Georgy L. Gimel'farb

Precise segmentation of multimodal images

We propose new techniques for unsupervised segmentation of multimodal grayscale images such that each region-of-interest relates to a single dominant mode of the empirical marginal probability distribution of grey levels. We follow the most conventional approaches in that initial images and desired maps of regions are described by a joint Markov-Gibbs random field (MGRF) model of independent image signals and interdependent region labels. However, our focus is on more accurate model identification. To better specify region borders, each empirical distribution of image signals is precisely approximated by a linear combination of Gaussians (LCG) with positive and negative components. We modify an expectation-maximization (EM) algorithm to deal with the LCGs and also propose a novel EM-based sequential technique to get a close initial LCG approximation with which the modified EM algorithm should start. The proposed technique identifies individual LCG models in a mixed empirical distribution, including the number of positive and negative Gaussians. Initial segmentation based on the LCG models is then iteratively refined by using the MGRF with analytically estimated potentials. The convergence of the overall segmentation algorithm at each stage is discussed. Experiments show that the developed techniques segment different types of complex multimodal medical images more accurately than other known algorithms.

Computer-Aided Diagnosis Systems for Lung Cancer: Challenges and Methodologies

This paper overviews one of the most important, interesting, and challenging problems in oncology, the problem of lung cancer diagnosis. Developing an effective computer-aided diagnosis (CAD) system for lung cancer is of great clinical importance and can increase the patients chance of survival. For this reason, CAD systems for lung cancer have been investigated in a huge number of research studies. A typical CAD system for lung cancer diagnosis is composed of four main processing steps: segmentation of the lung fields, detection of nodules inside the lung fields, segmentation of the detected nodules, and diagnosis of the nodules as benign or malignant. This paper overviews the current state-of-the-art techniques that have been developed to implement each of these CAD processing steps. For each technique, various aspects of technical issues, implemented methodologies, training and testing databases, and validation methods, as well as achieved performances, are described. In addition, the paper addresses several challenges that researchers face in each implementation step and outlines the strengths and drawbacks of the existing approaches for lung cancer CAD systems.

Texture modeling by multiple pairwise pixel interactions

A Markov random field model with a Gibbs probability distribution (GPD) is proposed for describing particular classes of grayscale images which can be called spatially uniform stochastic textures. The model takes into account only multiple short- and long-range pairwise interactions between the gray levels in the pixels. An effective learning scheme is introduced to recover structure and strength of the interactions using maximal likelihood estimates of the potentials in the GPD as desired parameters. The scheme is based on an analytic initial approximation of the estimates and their subsequent refinement by a stochastic approximation. Experiments in modeling natural textures show the utility of the proposed model.

On retrieving textured images from an image database

Abstract We discuss the problem of an image-based query for retrieving images represented by sufficiently large regions of uniform textures from image data bases. A distance measure to match the query image to the database content under possible orientation and scale differences between the textures of the same type is proposed. The measure is based on comparing the gray-level difference histograms collected in accord with the structure of multiple pairwise pixel interactions in the subimages to be matched. The interaction structure is recovered with a proposed learning scheme for a Markov random field image model with Gibbs probability distribution. Texture rotation and scaling are handled to some extent by similar transformations of the interaction structures. Several results on experimental databases containing digitized textured images are presented.

EM Based Approximation of Empirical Distributions with Linear Combinations of Discrete Gaussians

We propose novel expectation maximization (EM) based algorithms for accurate approximation of an empirical probability distribution of discrete scalar data. The algorithms refine our previous ones in that they approximate the empirical distribution with a linear combination of discrete Gaussians (LCDG). The use of the DGs results in closer approximation and considerably better convergence to a local likelihood maximum compared to previously involved conventional continuous Gaussian densities. Experiments in segmenting multimodal medical images show the proposed algorithms produce more adequate region borders.

