Segmental longitudinal strain (SLS) of the left ventricle (LV) is an important prognostic indicator for evaluating regional LV dysfunction, in particular for diagnosing and managing myocardial ischemia. Current techniques for strain estimation require significant manual intervention and expertise, limiting their efficiency and making them too resource-intensive for monitoring purposes. This study introduces the first automated pipeline, autoStrain, for SLS estimation in transesophageal echocardiography (TEE) using deep learning (DL) methods for motion estimation. We present a comparative analysis of two DL approaches: TeeFlow, based on the RAFT optical flow model for dense frame-to-frame predictions, and TeeTracker, based on the CoTracker point trajectory model for sparse long-sequence predictions. As ground truth motion data from real echocardiographic sequences are hardly accessible, we took advantage of a unique simulation pipeline (SIMUS) to generate a highly realistic synthetic TEE (synTEE) dataset of 80 patients with ground truth myocardial motion to train and evaluate both models. Our evaluation shows that TeeTracker outperforms TeeFlow in accuracy, achieving a mean distance error in motion estimation of 0.65 $\pm$ 0.20 mm on a synTEE test dataset. Clinical validation on 16 patients further demonstrated that SLS estimation with our autoStrain pipeline aligned with clinical references, achieving a mean difference (95% limits of agreement) of 1.09% (-8.90% to 11.09%). Incorporation of simulated ischemia in the synTEE data improved the accuracy of the models in quantifying abnormal deformation. Our findings indicate that integrating AI-driven motion estimation with TEE can significantly enhance the precision and efficiency of cardiac function assessment in clinical settings.

Domain adaptation methods aim to bridge the gap between datasets by enabling knowledge transfer across domains, reducing the need for additional expert annotations. However, many approaches struggle with reliability in the target domain, an issue particularly critical in medical image segmentation, where accuracy and anatomical validity are essential. This challenge is further exacerbated in spatio-temporal data, where the lack of temporal consistency can significantly degrade segmentation quality, and particularly in echocardiography, where the presence of artifacts and noise can further hinder segmentation performance. To address these issues, we present RL4Seg3D, an unsupervised domain adaptation framework for 2D + time echocardiography segmentation. RL4Seg3D integrates novel reward functions and a fusion scheme to enhance key landmark precision in its segmentations while processing full-sized input videos. By leveraging reinforcement learning for image segmentation, our approach improves accuracy, anatomical validity, and temporal consistency while also providing, as a beneficial side effect, a robust uncertainty estimator, which can be used at test time to further enhance segmentation performance. We demonstrate the effectiveness of our framework on over 30,000 echocardiographic videos, showing that it outperforms standard domain adaptation techniques without the need for any labels on the target domain. Code is available at https://github.com/arnaudjudge/RL4Seg3D.

Motion estimation in echocardiography plays an important role in the characterization of cardiac function, allowing the computation of myocardial deformation indices. However, there exist limitations in clinical practice, particularly with regard to the accuracy and robustness of measurements extracted from images. We therefore propose a novel deep learning solution for motion estimation in echocardiography. Our network corresponds to a modified version of PWC-Net which achieves high performance on ultrasound sequences. In parallel, we designed a novel simulation pipeline allowing the generation of a large amount of realistic B-mode sequences. These synthetic data, together with strategies during training and inference, were used to improve the performance of our deep learning solution, which achieved an average endpoint error of 0.07 ± 0.06 mm per frame and 1.20 ± 0.67 mm between ED and ES on our simulated dataset. The performance of our method was further investigated on 30 patients from a publicly available clinical dataset acquired from a GE system. The method showed promise by achieving a mean absolute error of the global longitudinal strain of 2.5 ± 2.1% and a correlation of 0.77 compared to GLS derived from manual segmentation, much better than one of the most efficient methods in the state-of-the-art (namely the FFT-Xcorr block-matching method). We finally evaluated our method on an auxiliary dataset including 30 patients from another center and acquired with a different system. Comparable results were achieved, illustrating the ability of our method to maintain high performance regardless of the echocardiographic data processed.

