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Multi-view 3D Reconstruction with Volumetric Registration in a Freehand Ultrasound Imaging System Honggang Yua*, Marios S. Pattichisa**, and M. Beth Goensb a image and video Processing and Communications Lab, Dept. of Electrical and Computer Engineering, b Dept. of Pediatrics, Division of Cardiology, The University of New Mexico, Albuquerque, NM, USA 87131 ABSTRACT In this paper, we describe a new freehand ultrasound imaging system for reconstructing the left ventricle from 2D echocardiography slices. An important contribution of the proposed system is its ability to reconstruct from multiple standard views. The multi-view reconstruction procedure results in significant reduction in reconstruction error over single view reconstructions. The system uses object-based 3D volumetric registration, allowing for arbitrary rigid object movements in inter-view acquisition. Furthermore, a new segmentation procedure that combines level set methods with gradient vector flow(GVF) is used for automatically segmenting the 2D ultrasound images, in which low level of contrast, high level of speckle noise, and weak boundaries are common. The new segmentation approach is shown to be robust to these artifacts and is found to converge to the boundary from a wider range of initial conditions than competitive methods. The proposed system has been validated on a physical, 3D ultrasound calibration phantom and evaluated on one actual cardiac echocardiography data set. In the phantom experiment, two calibrated volumetric egg-shape objects were scanned from the top and side windows and reconstructed using the new method. The volume error was measured to be less than 4%. In a real heart data set experiment, qualitative results of 3D surface reconstruction from parasternal and apical views appear significantly improved over single view reconstructions. The estimated volumes from the 3D reconstructions were also found to be in agreement with the manual clinical measurements from 2D slices. Further extension of this work is to compare the quantitative results with more accuracy MRI data. Keywords: 3D freehand ultrasound, 3D reconstruction, multi-view reconstruction, volume registration, segmentation 1. INTRODUCTION Freehand 3D ultrasound imaging techniques can be used to reconstruct 3D objects from a set of registered 2D image slices. The 2D slices can be located at any arbitrary orientation and position throughout space, and can be acquired using any standard, 2D ultrasound transducer in conjunction with an orientation and position sensor. This strategy allows large volumes to be imaged and offers the possibility to upgrade a conventional 2D scanner to a 3D scanner, at a very low cost. Recently, 3D ultrasound imaging systems have been used for diagnosis in clinical echocardiography[1]. Most research on 3D freehand echocardiography has been focused on reconstructing the left ventricle from a single, standard view. We propose a new, multi-view reconstruction system, which can combine information from different sets of 2D slices, resulting in a significant reduction in the reconstruction error. This is useful as for example; multi- view reconstruction can supply data in shadow regions in single view sweeps by combining information from different views to improve the quality of reconstruction. * email: honggang@ece.unm.edu, ** email: pattichis@ece.unm.edu Ultrasound imaging research on multi-view reconstruction methods is primarily focused on reconstructing the left- ventricle. An example can be found in Ye et al., where a 3D rotational probe and a position sensor are used to track the parasternal short-axis view and apical long-axis view[2]. Unfortunately, the controller for a rotational probe tended to be bulky and inconvenient to use. It was limited to a fixed and regular geometry of acquired 2D images. The method assumes there is a good spatial alignment between different view sweeps. This is impractical in reality. Legget et al. used a 2D freehand scanning protocol to combine parasternal short-axis, and apical rotation[3]. The 2D images were manually registered by manual tracing of the left ventricular boundaries with some visual feedback. Neither study addressed the problem of how to automatically register 3D reconstructions between different views. Misregistration is a big problem in freehand 3D ultrasound that affects the accuracy of reconstruction and volume measurement. In general, there are three sources that cause misregistration in freehand 3D ultrasound: (i) error