François Destrempes

Segmentation in Ultrasonic B -Mode Images of Healthy Carotid Arteries Using Mixtures of Nakagami Distributions and Stochastic Optimization

The goal of this work is to perform a segmentation of the intimamedia thickness (IMT) of carotid arteries in view of computing various dynamical properties of that tissue, such as the elasticity distribution (elastogram). The echogenicity of a region of interest comprising the intima-media layers, the lumen, and the adventitia in an ultrasonic B-mode image is modeled by a mixture of three Nakagami distributions. In a first step, we compute the maximum a posteriori estimator of the proposed model, using the expectation maximization (EM) algorithm. We then compute the optimal segmentation based on the estimated distributions as well as a statistical prior for disease-free IMT using a variant of the exploration/selection (ES) algorithm. Convergence of the ES algorithm to the optimal solution is assured asymptotically and is independent of the initial solution. In particular, our method is well suited to a semi-automatic context that requires minimal manual initialization. Tests of the proposed method on 30 sequences of ultrasonic B-mode images of presumably disease-free control subjects are reported. They suggest that the semi-automatic segmentations obtained by the proposed method are within the variability of the manual segmentations of two experts.

A Critical Review and Uniformized Representation of Statistical Distributions Modeling the Ultrasound Echo Envelope

In ultrasound imaging, various statistical distributions have been proposed to model the first-order statistics of the amplitude of the echo envelope. We present an overview of these distributions based on their compound representation, which comprises three aspects: the modulated distribution (Rice or Nakagami); the modulating distribution (gamma, inverse Gaussian or even generalized inverse Gaussian); and the modulated parameters (the diffuse signal power with or without the coherent signal component or the coherent signal power). This unifying point of view makes the comparison of the various models conceptually easier. In particular, we discuss the implications of the modulated parameters on the mean intensity and the signal-to-noise ratio of the intensity in the case of a vanishing diffuse signal. We conclude that the homodyned K-distribution is the only model among the literature for which the parameters have a physical meaning that is consistent with the limiting case, although the other distributions may fit real data.

Segmentation of Plaques in Sequences of Ultrasonic B-Mode Images of Carotid Arteries Based on Motion Estimation and a Bayesian Model

The goal of this paper is to perform a segmentation of atherosclerotic plaques in view of evaluating their burden and to provide boundaries for computing properties such as the plaque deformation and elasticity distribution (elastogram and modulogram). The echogenicity of a region of interest comprising the plaque, the vessel lumen, and the adventitia of the artery wall in an ultrasonic B-mode image was modeled by mixtures of three Nakagami distributions, which yielded the likelihood of a Bayesian segmentation model. The main contribution of this paper is the estimation of the motion field and its integration into the prior of the Bayesian model that included a local geometrical smoothness constraint, as well as an original spatiotemporal cohesion constraint. The Maximum A Posteriori of the proposed model was computed with a variant of the exploration/selection algorithm. The starting point is a manual segmentation of the first frame. The proposed method was quantitatively compared with manual segmentations of all frames by an expert technician. Various measures were used for this evaluation, including the mean point-to-point distance and the Hausdorff distance. Results were evaluated on 94 sequences of 33 patients (for a total of 8988 images). We report a mean point-to-point distance of 0.24 ± 0.08 mm and a Hausdorff distance of 1.24 ± 0.40 mm. Our tests showed that the algorithm was not sensitive to the degree of stenosis or calcification.

Ultrasound characterization of red blood cell aggregation with intervening attenuating tissue-mimicking phantoms

The analysis of the ultrasonic frequency-dependent backscatter coefficient of aggregating red blood cells reveals information about blood structural properties. The difficulty in applying this technique in vivo is due to the frequency-dependent attenuation caused by intervening tissue layers that distorts the spectral content of signals backscattered by blood. An optimization method is proposed to simultaneously estimate tissue attenuation and blood structure properties, and was termed the structure factor size and attenuation estimator (SFSAE). An ultrasound scanner equipped with a wide-band 25 MHz probe was used to insonify porcine blood sheared in both Couette and tubular flow devices. Since skin is one of the most attenuating tissue layers during in vivo scanning, four skin-mimicking phantoms with different attenuation coefficients were introduced between the transducer and the blood flow. The SFSAE gave estimates with relative errors below 25% for attenuations between 0.115 and 0.411 dBMHz and kR<2.08 (k being the wave number and R the aggregate radius). The SFSAE can be useful to examine in vivo and in situ abnormal blood conditions suspected to promote pathophysiological cardiovascular consequences.