Convolutional neural networks (CNN) have demonstrated their ability to segment 2D cardiac ultrasound images. However, despite recent successes according to which the intra-observer variability on end-diastole and end-systole images has been reached, CNNs still struggle to leverage temporal information to provide accurate and temporally consistent segmentation maps across the whole cycle. Such consistency is required to accurately describe the cardiac function, a necessary step in diagnosing many cardiovascular diseases. In this paper, we propose a framework to learn the 2D+time apical long-axis cardiac shape such that the segmented sequences can benefit from temporal and anatomical consistency constraints. Our method is a post-processing that takes as input segmented echocardiographic sequences produced by any state-of-the-art method and processes it in two steps to (i) identify spatio-temporal inconsistencies according to the overall dynamics of the cardiac sequence and (ii) correct the inconsistencies. The identification and correction of cardiac inconsistencies relies on a constrained autoencoder trained to learn a physiologically interpretable embedding of cardiac shapes, where we can both detect and fix anomalies. We tested our framework on 98 full-cycle sequences from the CAMUS dataset, which are available alongside this paper. Our temporal regularization method not only improves the accuracy of the segmentation across the whole sequences, but also enforces temporal and anatomical consistency.

Convolutional neural networks (CNN) have had unprecedented success in medical imaging and, in particular, in medical image segmentation. However, despite the fact that segmentation results are closer than ever to the inter-expert variability, CNNs are not immune to producing anatomically inaccurate segmentations, even when built upon a shape prior. In this paper, we present a framework for producing cardiac image segmentation maps that are guaranteed to respect pre-defined anatomical criteria, while remaining within the inter-expert variability. The idea behind our method is to use a well-trained CNN, have it process cardiac images, identify the anatomically implausible results and warp these results toward the closest anatomically valid cardiac shape. This warping procedure is carried out with a constrained variational autoencoder (cVAE) trained to learn a representation of valid cardiac shapes through a smooth, yet constrained, latent space. With this cVAE, we can project any implausible shape into the cardiac latent space and steer it toward the closest correct shape. We tested our framework on short-axis MRI as well as apical two and four-chamber view ultrasound images, two modalities for which cardiac shapes are drastically different. With our method, CNNs can now produce results that are both within the inter-expert variability and always anatomically plausible without having to rely on a shape prior.

Delineation of the cardiac structures from 2D echocardiographic images is a common clinical task to establish a diagnosis. Over the past decades, the automation of this task has been the subject of intense research. In this paper, we evaluate how far the state-of-the-art encoder-decoder deep convolutional neural network methods can go at assessing 2D echocardiographic images, i.e., segmenting cardiac structures and estimating clinical indices, on a dataset, especially, designed to answer this objective. We, therefore, introduce the cardiac acquisitions for multi-structure ultrasound segmentation dataset, the largest publicly-available and fully-annotated dataset for the purpose of echocardiographic assessment. The dataset contains two and four-chamber acquisitions from 500 patients with reference measurements from one cardiologist on the full dataset and from three cardiologists on a fold of 50 patients. Results show that encoder-decoder-based architectures outperform state-of-the-art non-deep learning methods and faithfully reproduce the expert analysis for the end-diastolic and end-systolic left ventricular volumes, with a mean correlation of 0.95 and an absolute mean error of 9.5 ml. Concerning the ejection fraction of the left ventricle, results are more contrasted with a mean correlation coefficient of 0.80 and an absolute mean error of 5.6%. Although these results are below the inter-observer scores, they remain slightly worse than the intra-observer's ones. Based on this observation, areas for improvement are defined, which open the door for accurate and fully-automatic analysis of 2D echocardiographic images.

Delineation of the left ventricular cavity, myocardium, and right ventricle from cardiac magnetic resonance images (multi-slice 2-D cine MRI) is a common clinical task to establish diagnosis. The automation of the corresponding tasks has thus been the subject of intense research over the past decades. In this paper, we introduce the "Automatic Cardiac Diagnosis Challenge" dataset (ACDC), the largest publicly available and fully annotated dataset for the purpose of cardiac MRI (CMR) assessment. The dataset contains data from 150 multi-equipments CMRI recordings with reference measurements and classification from two medical experts. The overarching objective of this paper is to measure how far state-of-the-art deep learning methods can go at assessing CMRI, i.e., segmenting the myocardium and the two ventricles as well as classifying pathologies. In the wake of the 2017 MICCAI-ACDC challenge, we report results from deep learning methods provided by nine research groups for the segmentation task and four groups for the classification task. Results show that the best methods faithfully reproduce the expert analysis, leading to a mean value of 0.97 correlation score for the automatic extraction of clinical indices and an accuracy of 0.96 for automatic diagnosis. These results clearly open the door to highly accurate and fully automatic analysis of cardiac CMRI. We also identify scenarios for which deep learning methods are still failing. Both the dataset and detailed results are publicly available online, while the platform will remain open for new submissions.