in position and orientation measurements, (ii) target movement during intra-view (deformation by cardiac motion and respiration) and inter-view sweeps (rigid movement of the target), and (iii) probe pressure applied on the scanning surface. We note that rigid movement of the target and inaccurate sensor measurements cause the majority of the registration errors. Rohling et. al. first reported a automatic registration of multiple sweeps for gall bladder reconstruction[4]. They used six, slightly different sweeps for acquiring the images. Registration was based on the correlation of magnitude of the 3D gradient and no landmark identification was required. In our multi-view left ventricle reconstruction system, 3D volumes from different view sweeps may exhibit partial or no overlap because of the movement of the patient and position measurements errors. To achieve accurate and robust registration performance, we use an efficient, geometric registration method. First, we initialize the search of the optimal registration parameters using a 3D Hotelling transform to construct an object-based reference volume to coarsely register 3D volumes from different views. Then high accuracy registration is computed using a robust, non-linear least squares method. To avoid any issues with the strong variability in echoardiographic images, such as muscle tissue, blood flow, much noise and artifacts in the endocardial cavity, we set pixel values to one around the boundary in the segmented images from each view, which are common features for the volumes from different views. We have found the proposed registration procedure to be very efficient and robust, converging to the same registration parameters from a wide variety of initializations. Left ventricular volume can be estimated by the 3D surface reconstruction generated by the boundaries segmented from multiple 2D imaging planes. Manual tracing of cardiac boundaries is tedious, time-consuming and subject to inter- reader variability. Automatic segmentation techniques of echocardiographic images face a number of challenges due to the characteristics of the images: poor image contrast, high-level speckle noise, weak endocardial boundaries, boundary gaps etc. Deformable models have been extensively studied and used for segmentation. There are mainly two types of deformable models: parametric and geometric deformable models. The evolved curve is explicitly presented by the parametric forms in parametric models while it is implicitly expressed as level sets of a higher dimensional scalar function in geometric models. Geometric deformable models can handle topological changes automatically. Corsi et.al.[5] applied level set techniques to semi-automatically segment real-time 3D echocardiographic data, reconstruct the shape of the left ventricle and estimate its volume. They threw away the balloon term in the speed function to prevent the expansion of the evolving curve passing through weak edges and boundary gaps. We have found that this scheme only works when the initial curves are very close to the actual boundaries. We did not obtain satisfactory solutions for very weak edges at loose initial conditions. In our approach, we considered integrating the gradient vector flow (GVF) method[6] , which has been shown to be a powerful external force in parametric deformable models, with geodesic active contour flow (typical geometric deformable model). GVF can diffuse the image gradient information toward the homogenous background. We have found three research groups that used three different models for geometric GVF active contours[7-9]. Paragios et. al. developed a more general, robust and fast geometric GVF active contour model[9]. We will apply a variation of this approach to automatically segment 2D ultrasound image slices. The remainder of this paper is organized as follows: section 2 describes the proposed methods in detail. Section 3 presents qualitative and quantitative results for multi-view reconstruction for in vitro and in vivo data. Some initial results on segmentation are also presented. Concluding remarks and a discussion for future work are given in Section 4. 