Zhu L, Gao Y, Appia V, Yezzi A, Arepalli C, Faber T, Stillman A, Tannenbaum A. Automatic delineation of the myocardial wall from CT images via shape segmentation and variational region growing. IEEE Trans Biomed Eng. 2013;60 (10) :2887-95.Abstract
Prognosis and diagnosis of cardiac diseases frequently require quantitative evaluation of the ventricle volume, mass, and ejection fraction. The delineation of the myocardial wall is involved in all of these evaluations, which is a challenging task due to large variations in myocardial shapes and image quality. In this paper, we present an automatic method for extracting the myocardial wall of the left and right ventricles from cardiac CT images. In the method, the left and right ventricles are located sequentially, in which each ventricle is detected by first identifying the endocardium and then segmenting the epicardium. To this end, the endocardium is localized by utilizing its geometric features obtained on-line from a CT image. After that, a variational region-growing model is employed to extract the epicardium of the ventricles. In particular, the location of the endocardium of the left ventricle is determined via using an active contour model on the blood-pool surface. To localize the right ventricle, the active contour model is applied on a heart surface extracted based on the left ventricle segmentation result. The robustness and accuracy of the proposed approach is demonstrated by experimental results from 33 human and 12 pig CT images.
Mostayed A, Garlapati RR, Joldes GR, Wittek A, Roy A, Kikinis R, Warfield SK, Miller K. Biomechanical model as a registration tool for image-guided neurosurgery: evaluation against BSpline registration. Ann Biomed Eng. 2013;41 (11) :2409-25.Abstract
In this paper we evaluate the accuracy of warping of neuro-images using brain deformation predicted by means of a patient-specific biomechanical model against registration using a BSpline-based free form deformation algorithm. Unlike the BSpline algorithm, biomechanics-based registration does not require an intra-operative MR image which is very expensive and cumbersome to acquire. Only sparse intra-operative data on the brain surface is sufficient to compute deformation for the whole brain. In this contribution the deformation fields obtained from both methods are qualitatively compared and overlaps of Canny edges extracted from the images are examined. We define an edge based Hausdorff distance metric to quantitatively evaluate the accuracy of registration for these two algorithms. The qualitative and quantitative evaluations indicate that our biomechanics-based registration algorithm, despite using much less input data, has at least as high registration accuracy as that of the BSpline algorithm.
San José Estépar R, Kinney GL, Black-Shinn JL, Bowler RP, Kindlmann GL, Ross JC, Kikinis R, Han MLK, Come CE, Diaz AA, et al. Computed Tomographic Measures Of Pulmonary Vascular Morphology In Smokers And Their Clinical Implications. Am J Respir Crit Care Med. 2013;188 (2) :231-9.Abstract
RATIONALE: Angiographic investigation suggests that pulmonary vascular remodeling in smokers is characterized by distal pruning of the blood vessels. OBJECTIVES: Using volumetric computed tomography scans of the chest we sought to quantitatively evaluate this process and assess its clinical associations. METHODS: Pulmonary vessels were automatically identified, segmented, and measured. Total blood vessel volume (TBV) and the aggregate vessel volume for vessels less than 5 mm(2) (BV5) were calculated for all lobes. The lobe-specific BV5 measures were normalized to the TBV of that lobe and the nonvascular tissue volume (BV5/T(issue)V) to calculate lobe-specific BV5/TBV and BV5/T(issue)V ratios. Densitometric measures of emphysema were obtained using a Hounsfield unit threshold of -950 (%LAA-950). Measures of chronic obstructive pulmonary disease severity included single breath measures of diffusing capacity of carbon monoxide, oxygen saturation, the 6-minute-walk distance, St George's Respiratory Questionnaire total score (SGRQ), and the body mass index, airflow obstruction, dyspnea, and exercise capacity (BODE) index. MEASUREMENTS AND MAIN RESULTS: The %LAA-950 was inversely related to all calculated vascular ratios. In multivariate models including age, sex, and %LAA-950, lobe-specific measurements of BV5/TBV were directly related to resting oxygen saturation and inversely associated with both the SGRQ and BODE scores. In similar multivariate adjustment lobe-specific BV5/T(issue)V ratios were inversely related to resting oxygen saturation, diffusing capacity of carbon monoxide, 6-minute-walk distance, and directly related to the SGRQ and BODE. CONCLUSIONS: Smoking-related chronic obstructive pulmonary disease is characterized by distal pruning of the small blood vessels (<5 mm(2)) and loss of tissue in excess of the vasculature. The magnitude of these changes predicts the clinical severity of disease.