The use of synthetic sequences is one of the most promising tools for advanced in silico evaluation of the quantification of cardiac deformation and strain through 3-D ultrasound (US) and magnetic resonance (MR) imaging. In this paper, we propose the first simulation framework which allows the generation of realistic 3-D synthetic cardiac US and MR (both cine and tagging) image sequences from the same virtual patient. A state-of-the-art electromechanical (E/M) model was exploited for simulating groundtruth cardiac motion fields ranging from healthy to various pathological cases, including both ventricular dyssynchrony and myocardial ischemia. The E/M groundtruth along with template MR/US images and physical simulators were combined in a unified framework for generating synthetic data. We efficiently merged several warping strategies to keep the full control of myocardial deformations while preserving realistic image texture. In total, we generated 18 virtual patients, each with synthetic 3-D US, cine MR, and tagged MR sequences. The simulated images were evaluated both qualitatively by showing realistic textures and quantitatively by observing myocardial intensity distributions similar to real data. In particular, the US simulation showed a smoother myocardium/background interface than the state-of-the-art. We also assessed the mechanical properties. The pathological subjects were discriminated from the healthy ones by both global indexes (ejection fraction and the global circumferential strain) and regional strain curves. The synthetic database is comprehensive in terms of both pathology and modality, and has a level of realism sufficient for validation purposes. All the 90 sequences are made publicly available to the research community via an open-access database.

Cardiac volume/function assessment remains a critical step in daily cardiology, and 3-D ultrasound plays an increasingly important role. Fully automatic left ventricular segmentation is, however, a challenging task due to the artifacts and low contrast-to-noise ratio of ultrasound imaging. In this paper, a fast and fully automatic framework for the full-cycle endocardial left ventricle segmentation is proposed. This approach couples the advantages of the B-spline explicit active surfaces framework, a purely image information approach, to those of statistical shape models to give prior information about the expected shape for an accurate segmentation. The segmentation is propagated throughout the heart cycle using a localized anatomical affine optical flow. It is shown that this approach not only outperforms other state-of-the-art methods in terms of distance metrics with a mean average distances of 1.81±0.59 and 1.98±0.66 mm at end-diastole and end-systole, respectively, but is computationally efficient (in average 11 s per 4-D image) and fully automatic.

The theory of compressed sensing (CS) leverages upon structure of signals in order to reduce the number of samples needed to reconstruct a signal, compared to the Nyquist rate. Although CS approaches have been proposed for ultrasound (US) imaging with promising results, practical implementations are hard to achieve due to the impossibility to mimic random sampling on a US probe and to the high memory requirements of the measurement model. In this paper, we propose a CS framework for US imaging based on an easily implementable acquisition scheme and on a delay-and-sum measurement model.

A plethora of techniques for cardiac deformation imaging with 3D ultrasound, typically referred to as 3D speckle tracking techniques, are available from academia and industry. Although the benefits of single methods over alternative ones have been reported in separate publications, the intrinsic differences in the data and definitions used makes it hard to compare the relative performance of different solutions. To address this issue, we have recently proposed a framework to simulate realistic 3D echocardiographic recordings and used it to generate a common set of ground-truth data for 3D speckle tracking algorithms, which was made available online. The aim of this study was therefore to use the newly developed database to contrast non-commercial speckle tracking solutions from research groups with leading expertise in the field. The five techniques involved cover the most representative families of existing approaches, namely block-matching, radio-frequency tracking, optical flow and elastic image registration. The techniques were contrasted in terms of tracking and strain accuracy. The feasibility of the obtained strain measurements to diagnose pathology was also tested for ischemia and dyssynchrony.