2. METHODS 2.1 System and Data Acquisition Figure 1 shows a block diagram of the 3D freehand ultrasound imaging system. The system has been built at the Pediatric Cardiology Clinic of the Children’s Hospital Heart Center, at the University of New Mexico. This system has three components: (i) the ultrasound machine, an ACUSON Sequoia C256 with 7 MHz vector wide-view array transducer (7V3C), (ii) a six-degrees of freedom, electromagnetic position and orientation measurement device (Flock of Birds, Ascension, Burlington, VT, USA), and (iii) a desktop computer (Intel Pentium 4, 2GB memory, 2.6G Hz) equipped with an 8-bit Meteor-Π Standard framegrabber (Matrox, Canada). Position & Orientatio PC EPOM Hard Disk (Flock of Birds) RAM Framegrabber Transmitter B-mode Images & ECG Echo Ultrasound Machine Sensor (Acuson Sequoia Transducer Figure 1. 3D freehand ultrasound imaging Flock of Birds is an electromagnetic six degrees-of-freedom measurement device that uses pulsed DC magnetic fields to measure the position and orientation of the sensor relative to the transmitter. The transmitter is approximately in the shape of a cube with approximate dimensions of 95×95×95mm and was fixed on the top of the nonferrous patient bed. The receiver has dimensions 25.4×25.4×20.3mm and was attached on the ultrasound transducer by a specially designed housing. The physical characteristics of the receiver are important since it should not interfere with probe handling when it is attached to the ultrasound probe. The scanning range of the sensor is within 90cm from the transmitter. 2D ultrasound video and images (640×480 pixels) with the corresponding orientation and position sensor data are collected at 30 Hz. Additionally, an interference detection technique[10], which is based on the estimates of the probability density functions for both position and angle measurements was performed before initial setup of the 3D system. We want to avoid any ferrous or electromagnetic interference that might corrupt tracking accuracy from the scanning environment. 2.2 3D reconstructions from multiple-view sweeps The 3D system uses a set of acquired arbitrary located 2D image slices in space to reconstruct a regular 3D data set. From each image slice, each pixel position is denoted by a homogeneous position vector and transformed to its corrected 3D coordinates in the reference volume. Firstly, we transform the 2D image coordinates to 3D sensor coordinates, relative to the origin of sensor coordinate frame. This transformation is constant throughout the reconstruction procedure and determined by calibration. A calibration phantom is built by stretching a cotton cross-wire under a plastic water tank. Multiple B-scans (40-50) are acquired, imaging the centre of a cross-wire from the top and through the side wall of the water tank. The point target is located using the brightest intensity in the 2D images while tilting the transducer to align the target with the center of the ultrasound beam. An iterative non-linear least square algorithm was used to solve the over-determined problem to determine the six parameters of this transformation[11],[12]. Acquired sensor position and orientation measurement data are used to be the second transformation, which transform the sensor coordinates to 3D world coordinates, relative to the origin of transmitter coordinate frame, which is the reconstructed volume. Figure 2 depicts the three coordinates in reconstruction. An averaging strategy is used for combining 3D reconstructions from multiple scanning sweeps. The intensity of each voxel in the reconstructed volume is estimated by averaging the reconstructed intensities from each view. Sensor y Centre of transducer face x v1 z Transducer ROI vy vx ROI point Y X Image plane Z Transmitter Figure 2. Illustration of spatial coordinates in 3D freehand ultrasound imaging 2.3 3D registration using the Hotelling Transform Automatic registration is necessary and important in multi-view reconstruction. The Hotelling transform (also called Principal Component Analysis or Karhunen-Loeve transform) is a statistical method that can be used for developing our registration method. In our case, the data population is the collection of 3D position coordinates of each segmented object point given as a random vector X = [ X 1 , X 2 , X 3 ] . The mean vector gives the center of gravity of the object T given by m X = E {X} . The covariance matrix is given by { C X = E ( X − m X )( X − m X ) T }. Each matrix element cii of CX denotes the variance of X i , the ith component of the X vectors. Element cij is the covariance between components X i and X j . For N vector samples from a random population, the mean vector and covariance matrix can be estimated using 1 N 1 N mX = ∑ xi , CX = N ∑ xi xiT − m Xm XT . N i =1 i =1 Define A to be a matrix whose rows are the eigenvectors of CX , ordered so that the first row of A is the eigenvector that corresponds to the largest