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R.: 4d shape priors for level set segmentation of the left myocardium in SPECT sequences
 In: Medical Image Computing and Computer Assisted Intervention. Volume 4190 of LNCS. (2006) 92–100
"... Abstract. We develop a 4D (3D plus time) statistical shape model for implicit level set based shape representations. To this end, we represent hand segmented training sequences of the left ventricle by respective 4dimensional embedding functions and approximate these by a principal component analys ..."
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Cited by 16 (1 self)
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Abstract. We develop a 4D (3D plus time) statistical shape model for implicit level set based shape representations. To this end, we represent hand segmented training sequences of the left ventricle by respective 4dimensional embedding functions and approximate these by a principal component analysis. In contrast to recent 4D models on explicit shape representations, the implicit shape model developed in this work does not require the computation of point correspondences which is known to be quite challenging, especially in higher dimensions. Experimental results on the segmentation of SPECT sequences of the left myocardium confirm that the 4D shape model outperforms respective 3D models, because it takes into account a statistical model of the temporal shape evolution. 1
Embedding overlap priors in variational left ventricle tracking
 IEEE Transactions on Medical Imaging
, 2009
"... Abstract—We propose to embed overlap priors in variational tracking of the left ventricle (LV) in cardiac magnetic resonance (MR) sequences. The method consists of evolving two curves toward the LV endo and epicardium boundaries. We derive the curve evolution equations by minimizing two functionals ..."
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Cited by 16 (5 self)
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Abstract—We propose to embed overlap priors in variational tracking of the left ventricle (LV) in cardiac magnetic resonance (MR) sequences. The method consists of evolving two curves toward the LV endo and epicardium boundaries. We derive the curve evolution equations by minimizing two functionals each containing an original overlap prior constraint. The latter measures the conformity of the overlap between the nonparametric (kernelbased) intensity distributions within the three target regions—LV cavity, myocardium and backgroundto a prior learned from a given segmentation of the first frame. The Bhattacharyya coefficient is used as an overlap measure. Different from existing intensitydriven constraints, the proposed priors do not assume implicitly that the overlap between the intensity distributions within different regions has to be minimal. This prevents both the papillary muscles from being included erroneously in the myocardium and the curves from spilling into the background. Although neither geometric training nor preprocessing were used, quantitative evaluation of the similarities between automatic and independent manual segmentations showed that the proposed method yields a competitive score in comparison with existing methods. This allows more flexibility in clinical use because our solution is based only on the current intensity data, and consequently, the results are not bounded to the characteristics, variability, and mathematical description of a finite training set. We also demonstrate experimentally that the overlap measures are approximately constant over a cardiac sequence, which allows to learn the overlap priors from a single frame. Index Terms—Active contours, cardiac magnetic resonance images (cardiac MRI), left ventricle tracking, level sets, overlap priors, variational image segmentation. I.
I.: Left ventricle tracking using overlap priors
 MICCAI 2008, Part I. LNCS
, 2008
"... Abstract. This study investigates overlap priors for tracking the Left Ventricle (LV) endo and epicardium boundaries in cardiac Magnetic Resonance (MR) sequences. It consists of evolving two curves following the EulerLagrange minimization of two functionals each containing an original overlap pri ..."
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Cited by 11 (2 self)
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Abstract. This study investigates overlap priors for tracking the Left Ventricle (LV) endo and epicardium boundaries in cardiac Magnetic Resonance (MR) sequences. It consists of evolving two curves following the EulerLagrange minimization of two functionals each containing an original overlap prior constraint. The latter measures the conformity of the overlap between the nonparametric (kernelbased) intensity distributions within the three target regions–LV cavity, myocardium and background–to a prior learned from a given segmentation of the first frame. The Bhattacharyya coefficient is used as an overlap measure. Different from existing intensitydriven constraints, the overlap priors do not assume implicitly that the overlap between the distributions within different regions has to be minimal. Although neither shape priors nor curve coupling were used, quantitative evaluation showed that the results correlate well with independent manual segmentations and the method compares favorably with other recent methods. The overlap priors lead to a LV tracking which is more versatile than existing methods because the solution is not bounded to the shape/intensity characteristics of a training set. We also demonstrate experimentally that the used overlap measures are approximately constant over a cardiac sequence. 1
Left ventricle segmentation via graph cut distribution matching
, 2009
"... Abstract. We present a discrete kernel density matching energy for segmenting the left ventricle cavity in cardiac magnetic resonance sequences. The energy and its graph cut optimization based on an original firstorder approximation of the Bhattacharyya measure have not been proposed previously, an ..."