Real-time 3D Echocardiography (RT3DE) has been proven to be an accurate tool for left ventricular (LV) volume assessment. However, identification of the LV endocardium remains a challenging task, mainly because of the low tissue/blood contrast of the images combined with typical artifacts. Several semi and fully automatic algorithms have been proposed for segmenting the endocardium in RT3DE data in order to extract relevant clinical indices, but a systematic and fair comparison between such methods has so far been impossible due to the lack of a publicly available common database. Here, we introduce a standardized evaluation framework to reliably evaluate and compare the performance of the algorithms developed to segment the LV border in RT3DE. A database consisting of 45 multivendor cardiac ultrasound recordings acquired at different centers with corresponding reference measurements from three experts are made available. The algorithms from nine research groups were quantitatively evaluated and compared using the proposed online platform. The results showed that the best methods produce promising results with respect to the experts' measurements for the extraction of clinical indices, and that they offer good segmentation precision in terms of mean distance error in the context of the experts' variability range. The platform remains open for new submissions.

Quantification of cardiac deformation and strain with 3D ultrasound takes considerable research efforts. Nevertheless, a widespread use of these techniques in clinical practice is still held back due to the lack of a solid verification process to quantify and compare performance. In this context, the use of fully synthetic sequences has become an established tool for initial in silico evaluation. Nevertheless, the realism of existing simulation techniques is still too limited to represent reliable benchmarking data. Moreover, the fact that different centers typically make use of in-house developed simulation pipelines makes a fair comparison difficult. In this context, this paper introduces a novel pipeline for the generation of synthetic 3D cardiac ultrasound image sequences. State-of-the art solutions in the fields of electromechanical modeling and ultrasound simulation are combined within an original framework that exploits a real ultrasound recording to learn and simulate realistic speckle textures. The simulated images show typical artifacts that make motion tracking in ultrasound challenging. The ground-truth displacement field is available voxelwise and is fully controlled by the electromechanical model. By progressively modifying mechanical and ultrasound parameters, the sensitivity of 3D strain algorithms to pathology and image properties can be evaluated. The proposed pipeline is used to generate an initial library of 8 sequences including healthy and pathological cases, which is made freely accessible to the research community via our project web-page.

In this paper we present a compressed sensing (CS) method adapted to 3D ultrasound imaging (US). In contrast to previous work, we propose a new approach based on the use of learned overcomplete dictionaries that allow for much sparser representations of the signals since they are optimized for a particular class of images such as US images. In this study, the dictionary was learned using the K-SVD algorithm and CS reconstruction was performed on the non-log envelope data by removing 20% to 80% of the original data. Using numerically simulated images, we evaluate the influence of the training parameters and of the sampling strategy. The latter is done by comparing the two most common sampling patterns, i.e., point-wise and line-wise random patterns. The results show in particular that line-wise sampling yields an accuracy comparable to the conventional point-wise sampling. This indicates that CS acquisition of 3D data is feasible in a relatively simple setting, and thus offers the perspective of increasing the frame rate by skipping the acquisition of RF lines. Next, we evaluated this approach on US volumes of several ex vivo and in vivo organs. We first show that the learned dictionary approach yields better performances than conventional fixed transforms such as Fourier or discrete cosine. Finally, we investigate the generality of the learned dictionary approach and show that it is possible to build a general dictionary allowing to reliably reconstruct different volumes of different ex vivo or in vivo organs.

Tracking of moving objects in an image sequence is an important task in many application (e.g. medical imaging, robotics). However, this task is usually difficult due to inherent problems that could happen in sequences (i.e. possible occlusion of the object, large interframe motion). In this paper, we describe a new approach to integrate a priori motion information into a level-set-based active contour approach. Specifically, we introduce a new constraint that enforces the conservation of the levels of the implicit function along the image sequence. This constraint is formulated as a motion prior energy and is used in a tracking algorithm. The method is validated quantitatively on a clinical application based on 10 echocar-diographic and 5 cine-MRI sequences (≈ 700 images).

In this paper we propose a compressed sensing (CS) method adapted to 3D ultrasound imaging (US). In contrast to previous work, we propose a new approach based on the use of learned overcomplete dictionaries. Such dictionaries allow for much sparser representations of the signals since they are optimized for a particular class of images such as US images. We will investigate two undersampling patterns of the 3D US imaging: a spatially uniform random acquisition and a line-wise random acquisition. The latter being extremely interesting for 3D imaging: it would indeed allow skipping the acquisition of many lines among the several thousands required in 3D acquisitions, thus, speeding up the whole acquisition process and incrementing the imaging rate. In this study, the dictionary was learned using the K-SVD algorithm on patches extracted from a training dataset constituted of simulated 3D non-log envelope US volumes. Experiments were performed on a testing dataset made of a simulated 3D US log-envelope volume not included in the testing dataset. CS reconstruction was performed by removing 20% to 80% of the original samples according to the two undersampling patterns. Reconstructions using a K-SVD dictionary previously trained dictionary indicate minimal information loss, thus showing the potential of the overcomplete dictionaries.