Models and methods for analyzing DCE‐MRI: A review

PURPOSE To present a review of most commonly used techniques to analyze dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), discusses their strengths and weaknesses, and outlines recent clinical applications of findings from these approaches. METHODS DCE-MRI allows for noninvasive quantitative analysis of contrast agent (CA) transient in soft tissues. Thus, it is an important and well-established tool to reveal microvasculature and perfusion in various clinical applications. In the last three decades, a host of nonparametric and parametric models and methods have been developed in order to quantify the CAs perfusion into tissue and estimate perfusion-related parameters (indexes) from signal- or concentration-time curves. These indexes are widely used in various clinical applications for the detection, characterization, and therapy monitoring of different diseases. RESULTS Promising theoretical findings and experimental results for the reviewed models and techniques in a variety of clinical applications suggest that DCE-MRI is a clinically relevant imaging modality, which can be used for early diagnosis of different diseases, such as breast and prostate cancer, renal rejection, and liver tumors. CONCLUSIONS Both nonparametric and parametric approaches for DCE-MRI analysis possess the ability to quantify tissue perfusion.

Probabilistic regularisation and symmetry in binocular dynamic programming stereo

Conventional binocular dynamic programming stereo is based on matching images of a given stereopair in order to obtain Bayesian or maximum likelihood estimates of hidden Markov models of epipolar terrain profiles. Because of partial occlusions and homogeneous textures, this problem is ill-posed and has to be regularised for getting a unique solution. Regularised matching involves usually heuristic weights of occluded points to make them comparable to binocularly visible points. An alternative way of regularisation is based on explicit Markov models of the profiles that allow to uniquely determine transition probabilities for the binocularly visible and occluded points. A desired profile maximises the likelihood ratio that relates the model derived from a stereopair to a purely random model. Transition probabilities for this latter act as the regularising parameters. Experiments with natural and artificial stereopairs outline a specific area in the parameter space where the reconstructed terrains more closely correspond to visual perception.

Geometric Feature Extraction by a Multimarked Point Process

This paper presents a new stochastic marked point process for describing images in terms of a finite library of geometric objects. Image analysis based on conventional marked point processes has already produced convincing results but at the expense of parameter tuning, computing time, and model specificity. Our more general multimarked point process has simpler parametric setting, yields notably shorter computing times, and can be applied to a variety of applications. Both linear and areal primitives extracted from a library of geometric objects are matched to a given image using a probabilistic Gibbs model, and a Jump-Diffusion process is performed to search for the optimal object configuration. Experiments with remotely sensed images and natural textures show that the proposed approach has good potential. We conclude with a discussion about the insertion of more complex object interactions in the model by studying the compromise between model complexity and efficiency.

Non-invasive image-based approach for early detection of acute renal rejection

Abstract. A promising approach for the automatic classification of normal and acute rejection transplants from Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) is proposed. The proposed approach consists of three main steps. The first step segments the kidney from the surrounding abdominal tissues by a level-set based deformable model with a speed function that accounts for a learned spatially variant statistical shape prior, 1st-order visual appearance descriptors of the contour interior and exterior (associated with the object and background, respectively), and a spatially invariant 2nd-order homogeneity descriptor. In the second step, to handle local object deformations due to kidney motion caused by patient breathing, we proposed a new nonrigid approach to align the object by solving Laplaces equation between closed equis-paced contours (iso-contours) of the reference and target objects. Finally, the perfusion curves that show the transportation of the contrast agent into the tissue are obtained from the segmented kidneys and used in the classification of normal and acute rejection transplants. Applications of the proposed approach yield promising results that would, in the near future, replace the use of current technologies such as nuclear imaging and ultrasonography, which are not specific enough to determine the type of kidney dysfunction.

Expectation-maximization for a linear combination of Gaussians

We propose a modified expectation-maximization algorithm that approximates an empirical probability density function of scalar data with a linear combination of Gaussians (LCG). Due to both positive and negative components, the LCG approximates inter-class transitions more accurately than a conventional mixture of only positive Gaussians. Experiments in segmenting multi-modal medical images show the proposed LCG-approximation results in more adequate region borders.