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Cited by 10 (3 self)
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Abstract. We present a discrete kernel density matching energy for segmenting the left ventricle cavity in cardiac magnetic resonance sequences. The energy and its graph cut optimization based on an original firstorder approximation of the Bhattacharyya measure have not been proposed previously, and yield competitive results in nearly realtime. The algorithm seeks a region within each frame by optimization of two priors, one geometric (distancebased) and the other photometric, each measuring a distribution similarity between the region and a model learned from the first frame. Based on global rather than pixelwise information, the proposed algorithm does not require complex training and optimization with respect to geometric transformations. Unlike related active contour methods, it does not compute iterative updates of computationally expensive kernel densities. Furthermore, the proposed firstorder analysis can be used for other intractable energies and, therefore, can lead to segmentation algorithms which share the flexibility of active contours and computational advantages of graph cuts. Quantitative evaluations over 2280 images acquired from 20 subjects demonstrated that the results correlate well with independent manual segmentations by an expert. 1
Deform PFMT: Particle Filter With Mode Tracker for Tracking Nonaffine Contour Deformations
"... Abstract—We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deform ..."
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Cited by 6 (2 self)
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Abstract—We propose algorithms for tracking the boundary contour of a deforming object from an image sequence, when the nonaffine (local) deformation over consecutive frames is large and there is overlapping clutter, occlusions, low contrast, or outlier imagery. When the object is arbitrarily deforming, each, or at least most, contour points can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters (PF) for large dimensional problems is impractically expensive. However, in most real problems, at any given time, most of the contour deformation occurs in a small number of dimensions (“effective basis space”) while the residual deformation in the rest of the state space (“residual space”) is small. This property enables us to apply the particle filtering with mode tracking (PFMT) idea that was proposed for such large dimensional problems in recent work. Since most contour deformation is low spatial frequency, we propose to use the space of deformation at a subsampled set of locations as the effective basis space. The resulting algorithm is called deform PFMT. It requires significant modifications compared to the original PFMT because the space of contours is a nonEuclidean infinite dimensional space. I.
Adaptively Learning Local Shape Statistics for Prostate Segmentation in Ultrasound
"... Abstract—Automatic segmentation of the prostate from 2D transrectal ultrasound (TRUS) is a highly desired tool in many clinical applications. However, it is a very challenging task, especially for segmenting the base and apex of the prostate due to the large shape variations in those areas compared ..."
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Cited by 6 (1 self)
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Abstract—Automatic segmentation of the prostate from 2D transrectal ultrasound (TRUS) is a highly desired tool in many clinical applications. However, it is a very challenging task, especially for segmenting the base and apex of the prostate due to the large shape variations in those areas compared to the midgland, which leads many existing segmentation methods to fail. To address the problem, this paper presents a novel TRUS video segmentation algorithm using both global populationbased and patientspecific local shape statistics as shape constraint. By adaptively learning shape statistics in a local neighborhood during the segmentation process, the algorithm can effectively capture the patientspecific shape statistics and quickly adapt to the local shape changes in the base and apex areas. The learned shape statistics is then used as the shape constraint in a deformable model for TRUS video segmentation. The proposed method can robustly segment the entire gland of the prostate with significantly improved performance in the base and apex regions, compared to other previously reported methods. Our method was evaluated using 19 video sequences obtained from different patients and the average mean absolute distance error was 1.65 ± 0.47 mm. Index Terms—Deformable model, prostate, segmentation, shape statistics, transrectal ultrasound (TRUS). I.
Segmentation of Left Ventricle from 3D Cardiac MR Image Sequences Using a SubjectSpecific Dynamical Model
 Proc. IEEE Conf. Computer Vision and Pattern Recognition
, 2008
"... Statistical modelbased segmentation of the left ventricle from cardiac images has received considerable attention in recent years. While a variety of statistical models have been shown to improve segmentation results, most of them are either static models (SM) which neglect the temporal coherence o ..."
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Cited by 6 (0 self)
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Statistical modelbased segmentation of the left ventricle from cardiac images has received considerable attention in recent years. While a variety of statistical models have been shown to improve segmentation results, most of them are either static models (SM) which neglect the temporal coherence of a cardiac sequence or generic dynamical models (GDM) which neglect the intersubject variability of cardiac shapes and deformations. In this paper, we use a subjectspecific dynamical model (SSDM) that handles intersubject variability and temporal dynamics (intrasubject variability) simultaneously. It can progressively identify the specific motion patterns of a new cardiac sequence based on the segmentations observed in the past frames. We formulate the integration of the SSDM into the segmentation process in a recursive Bayesian framework in order to segment each frame based on the intensity information from the current frame and the prediction from the past frames. We perform “Leaveoneout ” test on 32 sequences to validate our approach. Quantitative analysis of experimental results shows that the segmentation with the SSDM outperforms those with the SM and GDM by having better global and local consistencies with the manual segmentation. 1.