eigenvalue of CX , and the last row corresponds its smallest eigenvalue. Then transform Y = A( X − m X ) is called the Hotelling transform. Cy is a diagonal matrix whose diagonal elements are the eigenvalues of CX and the components of Y are uncorrelated. The new position vectors generated by the Hotelling transform are such that the origin is at the centroid of the object, correcting any object translation, and the transformed object's axes are in the direction of the eigenvectors of CX , correcting arbitrary object rotation. The new axes are aligned with the object’s principal axes (eigenvectors). The maximal sample variance is located in the horizontal axes. Thus, 3D reconstruction from different views can be registered to the same object-based reference volume by using the 3D Hotelling transform, provided that all views image the entire 3D object. In general, this assumption could not always hold since we cannot guarantee that the entire 3D object will be imaged. Thus the registration results from using the Hotelling transform are used to initialize a more accurate registration procedure. To achieve high accuracy registration, we used non-linear least squares (Levenberg-Marquardt) to estimate the parameters for rigid-body registration between the views. We note that echocardiographic images from the different views can appear substantially different, and the majority of the pixels in 2D echocardiographic images exhibit non- constant features, especially inside the endocardial cavity, where there are muscle tissue, blood flow and much noise and artifacts, including the use of different gains at different depths. Thus, registration by the original intensity images is not likely to succeed. Instead we apply a threshold to binarize the ECG-gated endocardial boundaries, which are shared between different views. For the registration method to converge, the complex surface structures from different views must exhibit some partial overlap. To help with the overlap computation, we first reconstruct the 3D view with the largest number of 2D slice planes over a regular Cartesian grid, then register the 2D slice planes from the rest of the view to it. In our experiment, we have found this procedure to be both efficient and robust. 2.4 Segmentation 3D surface reconstruction is generated using the boundaries segmented from multiple 2D imaging planes. Automatic endocardial boundary segmentation is generally needed for clinical 3D echocardiography. A new segmentation procedure that combines level set methods with gradient vector flow (GVF) is used for automatically segmenting 2D ultrasound images. Corsi et. al.[5] Applied level set techniques to semi-automatically segment 3D echocardiographic data in 2002: ϕ t = g ε K ∇ ϕ + β ∇ g g∇ ϕ r Where ϕ ( x, t ) is a higher-dimensional scalar function, called the level set function. It represents the moving front as the r zero level set where ϕ ( x, t ) = 0 , K is the mean curvature, g is a monotonically decreasing function that satisfies: g (0) = 1, lim g ( x ) → 0 . In echocardiographic image segmentation, g is usually used as an edge indicator applied x→∞ r to a smoothed image I ( x) : ( ( )⎭ −1 ⎧ ( )) ⎫ r 2 g = ⎨1 + ∇ Gσ ∗ I x α ⎬ . ⎩ The vector field ∇g is an advection term that always points towards image boundaries. The parameters β , ε are used to control the strength of advection and limit the regularization. In our experiments, this approached worked well only when the initial curve or surface is close enough to the actual endocardial boundaries. To overcome this weakness, we considered integrating gradient vector flow (GVF) in a geometric deformable model. Paragios[9] used fast GVF geometric active contours that are robust to the initial conditions and allow active contours to undergo topological changes: ⎢ ⎣ $$ ⎣ ⎦( ϕt = g ⎡ε K ∇ϕ − ⎡u, v ⎤ g∇ϕ ⎤ . ⎥ ⎦ ) Instead of ∇g , ⎡u, v ⎤ is called gradient vector flow(GVF), a two-dimensional vector filed that diffuses the image $$ ⎣ ⎦ gradient information toward the homogenous background. It is a bidirectional flow that propagates the curve toward to object boundary form either side. It has the advantage that it is not sensitive to the initial curve. In our experiments, we replaced g with coefficient β in front of the GVF vector to control the strength of the GVF boundary advection vector filed: ⎣ ⎦( ϕt = g ( ε K ∇ϕ ) − β ⎡u, v ⎤ g ϕ , $$ ∇ ) which yielded good results. 