructed using a 2D HMM, for deformable registration of multimodal images. The HMM is tailored to capture deformation via state transitions, and modality-specific representation via class-conditional emission probabilities. The latter aspect is premised on the realization that different modalities may provide very different representation for a given class of objects. Parameters of the HMM are learned from data, and hence the method is applicable to a wide array of datasets. In the final part of the dissertation, we describe a method for automated segmentation and subsequent tracking of cells in a challenging target image modality, wherein useful information from a complementary (source) modality is effectively utilized to assist segmentation. Labels are estimated in the source domain, and then transferred to generate preliminary segmentations in the target domain. A 1D HMM-based algorithm is used to refine segmentation boundaries in the target image, and subsequently track cells through a 3D image stack. This dissertation details techniques for classification, segmentation and registration, that together form a comprehensive system for automated analysis of multimodal biomedical datasets

Iterative Decoding of Two-Dimensional Hidden Markov Models

While the hidden Markov model (HMM) has been extensively ap-plied to one-dimensionalproblems, the complexity of its extension to two-dimensions grows exponentially with the data size and is in-tractable in most cases of interest. In this paper, we introduce an efficient algorithm for approximate decoding of 2-D HMMs, i.e., searching for the most likely state sequence. The basic idea is to approximate a 2-D HMM with a Turbo-HMM (T-HMM), which consists of horizontal and vertical I-D HMMs that "communi-cate", and allow iterated decoding (ID) of rows and columns by a modified version of the forward-backward algorithm. We derive the approach and its re-estimation equations. We then compare its performance to another algorithm designed for decoding 2-D HMMs: the Path Constrained Variable State Viterbi (PCVSV) al-gorithm [I]. Finally, we combine our approach with PCVSV and show that the combination outperforms each algorithm taken sep-arately. 1