O'Donnell LJ, Golby AJ, Westin C-F. Fiber Clustering versus the Parcellation-based Connectome. Neuroimage. 2013;80 :283-9.Abstract
We compare two strategies for modeling the connections of the brain's white matter: fiber clustering and the parcellation-based connectome. Both methods analyze diffusion magnetic resonance imaging fiber tractography to produce a quantitative description of the brain's connections. Fiber clustering is designed to reconstruct anatomically-defined white matter tracts, while the parcellation-based white matter segmentation enables the study of the brain as a network. From the perspective of white matter segmentation, we compare and contrast the goals and methods of the parcellation-based and clustering approaches, with special focus on reviewing the field of fiber clustering. We also propose a third category of new hybrid methods that combine the aspects of parcellation and clustering, for joint analysis of connection structure and anatomy or function. We conclude that these different approaches for segmentation and modeling of the white matter can advance the neuroscientific study of the brain's connectivity in complementary ways.
Karasev P, Kolesov I, Fritscher K, Vela P, Mitchell P, Tannenbaum A. Interactive medical image segmentation using PDE control of active contours. IEEE Trans Med Imaging. 2013;32 (11) :2127-39.Abstract
Segmentation of injured or unusual anatomic structures in medical imagery is a problem that has continued to elude fully automated solutions. In this paper, the goal of easy-to-use and consistent interactive segmentation is transformed into a control synthesis problem. A nominal level set partial differential equation (PDE) is assumed to be given; this open-loop system achieves correct segmentation under ideal conditions, but does not agree with a human expert's ideal boundary for real image data. Perturbing the state and dynamics of a level set PDE via the accumulated user input and an observer-like system leads to desirable closed-loop behavior. The input structure is designed such that a user can stabilize the boundary in some desired state without needing to understand any mathematical parameters. Effectiveness of the technique is illustrated with applications to the challenging segmentations of a patellar tendon in magnetic resonance and a shattered femur in computed tomography.
Gao Y, Bouix S, Shenton M, Tannenbaum A. Sparse texture active contour. IEEE Trans Image Process. 2013;22 (10) :3866-78.Abstract
In image segmentation, we are often interested in using certain quantities to characterize the object, and perform the classification based on criteria such as mean intensity, gradient magnitude, and responses to certain predefined filters. Unfortunately, in many cases such quantities are not adequate to model complex textured objects. Along a different line of research, the sparse characteristic of natural signals has been recognized and studied in recent years. Therefore, how such sparsity can be utilized, in a non-parametric way, to model the object texture and assist the textural image segmentation process is studied in this paper, and a segmentation scheme based on the sparse representation of the texture information is proposed. More explicitly, the texture is encoded by the dictionaries constructed from the user initialization. Then, an active contour is evolved to optimize the fidelity of the representation provided by the dictionary of the target. In doing so, not only a non-parametric texture modeling technique is provided, but also the sparsity of the representation guarantees the computation efficiency. The experiments are carried out on the publicly available image data sets which contain a large variety of texture images, to analyze the user interaction, performance statistics, and to highlight the algorithm's capability of robustly extracting textured regions from an image.
Vosburgh KG, Golby A, Pieper SD. Surgery, Virtual Reality, and the Future. Stud Health Technol Inform. 2013;184 :7-13.Abstract
MMVR has provided the leading forum for the multidisciplinary interaction and development of the use of Virtual Reality (VR) techniques in medicine, particularly in surgical practice. Here we look back at the foundations of our field, focusing on the use of VR in Surgery and similar interventional procedures, sum up the current status, and describe the challenges and opportunities going forward.