3. EXPERIMENTAL RESULTS 3.1 Multi-view reconstruction with in vitro data To compare the reconstruction accuracy for multi-view versus single view reconstructions, we tested the system on both a 3D calibration ultrasound calibration phantom, (Model 055, CIRS, USA) and in vivo data. These measurements have the disadvantage of being affected by the unsteady probe pressure, calibration error, spatial locator measurement error etc. All the 2D images slices were manually segmented. The phantom contains two calibrated volumetric test egg-shape objects, which can be scanned from two scan surfaces: top and side. Typical B-scans of a small egg target in the phantom are shown in Figures 3(a) and 3(b). In this experiment, 41 images are used with a region of interest (ROI) 70×70 pixels in the top window short-axis view and 44 images with ROI 110×60 pixels in the top window long-axis view. The manually segmented object contours are shown in Figures 3(c) and 3(d). Smoothed (5×5×5 Gaussian filter (σ = 0.65)) single view reconstructions are shown in Figures 3(e) and 3(f), respectively. We note that the long-axis view reconstruction loses some data in the z-axis direction; this is caused by missing data samples and inaccurate segmentation. The spatial location of object contours from two views show that if we reconstruct the object directly, we would not get the correct result. Using our method, the final reconstruction presents the right shape of object that are shown in figures 3(h). Quantitative measurements of object volume are listed in Table 1. We show volume estimates from single-view, two- view, and three-view reconstructions with 3D volume registration. We note that the multi-view reconstruction volumes with 3D registration are closer to the real volume than any of the single-view reconstruction volumes. (a) (b) (c) (d) (e) (f) (g) (h) Figure 3 Multiple-view reconstruction with volume registration using in vitro data. (a),(b) typical long-axis and short-axis B-scan images. (c),(d) contours in long-axis and short-axis view, respectively. (e),(f) smoothed long-axis and short-axis view reconstruction, respectively. (g) 3D scanning contours in two views. (h) two-view reconstruction by 3D Hotelling registration. Table 1 Phantom volume estimates and relative error Number of Relative Views Number of frames Volume(cc) views Error(%) Top window, short-axis 41 7.4218 3.08 Top window, long-axis 44 5.1246 -28.83 1 view Side window, short-axis 47 7.4441 3.39 Small Egg Side window, long-axis 44 4.7494 -34.04 (7.2cc) Short-axis 21 Top window 7.4072 2.88 Long-axis 22 2 views Short-axis 24 Side window 7.3697 2.36 Long-axis 22 Top window, short-axis 21 3 views Top & Side window Top window, long-axis 22 7.0045 -2.72 Side window, long-axis 22 Number of Relative Views Number of frames Volume(cc) views Error(%) Top window, short-axis 43 72.5433 -0.35 Top window, long-axis 47 40.9424 -43.76 1 view Side window, short-axis 49 76.8417 5.55 Large Egg Side window, long-axis 50 55.7554 -23.41 (72.8 cc) Short-axis 22 Top window 70.1324 -3.66 Long-axis 16 2 views Short-axis 25 Side window 75.3381 3.49 Long-axis 17 Top window, short-axis 15 Top window, long-axis 12 3 views Top & Side window 73.0414 0.33 Side window, long-axis 13 3.2 Multi-view reconstruction with in vivo data In this experiment, data sets were acquired from two acoustic windows: the parasternal short-axis view and the apical long-axis view from a healthy child volunteer. The ultrasound video images were acquired at 30 frames per second. Each single view scanning that were expecting to imaging the whole of the left ventricle. Each single view sweeps can be fully finished in 15 seconds (450 images) with respiratory and ECG gating. 2D images were captured continuously while freely manipulating the ultrasound probe to scan the left ventricle. There is no need to require that the volunteer remains still during the different view sweeps. And that is not easy for a patient in typical clinical practice. Our method can correct any rigid motion caused by the patient’s movement. The reconstruction and volume measurements were performed at end-of-diastole and end-of-systole phases separately. The end-of-diastole (ED) phase was defined as the first frame after the electrocardiographic R wave in which the mitral valve was closed and it was verified using M-mode images. The end-of-systole (ES) frame was selected from a sequence of frames in which the endocardial cavity visually appeared smallest. Figure 4 show 3D reconstructions using image slices from the parasternal short-axis and apical long-axis views in the ED and ES phases. Figures 4(a) and (b) show 2D image slices from each view. The locations of the scanning slices