Three-dimensional biplanar reconstruction of scoliotic rib cage using the estimation of a mixture of probabilistic prior models

In this paper, we present an original method for the three-dimensional (3-D) reconstruction of the scoliotic rib cage from a planar and a conventional pair of calibrated radiographic images (postero-anterior with normal incidence and lateral). To this end, we first present a robust method for estimating the model parameters in a mixture of probabilistic principal component analyzers (PPCA). This method is based on the stochastic expectation maximization (SEM) algorithm. Parameters of this mixture model are used to constrain the 3-D biplanar reconstruction problem of scoliotic rib cage. More precisely, the proposed PPCA mixture model is exploited for dimensionality reduction and to obtain a set of probabilistic prior models associated with each detected class of pathological deformations observed on a representative training scoliotic rib cage population. By using an appropriate likelihood, for each considered class-conditional prior model, the proposed 3-D reconstruction is stated as an energy function minimization problem, which is solved with an exploration/selection algorithm. The optimal 3-D reconstruction then corresponds to the class of deformation and parameters leading to the minimal energy. This 3-D method of reconstruction has been successfully tested and validated on a database of 20 pairs of biplanar radiographic images of scoliotic patients, yielding very promising results. As an alternative to computed tomography-scan 3-D reconstruction this scheme has the advantage of low radiation for the patient, and may also be used for diagnosis and evaluation of deformity of a scoliotic rib cage. The proposed method remains sufficiently general to be applied to other reconstruction problems for which a database of objects to be reconstructed is available (with two or more radiographic views).

Standardized evaluation methodology and reference database for evaluating IVUS image segmentation

This paper describes an evaluation framework that allows a standardized and quantitative comparison of IVUS lumen and media segmentation algorithms. This framework has been introduced at the MICCAI 2011 Computing and Visualization for (Intra)Vascular Imaging (CVII) workshop, comparing the results of eight teams that participated. We describe the available data-base comprising of multi-center, multi-vendor and multi-frequency IVUS datasets, their acquisition, the creation of the reference standard and the evaluation measures. The approaches address segmentation of the lumen, the media, or both borders; semi- or fully-automatic operation; and 2-D vs. 3-D methodology. Three performance measures for quantitative analysis have been proposed. The results of the evaluation indicate that segmentation of the vessel lumen and media is possible with an accuracy that is comparable to manual annotation when semi-automatic methods are used, as well as encouraging results can be obtained also in case of fully-automatic segmentation. The analysis performed in this paper also highlights the challenges in IVUS segmentation that remains to be solved.

A stochastic method for Bayesian estimation of hidden Markov random field models with application to a color model

We propose a new stochastic algorithm for computing useful Bayesian estimators of hidden Markov random field (HMRF) models that we call exploration/selection/estimation (ESE) procedure. The algorithm is based on an optimization algorithm of O. Francois, called the exploration/selection (E/S) algorithm. The novelty consists of using the a posteriori distribution of the HMRF, as exploration distribution in the E/S algorithm. The ESE procedure computes the estimation of the likelihood parameters and the optimal number of region classes, according to global constraints, as well as the segmentation of the image. In our formulation, the total number of region classes is fixed, but classes are allowed or disallowed dynamically. This framework replaces the mechanism of the split-and-merge of regions that can be used in the context of image segmentation. The procedure is applied to the estimation of a HMRF color model for images, whose likelihood is based on multivariate distributions, with each component following a Beta distribution. Meanwhile, a method for computing the maximum likelihood estimators of Beta distributions is presented. Experimental results performed on 100 natural images are reported. We also include a proof of convergence of the E/S algorithm in the case of nonsymmetric exploration graphs.