Gao Y, Tannenbaum A, Chen H, Torres M, Yoshida E, Yang X, Wang Y, Curran W, Liu T. Automated skin segmentation in ultrasonic evaluation of skin toxicity in breast cancer radiotherapy. Ultrasound Med Biol. 2013;39 (11) :2166-75.Abstract
Skin toxicity is the most common side effect of breast cancer radiotherapy and impairs the quality of life of many breast cancer survivors. We, along with other researchers, have recently found quantitative ultrasound to be effective as a skin toxicity assessment tool. Although more reliable than standard clinical evaluations (visual observation and palpation), the current procedure for ultrasound-based skin toxicity measurements requires manual delineation of the skin layers (i.e., epidermis-dermis and dermis-hypodermis interfaces) on each ultrasound B-mode image. Manual skin segmentation is time consuming and subjective. Moreover, radiation-induced skin injury may decrease image contrast between the dermis and hypodermis, which increases the difficulty of delineation. Therefore, we have developed an automatic skin segmentation tool (ASST) based on the active contour model with two significant modifications: (i) The proposed algorithm introduces a novel dual-curve scheme for the double skin layer extraction, as opposed to the original single active contour method. (ii) The proposed algorithm is based on a geometric contour framework as opposed to the previous parametric algorithm. This ASST algorithm was tested on a breast cancer image database of 730 ultrasound breast images (73 ultrasound studies of 23 patients). We compared skin segmentation results obtained with the ASST with manual contours performed by two physicians. The average percentage differences in skin thickness between the ASST measurement and that of each physician were less than 5% (4.8 ± 17.8% and -3.8 ± 21.1%, respectively). In summary, we have developed an automatic skin segmentation method that ensures objective assessment of radiation-induced changes in skin thickness. Our ultrasound technology offers a unique opportunity to quantify tissue injury in a more meaningful and reproducible manner than the subjective assessments currently employed in the clinic.
Zhu L, Gao Y, Yezzi A, Tannenbaum A. Automatic segmentation of the left atrium from MR images via variational region growing with a moments-based shape prior. IEEE Trans Image Process. 2013;22 (12) :5111-22.Abstract
The planning and evaluation of left atrial ablation procedures are commonly based on the segmentation of the left atrium, which is a challenging task due to large anatomical variations. In this paper, we propose an automatic approach for segmenting the left atrium from magnetic resonance imagery. The segmentation problem is formulated as a problem in variational region growing. In particular, the method starts locally by searching for a seed region of the left atrium from an MR slice. A global constraint is imposed by applying a shape prior to the left atrium represented by Zernike moments. The overall growing process is guided by the robust statistics of intensities from the seed region along with the shape prior to capture the entire atrial region. The robustness and accuracy of our approach are demonstrated by experimental results from 64 human MR images.
Mike A, Strammer E, Aradi M, Orsi G, Perlaki G, Hajnal A, Sandor J, Banati M, Illes E, Zaitsev A, et al. Disconnection mechanism and regional cortical atrophy contribute to impaired processing of facial expressions and theory of mind in multiple sclerosis: a structural MRI study. PLoS One. 2013;8 (12) :e82422.Abstract
Successful socialization requires the ability of understanding of others' mental states. This ability called as mentalization (Theory of Mind) may become deficient and contribute to everyday life difficulties in multiple sclerosis. We aimed to explore the impact of brain pathology on mentalization performance in multiple sclerosis. Mentalization performance of 49 patients with multiple sclerosis was compared to 24 age- and gender matched healthy controls. T1- and T2-weighted three-dimensional brain MRI images were acquired at 3Tesla from patients with multiple sclerosis and 18 gender- and age matched healthy controls. We assessed overall brain cortical thickness in patients with multiple sclerosis and the scanned healthy controls, and measured the total and regional T1 and T2 white matter lesion volumes in patients with multiple sclerosis. Performances in tests of recognition of mental states and emotions from facial expressions and eye gazes correlated with both total T1-lesion load and regional T1-lesion load of association fiber tracts interconnecting cortical regions related to visual and emotion processing (genu and splenium of corpus callosum, right inferior longitudinal fasciculus, right inferior fronto-occipital fasciculus, uncinate fasciculus). Both of these tests showed correlations with specific cortical areas involved in emotion recognition from facial expressions (right and left fusiform face area, frontal eye filed), processing of emotions (right entorhinal cortex) and socially relevant information (left temporal pole). Thus, both disconnection mechanism due to white matter lesions and cortical thinning of specific brain areas may result in cognitive deficit in multiple sclerosis affecting emotion and mental state processing from facial expressions and contributing to everyday and social life difficulties of these patients.