from each view in 3D space are shown in Figures 4(c) and (d), respectively. Two volume contours are manually segmented and shown in (e). Here, 14 images at the ED phase are used with a region of interest (ROI) of 240×210 pixels in the parasternal short-axis view and 9 images with an ROI of 240×220 pixels in the apical long-axis view. Note that the two volumes overlapped over a very small region. Using the proposed volume registration method, the two view sweeps can be aligned together and thus get a much better reconstruction of the left ventricle compared to each single view reconstruction. Figures 4(f)-(h) show 3D reconstructed endocardial surfaces from the parasternal short-axis view, the apical long-axis view, and combined views, respectively at the ED phase. A two-view reconstruction at the ES phase is shown in Figure 4(i). (a) (b) (c) (d) (e) (f) (g) (h) (i) Figure 4 Multiple-view reconstruction with volume registration using in vivo data. (a), (b) 2D image slices from parasternal short- axis and apical–long axis view, respectively. (c),(d) locations of the scanning planes of each view respectively. (e) two volume contours in 3D space. (f)-(h) show 3D reconstructed surfaces from the parasternal, apical and combined views, respectively at ED phase. (i)two-view reconstruction at ES frame. The volume of the left ventricle was estimated from the reconstructions at the ED and ES phases separately as summarized in Table 2. The values in % indicate the relative error with respect to the echocardiography specialist measurement. The results show that the volume estimated using the combined two acoustic views reconstruction agrees better with the volume measurement by the echocardiography specialist using a standard 2D clinical technique. A more objective and accurate comparison would be to compare these results with cardiac magnetic resonance (MR) data. MRI is a more accurate and reliable reference standard for cardiac parameters and heart function measurement. Table 2 Left ventricular volume estimates and relative error Echocardiography Phases Parasternal short-axis Apical long-axis Two views Specialist (cc) 47.6453(cc) 31.2359(cc) 46.1567(cc) ED 44.9 6.1% -30.4% 2.8% 20.2773(cc) 13.8729(cc) 19.7050(cc) ES 18.1 12.0% -23.4% 8.9% 3.3 Initial segmentation results Ultrasound phantom images have been used for testing of the proposed segmentation method. We set the parameters as, ε = 0.8, α = 0.1, β = 6. Figure 5 shows the comparison of the GVF geodesic active contour model and the Corsi[5] level set technique on a simulated image and an ultrasound phantom image. The simulated image was formed by adding speckle noise as J = J + n × I , to a grayscale image, where n is uniformly distributed random noise with zero mean and variance equal to 2 . Good results are obtained by first smoothing the image with a Guassian kernel ( σ = 4 ) before applying the GVF geodesic active contour method. We note that the strength of ∇g is too small to pull the propagating curve, especially when the expansion term is removed. We got a similar result even when we used the expansion term. Figure 6 shows satisfying segmentation results of two phantom ultrasound images for the small egg-shape object. All of the images have high-level speckle noise, very low contrast and weak edges. No matter how we initialize the propagating curve, inside or outside or even across the object, the proposed GVF geometric active contours still converge to the actual boundary of the object (Figure 5(c)). 4. CONCLUSIONS AND DISCUSSION In this paper, a new freehand 3D ultrasound imaging system has been developed. The proposed multi-view reconstruction system has been shown to give more accurate 3D reconstructions from both in vitro and in vivo data compared to the commonly used, single view reconstructions. Unlike previous methods, the new approach does not require that there is good spatial alignment between the different view sweeps, and it does not require manual registration by the users. Robust reconstruction is achieved through a geometric registration technique, which combines information from multiple views and improves on the reconstruction quality with the number of distinct views used. Our experimental results show that the new geometric deformable model, which combines level sets and gradient vector flow, is more robust to speckle noise and weak edges that are often found in ultrasound images. Also, this segmentation approach is robust with respect to previous semi-automatic segmentation methods used for echocardiographic images. A