Particle filtering for largedimensional state spaces with multimodal observation likelihoods
 IEEE Transactions on Signal Processing
"... Abstract—We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavytailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow ..."
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Cited by 5 (0 self)
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Abstract—We study efficient importance sampling techniques for particle filtering (PF) when either (a) the observation likelihood (OL) is frequently multimodal or heavytailed, or (b) the state space dimension is large or both. When the OL is multimodal, but the state transition pdf (STP) is narrow enough, the optimal importance density is usually unimodal. Under this assumption, many techniques have been proposed. But when the STP is broad, this assumption does not hold. We study how existing techniques can be generalized to situations where the optimal importance density is multimodal, but is unimodal conditioned on a part of the state vector. Sufficient conditions to test for the unimodality of this conditional posterior are derived. Our result is directly extendable to testing for unimodality of any posterior. The number of particles N to accurately track using a PF increases with state space dimension, thus making any regular PF impractical for large dimensional tracking problems. But in most such problems, most of the state change occurs in only a few dimensions, while the change in the rest of the dimensions is small. Using this property, we propose to replace importance sampling from a large part of the state space (whose conditional posterior is narrow enough) by just tracking the mode of the conditional posterior. This introduces some extra error, but it also greatly reduces the importance sampling dimension. The net effect is much smaller error for a given N, especially when the available N is small. An important class of large dimensional problems with multimodal OL is tracking spatially varying physical quantities such as temperature or pressure in a large area using a network of sensors which may be nonlinear and/or may have nonnegligible failure probabilities. Improved performance of our proposed algorithms over existing PFs is demonstrated for this problem. Index Terms—Importance sampling for multimodal posteriors, large dimensional sequential state estimation, particle filtering, posterior mode tracking, tracking spatially varying physical quantities. I.
Learning the dynamics and timerecursive boundary detection of deformable objects
 IEEE Trans. IP
, 2008
"... Abstract—We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with ..."
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Cited by 4 (0 self)
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Abstract—We propose a principled framework for recursively segmenting deformable objects across a sequence of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac cycle. The approach involves a technique for learning the system dynamics together with methods of particlebased smoothing as well as nonparametric belief propagation on a loopy graphical model capturing the temporal periodicity of the heart. The dynamic system state is a lowdimensional representation of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state estimation. By formulating the problem as one of state estimation, the segmentation at each particular time is based not only on the data observed at that instant, but also on predictions based on past and future boundary estimates. Although this paper focuses on left ventricle segmentation, the method generalizes to temporally segmenting any deformable object. Index Terms—Cardiac imaging, curve evolution, graphical models, image segmentation, learning, left ventricle (LV), level sets, magnetic resonance imaging, particle filtering, recursive estimation, smoothing. I.
PFMT (Particle Filter with Mode Tracker) for Tracking Contour Deformations
"... We consider the problem of tracking the boundary contour of a moving and deforming object from a sequence of images. If the motion of the “object ” or region of interest is constrained (e.g. rigid or approximately rigid), the contour motion can be efficiently represented by a small number of param ..."
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Cited by 4 (1 self)
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We consider the problem of tracking the boundary contour of a moving and deforming object from a sequence of images. If the motion of the “object ” or region of interest is constrained (e.g. rigid or approximately rigid), the contour motion can be efficiently represented by a small number of parameters, e.g. the affine group. But if the “object” is arbitrarily deforming, each contour point can move independently. Contour deformation then forms an infinite (in practice, very large), dimensional space. Direct application of particle filters for large dimensional problems is impractical, due to the reduction in effective particle size as dimension increases. But in most real problems, at any given time, “most of the contour deformation” occurs in a small number of dimensions (“effective basis”) while the residual deformation in the rest of the state space (“residual space”) is “small”. The effective basis may be fixed or time varying. Based on this assumption, we modify the particle filtering method to perform sequential importance sampling only on the effective basis dimensions, while replacing it with deterministic mode tracking in residual space (PFMT). We develop the PFMT idea for contour tracking. Techniques for detecting effective basis dimension change and estimating the new effective basis are presented. Tracking results on simulated and real sequences are shown and compared with past work.