Quantification of regional myocardial motion and deformation from cardiac ultrasound is fostering considerable research efforts. Despite the tremendous improvements done in the field, all existing approaches still face a common limitation which is intrinsically connected with the formation of the ultrasound images. Specifically, the reduced lateral resolution and the absence of phase information in the lateral direction highly limit the accuracy in the computation of lateral displacements. In this context, this paper introduces a novel setup for the estimation of cardiac motion with ultrasound. The framework includes an unconventional beamforming technique and a dedicated motion estimation algorithm. The beamformer aims at introducing phase information in the lateral direction by producing transverse oscillations. The estimator directly exploits the phase information in the two directions by decomposing the image into two 2-D single-orthant analytic signals. An in silico evaluation of the proposed framework is presented on five ultra-realistic simulated echocardiographic sequences, where the proposed motion estimator is contrasted against other two phase-based solutions exploiting the presence of transverse oscillations and against block-matching on standard images. An implementation of the new beamforming strategy on a research ultrasound platform is also shown along with a preliminary in vivo evaluation on one healthy subject.

We present a method for the analysis of heart motion from medical images. The algorithm exploits monogenic signal theory, recently introduced as an N-dimensional generalization of the analytic signal. The displacement is computed locally by assuming the conservation of the monogenic phase over time. A local affine displacement model is considered to account for typical heart motions as contraction/expansion and shear. A coarse-to-fine B-spline scheme allows a robust and effective computation of the model's parameters, and a pyramidal refinement scheme helps to handle large motions. Robustness against noise is increased by replacing the standard point-wise computation of the monogenic orientation with a robust least-squares orientation estimate. Given its general formulation, the algorithm is well suited for images from different modalities, in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption. This paper evaluates the method's feasibility on two emblematic cases: cardiac tagged magnetic resonance and cardiac ultrasound. In order to quantify the performance of the proposed method, we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known. A comparison is presented with state-of-the-art methods for cardiac motion analysis. On the data considered, these conventional approaches are outperformed by the proposed algorithm. A recent global optical-flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison. With respect to the latter, the proposed framework provides, along with higher accuracy, superior robustness to noise and a considerably shorter computation time.

This paper evaluates five 3D ultrasound tracking algorithms regarding their ability to quantify abnormal deformation in timing or amplitude. A synthetic database of B-mode image sequences modeling healthy, ischemic and dyssynchrony cases was generated for that purpose. This database is made publicly available to the community. It combines recent advances in electromechanical and ultrasound modeling. For modeling heart mechanics, the Bestel-Clement-Sorine electromechanical model was applied to a realistic geometry. For ultrasound modeling, we applied a fast simulation technique to produce realistic images on a set of scatterers moving according to the electromechanical simulation result. Tracking and strain accuracies were computed and compared for all evaluated algorithms. For tracking, all methods were estimating myocardial displacements with an error below 1 mm on the ischemic sequences. The introduction of a dilated geometry was found to have a significant impact on accuracy. Regarding strain, all methods were able to recover timing differences between segments, as well as low strain values. On all cases, radial strain was found to have a low accuracy in comparison to longitudinal and circumferential components.

This paper presents the Virtual Imaging Platform (VIP), a platform accessible at http://vip.creatis.insa-lyon.fr to facilitate the sharing of object models and medical image simulators, and to provide access to distributed computing and storage resources. A complete overview is presented, describing the ontologies designed to share models in a common repository, the workflow template used to integrate simulators, and the tools and strategies used to exploit computing and storage resources. Simulation results obtained in four image modalities and with different models show that VIP is versatile and robust enough to support large simulations. The platform currently has 200 registered users who consumed 33 years of CPU time in 2011.

Duplex ultrasonography is a mode of medical ultrasonography that allows one to visualize, at the same time, the inner structure of the body (B-mode) and the blood flow at a particular point in the body (Doppler mode). This mode requires a strategy for alternating B-mode and flow emissions. Traditional strategies either halve the maximum measurable velocity or introduce gaps in the flow data. The objective of this article is to propose a completely original method based on compressive sensing for reconstructing the Doppler signal segment by segment. Our approach is based on randomly alternating B-mode and flow emissions. The influence of the different parameters on the reconstruction quality is studied in detail. The technique is evaluated and its feasability is validated in simulation and from experimental in vivo data. It is also compared to the only method from the literature, proposed by Jensen, that reconstructs blood velocity estimates from sparse data sets.