natural extension of this work is to apply this segmentation method to echocardiographic image sequences that were acquired from multi-view sweeps. Then, we will investigate the use of the proposed multi-view reconstruction procedure using automated segmentation and registration. (a) (b) (c) Figure 5. (a) Curve evolution through time for GVF GAC (left), normalized GVF field (middle), final segmentation result for GVF GAC (right); (b) Curve evolution through time for Corsi’s method, normalized ∇g field (middle), final segmentation result for Corsi’s method (right); (c) Curve evolution and final segmentation result on a phantom image by GVF GAC (left two images), and for Corsi’s method (right two images). (a) (b) Figure 6. Boundary extraction using GVF GAC model for ultrasound phantom images. (a) small egg long-axis image; (b) small egg short-axis image. From left to right, the columns are original images, propagations of curve and final results. The proposed method needs to be further validated on additional data sets. In our experiment, we found our data set had low-quality images and did not follow a good scanning protocol that would have resulted from breath-holding, optimal view selection, and imaging the entire left ventricle. Thus, we would expect that better results could be achieved on more carefully collected data sets. Currently, we simply average all the single view reconstructions, in order to produce the final 3D reconstruction and volume estimate. We note that an advantage of multi-view reconstructions is that it allows us to consider weighted averaging methods, where shadowing and other artifacts can be removed from single view reconstructions, by simply putting zero weights over shadow and artifact regions. We also note that this approach allows for arbitrary rigid motions between views, which can correct patient movements during inter-view sweeps. The proposed methods could be extended to provide 3D cardiac reconstructions throughout the cardiac cycle, using cardiac and respiratory gating. REFERENCES 1. A.R.Snider, G.A.Serwer, S.B.Ritter, and R.A.Gersony, Echocardiography in pediatric heart disease, 2nd ed, St. Louis : Mosby, 1997 2. X.Ye, J.A.Noble and D.Atkinson, “3-D freehand echocardiography for automatic left ventricle reconstruction and analysis based on multiple acoustic windows”, IEEE transaction on medical imaging, vol.21, pp. 1051-1058, 2002. 3. M.E.Legget, D.F.Leotta, E.L.Bolson, J.A.McDonald, R.W.Martin, X.N.Li, C.M.Otto, and F.H.Sheehan, "System for quantitative three- dimensional echocardiography of the left ventricle based on a magnetic-field position and orientation sensing system," IEEE transactions on biomedical engineering, Vol.45, pp.494-504, 1998. 4. R.N.Rohling, A.H.Gee, and L.Berman, “Automatic registration of 3-D ultrasound images”, Ultrasound in medicine & biology, Vol.24, pp.841-854, 1998 5. C. Corsi, G. Saracino, A. Sarti, and C. Lamberti, “Left ventricular volume estimation for real-time three- dimensional echocardiography”, IEEE transaction on medical imaging, vol.21, pp. 1202-1208, 2002. 6. C. Xu, J.L. Prince, “Snake, shapes, and gradient vector flow”, IEEE transactions on image processing, vol.7, pp.359-369, 1998 7. C. Xu, A.Yezzi, J.L. Prince, “On the relationship between parametric and geometric active contours”, Proc. of 34th Asilomar Conference on Signals, Systems, and Computers, pp.483-489, 2000 8. X. Hang, N.L. Greenberg, J.D. Thomas, “A geometric deformable model for echocardiographic image segmentation”, IEEE Computer Society, Los Alamitos, CA; Computers in Cardiology, pp.77-80, 2002 9. N. Paragios, O. Mellina-Gottardo, and V. Ramesh, “Gradient vector flow fast geometric active contours”, IEEE transactions on Pattern Analysis and Machine Intelligence”, Vol. 26, pp.402-407, 2004 10. Honggang Yu, Marios S. Pattichis and M. Beth Goens, “A Robust Multi-view Freehand Three-dimensional Ultrasound Imaging System Using Volumetric Registration”, Proceedings of IEEE International Conference on System, Man and Cybernetics, October 2005. 11. P. R. Detmer, G. Bashein, T. Hodges, K. W. Beach, E. P. Filer, D. H. Burns, and S. D. E. Jr., "3D ultrasonic image feature localization based on magnetic scanhead tracking: In vitro calibration and validation," Ultrasound in Med.& Biol., vol. 20, pp. 923-936, 1994. 12. D. F. Leotta, P. R. Detmer, and R. W. Martin, "Performance of a miniature magnetic position sensor for three- dimensional ultrasound imaging," Ultrasound in Med.& Biol., vol. 23, pp. 597-609, 1997.

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