Denis Friboulet

Variational B-Spline Level-Set: A Linear Filtering Approach for Fast Deformable Model Evolution

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.

A Virtual Imaging Platform for Multi-Modality Medical Image Simulation

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 workίow 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.

Creaseg: A free software for the evaluation of image segmentation algorithms based on level-set

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.

Two-dimensional spatial and temporal displacement and deformation field fitting from cardiac magnetic resonance tagging

Tagged magnetic resonance imaging is a specially developed technique to noninvasively assess contractile function of the heart. Several methods have been developed to estimate myocardial deformation from tagged image data. Most of these methods do not explicitly impose a continuity constraint through time although myocardial motion is a continuous physical phenomenon. In this paper, we propose to model the spatio-temporal myocardial displacement field by a cosine series model fitted to the entire tagged dataset. The method has been implemented in two dimensions (2D)+time. Its accuracy was successively evaluated on actual tagged data and on a simulated two-dimensional (2D) moving heart model. The simulations show that an overall theoretical mean accuracy of 0.1 mm can be attained with adequate model orders. The influence of the tagging pattern was evaluated and computing time is provided as a function of the model complexity and data size. This method provides an analytical and hierarchical model of the 2D+time deformation inside the myocardium. It was applied to actual tagged data from a healthy subject and from a patient with ischemia. The results demonstrate the adequacy of the proposed model for this evaluation.

Compactly Supported Radial Basis Functions Based Collocation Method for Level-Set Evolution in Image Segmentation

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.

Tracking geometrical descriptors on 3-D deformable surfaces: application to the left-ventricular surface of the heart

Motion and deformation analysis of the myocardium are of utmost interest in cardiac imaging. Part of the research is devoted to the estimation of the heart function by analysis of the shape changes of the left-ventricular endocardial surface. However, most clinically used shape-based approaches are often two-dimensional (2-D) and based on the analysis of the shape at only two cardiac instants. Three-dimensional (3-D) approaches generally make restrictive hypothesis about the actual endocardium motion to be able to recover a point-to-point correspondence between two surfaces. The present work is a first step toward the automatic spatio-temporal analysis and recognition of deformable surfaces. A curvature-based and easily interpretable description of the surfaces is derived. Based on this description, shape dynamics is first globally estimated through the temporal shape spectra. Second, a regional curvature-based tracking approach is proposed assuming a smooth deformation. It combines geometrical and spatial information in order to analyze a specific endocardial region. These methods are applied both on true 3-D X-ray data and on simulated normal and abnormal left ventricles. The results are coherent and easily interpretable. Shape dynamics estimations and comparisons between deformable object sequences are now possible through these techniques. This promising framework is a suitable tool for a complete regional description of deformable surfaces.

Fast automatic myocardial segmentation in 4D cine CMR datasets.

A novel automatic 3D+time left ventricle (LV) segmentation framework is proposed for cardiac magnetic resonance (CMR) datasets. The proposed framework consists of three conceptual blocks to delineate both endo and epicardial contours throughout the cardiac cycle: (1) an automatic 2D mid-ventricular initialization and segmentation; (2) an automatic stack initialization followed by a 3D segmentation at the end-diastolic phase; and (3) a tracking procedure. Hereto, we propose to adapt the recent B-spline Explicit Active Surfaces (BEAS) framework to the properties of CMR images by integrating dedicated energy terms. Moreover, we extend the coupled BEAS formalism towards its application in 3D MR data by adapting it to a cylindrical space suited to deal with the topology of the image data. Furthermore, a fast stack initialization method is presented for efficient initialization and to enforce consistent cylindrical topology. Finally, we make use of an anatomically constrained optical flow method for temporal tracking of the LV surface. The proposed framework has been validated on 45 CMR datasets taken from the 2009 MICCAI LV segmentation challenge. Results show the robustness, efficiency and competitiveness of the proposed method both in terms of accuracy and computational load.

Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing.

Compressive sensing (CS) theory makes it possible - under certain assumptions - to recover a signal or an image sampled below the Nyquist sampling limit. In medical ultrasound imaging, CS could allow lowering the amount of acquired data needed to reconstruct the echographic image. CS thus offers the perspective of speeding up echographic acquisitions and could have many applications, e.g. triplex acquisitions for CFM/B-mode/Doppler imaging, high-frame-rate echocardiography, 3D imaging using matrix probes, etc. The objective of this paper is to study the feasibility of CS for the reconstruction of channel RF data, i.e. the 2D set of raw RF lines gathered at the receive elements. Successful application of CS implies selecting a representation basis where the data to be reconstructed have a sparse expansion. Because they consist mainly in warped oscillatory patterns, channel RF data do not easily lend themselves to a sparse representation and thus represent a specific challenge. Within this perspective, we propose to perform and assess CS reconstruction of channel RF data using the recently introduced wave atoms [1] representation, which exhibit advantageous properties for sparsely representing such oscillatory patterns. Reconstructions obtained using wave atoms are compared with the reconstruction performed with two conventional representation bases, namely Fourier and Daubechies wavelets. The first experiment was conducted on simulated channel RF data acquired from a numerical cyst phantom. The quality of the reconstructions was quantified through the mean absolute error at varying subsampling rates by removing 50-90% of the original samples. The results obtained for channel RF data reconstruction yield error ranges of [0.6-3.0]×10(-2), [0.2-2.6]×10(-2), [0.1-1.5]×10(-2), for wavelets, Fourier and wave atoms respectively. The error ranges observed for the associated beamformed log-envelope images are [2.4-20.6]dB, [1.1-12.2]dB, and [0.5-8.8dB] using wavelets, Fourier, and wave atoms, respectively. These results thus show the superiority of the wave atom representation and the feasibility of CS for the reconstruction of US RF data. The second experiment aimed at showing the experimental feasibility of the method proposed using a data set acquired by imaging a general-purpose phantom (CIRS Model 054GS) using an Ultrasonix MDP scanner. The reconstruction was performed by removing 80% of the initial samples and using wave atoms. The reconstructed image was found to reliably preserve the speckle structure and was associated with an error of 5.5dB.

Detection of the whole myocardium in 2D-echocardiography for multiple orientations using a geometrically constrained level-set

The segmentation of the myocardium in echocardiographic images is an important task for the diagnosis of heart disease. This task is difficult due to the inherent problems of echographic images (i.e. low contrast, speckle noise, signal dropout, presence of shadows). In this article, we propose a method to segment the whole myocardium (endocardial and epicardial contours) in 2D echographic images. This is achieved using a level-set model constrained by a new shape formulation that allows to model both contours. The novelty of this work also lays in the fact that our framework allows to segment the whole myocardium for the four main views used in clinical routine. The method is validated on a dataset of clinical images and compared with expert segmentation.

Towards ultrasound cardiac image segmentation based on the radiofrequency signal

In echocardiography, the radio-frequency (RF) image is a rich source of information about the investigated tissues. Nevertheless, very few works are dedicated to boundary detection based on the RF image, as opposed to envelope image. In this paper, we investigate the feasibility and limitations of boundary detection in echocardiographic images based on the RF signal. We introduce two types of RF-derived parameters: spectral autoregressive parameters and velocity-based parameters, and we propose a discontinuity adaptive framework to perform the detection task. In classical echographic cardiac acquisitions, we show that it is possible to use the spectral contents for boundary detection, and that improvement can be expected with respect to traditional methods. Using the system approach, we study on simulations how the spectral contents can be used for boundary detection. We subsequently perform boundary detection in high frame rate simulated and in vivo cardiac sequences using the variance of velocity, obtaining very promising results. Our work opens the perspective of a RF-based framework for ultrasound cardiac image segmentation and tracking.