Segmentation method of intravascular ultrasound images of human coronary arteries

The goal of this study was to show the feasibility of a 2D segmentation fast-marching method (FMM) in the context of intravascular ultrasound (IVUS) imaging of coronary arteries. The original FMM speed function combines gradient-based contour information and region information, that is the gray level probability density functions of the vessel structures, that takes into account the variability in appearance of the tissues and the lumen in IVUS images acquired at 40 MHz. Experimental results on 38 in vivo IVUS sequences yielded mean point-to-point distances between detected vessel wall boundaries and manual validation contours below 0.11 mm, and Hausdorff distances below 0.33 mm, as evaluated on 3207 images. The proposed method proved to be robust in taking into account various artifacts in ultrasound images: partial shadowing due to calcium inclusions within the plaque, side branches adjacent to the main artery to segment, the presence of a stent, injection of contrast agent or dissection, as tested on 209 images presenting such artifacts.

Fusion of Hidden Markov Random Field Models and Its Bayesian Estimation

In this paper, we present a Hidden Markov Random Field (HMRF) data-fusion model. The proposed model is applied to the segmentation of natural images based on the fusion of colors and textons into Julesz ensembles. The corresponding Exploration/Selection/Estimation (ESE) procedure for the estimation of the parameters is presented. This method achieves the estimation of the parameters of the Gaussian kernels, the mixture proportions, the region labels, the number of regions, and the Markov hyper-parameter. Meanwhile, we present a new proof of the asymptotic convergence of the ESE procedure, based on original finite time bounds for the rate of convergence

ESTIMATION METHOD OF THE HOMODYNED K-DISTRIBUTION BASED ON THE MEAN INTENSITY AND TWO LOG-MOMENTS.

The homodyned K-distribution appears naturally in the context of random walks and provides a useful model for the distribution of the received intensity in a wide range of non-Gaussian scattering configurations, including medical ultrasonics. An estimation method for the homodyned K-distribution based on the first moment of the intensity and two log-moments (XU method), namely the X and U-statistics previously studied in the special case of the K-distribution, is proposed as an alternative to a method based on the first three moments of the intensity (MI method) or the amplitude (MA method), and a method based on the signal-to-noise ratio (SNR), the skewness and the kurtosis of two fractional orders of the amplitude (labeled RSK method). Properties of the X and U statistics for the homodyned K-distribution are proved, except for one conjecture. Using those properties, an algorithm based on the bisection method for monotonous functions was developed. The algorithm has a geometric rate of convergence. Various tests were performed to study the behavior of the estimators. It was shown with simulated data samples that the estimations of the parameters 1/α and 1/(κ + 1) of the homodyned K-distribution are preferable to the direct estimations of the clustering parameter α and the structure parameter κ (with respective relative root mean squared errors (RMSEs) of 0.63 and 0.13 as opposed to 1.04 and 4.37, when N = 1000). Tests on simulated ultrasound images with only diffuse scatterers (up to 10 per resolution cell) indicated that the XU estimator is overall more reliable than the other three estimators for the estimation of 1/α, with relative RMSEs of 0.79 (MI), 0.61 (MA), 0.53 (XU) and 0.67 (RSK). For the parameter 1/(κ + 1), the relative RMSEs were equal to 0.074 (MI), 0.075 (MA), 0.069 (XU) and 0.100 (RSK). In the case of a large number of scatterers (11 to 20 per resolution cell), the relative RMSEs of 1/α were equal to 1.43 (MI), 1.27 (MA), 1.25 (XU) and 1.33 (RSK), and the relative RMSEs of 1/(κ + 1) were equal to 0.14 (MI), 0.16 (MA), 0.17 (XU) and 0.20 (RSK). The four methods were also tested on simulated ultrasound images with a variable density of periodic scatterers to test images with a coherent component. The addition of noise on ultrasound images was also studied. Results showed that the XU estimator was overall better than the three other ones. Finally, on the simulated ultrasound images, the average computation times per image were equal to 6.0 ms (MI), 8.0 ms (MA), 6.8 ms (XU) and 500 ms (RSK). Thus, a fast, reliable, and novel algorithm for the estimation of the homodyned K-distribution was proposed.