We present a framework for the simulation of realistic cardiac ultrasound sequences. Both the visual aspect and the synthesized motion mimic a real echocardiography sequence used as template. The resulting simulation appears virtually indistinguishable from a real scan. As the true tissue motion is known, these synthetic sequences can provide a trustful benchmark for the analysis of heart motion. This possibility is illustrated by comparing the performance of two well known motion estimation algorithms.

Level-set methods have proven to be powerful and flexible tools in computer vision and medical imaging. Unfortunately, the flexibility of such models has historically resulted in long computational times and therefore limited clinical utility. In this context, we propose the first rigorous GPU implementation of the sparse field algorithm. We show that this model is able to reach high computational efficiency with no reduction in segmentation accuracy compared to its sequential counter-part.

A new formulation of active contours based on explicit functions has been recently suggested. This novel framework allows real-time 3-D segmentation since it reduces the dimensionality of the segmentation problem. In this paper, we propose a B-spline formulation of this approach, which further improves the computational efficiency of the algorithm. We also show that this framework allows evolving the active contour using local region-based terms, thereby overcoming the limitations of the original method while preserving computational speed. The feasibility of real-time 3-D segmentation is demonstrated using simulated and medical data such as liver computer tomography and cardiac ultrasound images.

We introduce in this paper a formulation of region-based active contours using explicit surfaces. By formally relating the explicit formulation to the usual implicit formulation, we show that it allows to take advantage of the local or global region-based functionals designed in the level-set framework, while providing a fast algorithm yielding close to real-time segmentation of 3D objects. We compare the segmentation performance of the proposed method with the fast level-set based method of Shi [8]. In similar conditions, the proposed method is 26x to 46x faster. Furthermore, we show that it can handle challenging, inhomogeneous data, while keeping a low computational burden.

In this paper we address the segmentation of shapes which may be approximated by two elliptical contours. Such patterns are indeed recurrent in many image processing applications. In this context, we develop a level-set framework especially dedicated to the detection of annular-like shapes. The behavior of this approach is illustrated on images from different fields. An evaluation is then performed for myocardium detection in medical images.

This paper describes a free open source software in Matlab (named Creaseg, http://www.creatis.insa-lyon. fr/~bernard/creaseg) for the evaluation of the performance of different level-set based algorithms in the context of 2D image segmentation. The platform gives access to the implementation of six level-set methods that have been chosen in order to cover a wide range of data attachment terms (contour, region and localized approaches). The software also gives the possibility to compare the performance of the proposed algorithms on any kind of images. The performance can be evaluated either visually, or from similarity measurements between a reference and the results of the segmentation.

In the field of image segmentation, most level-set-based active-contour approaches take advantage of a discrete representation of the associated implicit function. We present in this paper a different formulation where the implicit function is modeled as a continuous parametric function expressed on a B-spline basis. Starting from the active-contour energy functional, we show that this formulation allows us to compute the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-spline coefficients. We also show that each step of this minimization may be expressed through a convolution operation. Because the B-spline functions are separable, this convolution may in turn be performed as a sequence of simple 1-D convolutions, which yields an efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can be controlled explicitly via the degree and the scale of the chosen B-spline kernel. We illustrate the behavior of this approach on simulated as well as experimental images from various fields.

This work presents an algorithm for the segmentation of myocardial regions in echocardiography imaging based on the statistics of the radiofrequency image. We formulate the problem of segmentation in a maximum likelihood framework using the Generalized Gaussian as an a priori distribution. We minimize the resulting functional using a radial basis functions-based multiphase level set model. Numerical results obtained on both simulation and in vivo data demonstrate the capacity of our approach to segment myocardial regions in echocardiography imaging.

We consider a recent parametric level-set segmentation approach where the implicit interface is the zero level of a continuous function expanded onto compactly supported radial basis functions, defined by their centers, coefficients and supports. We propose to introduce prior knowledge of the shape to be recovered by placing the centers quasi-uniformly over an uncertainty area.

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.