Liu S, Cai W, Song Y, Pujol S, Kikinis R, Wen L, Feng DD. Localized Sparse Code Gradient in Alzheimer's disease staging. Conf Proc IEEE Eng Med Biol Soc. 2013;2013 :5398-401.Abstract
The accurate diagnosis of Alzheimer's disease (AD) at different stages is essential to identify patients at high risk of dementia and plan prevention or treatment measures accordingly. In this study, we proposed a new AD staging method for the entire spectrum of AD including the AD, Mild Cognitive Impairment with and without AD conversions, and Cognitive Normal groups. Our method embedded the high dimensional multi-view features derived from neuroimaging data into a low dimensional feature space and could form a more distinctive representation than the naive concatenated features. It also updated the testing data based on the Localized Sparse Code Gradients (LSCG) to further enhance the classification. The LSCG algorithm, validated using Magnetic Resonance Imaging data from the ADNI baseline cohort, achieved significant improvements on all diagnosis groups compared to using the original sparse coding method.
Cavallari M, Moscufo N, Skudlarski P, Meier D, Panzer VP, Pearlson GD, White WB, Wolfson L, Guttmann CRG. Mobility impairment is associated with reduced microstructural integrity of the inferior and superior cerebellar peduncles in elderly with no clinical signs of cerebellar dysfunction. Neuroimage Clin. 2013;2 :332-40.Abstract
While the cerebellum plays a critical role in motor coordination and control no studies have investigated its involvement in idiopathic mobility impairment in community-dwelling elderly. In this study we tested the hypothesis that structural changes in the cerebellar peduncles not detected by conventional magnetic resonance imaging are associated with reduced mobility performance. The analysis involved eighty-five subjects (age range: 75-90 years) who had no clinical signs of cerebellar dysfunction. Based on the short physical performance battery (SPPB) score, we defined mobility status of the subjects in the study as normal (score 11-12, n = 26), intermediate (score 9-10, n = 27) or impaired (score < 9, n = 32). We acquired diffusion tensor imaging data to obtain indices of white matter integrity: fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD). Using a parcellation atlas, regional indices within the superior, middle, and inferior cerebellar peduncles (ICP, MCP, SCP) were calculated and their associations with mobility performance were analyzed. Subjects with impaired mobility showed reduced FA and AD values in the ICP and SCP but not in the MCP. The ICP-FA, ICP-AD and SCP-FA indices showed a significant association with the SPPB score. We also observed significant correlation between ICP-FA and walk time (r = - 0.311, p = 0.004), as well as between SCP-AD and self-paced maximum walking velocity (r = 0.385, p = 0.003) and usual walking velocity (r = 0.400, p = 0.002). In logistic regression analysis ICP-FA and ICP-AD together explained 51% of the variability in the mobility status of a sample comprising the normal and impaired subgroups, and correctly classified more than three-quarters of those subjects. Our findings suggest that presence of microstructural damage, likely axonal, in afferent and efferent connections of the cerebellum contributes to the deterioration of motor performance in older people.
Lou Y, Irimia A, Vela PA, Chambers MC, Van Horn JD, Vespa PM, Tannenbaum AR. Multimodal deformable registration of traumatic brain injury MR volumes via the Bhattacharyya distance. IEEE Trans Biomed Eng. 2013;60 (9) :2511-20.Abstract
An important problem of neuroimaging data analysis for traumatic brain injury (TBI) is the task of coregistering MR volumes acquired using distinct sequences in the presence of widely variable pixel movements which are due to the presence and evolution of pathology. We are motivated by this problem to design a numerically stable registration algorithm which handles large deformations. To this end, we propose a new measure of probability distributions based on the Bhattacharyya distance, which is more stable than the widely used mutual information due to better behavior of the square root function than the logarithm at zero. Robustness is illustrated on two TBI patient datasets, each containing 12 MR modalities. We implement our method on graphics processing units (GPU) so as to meet the clinical requirement of time-efficient processing of TBI data. We find that 6 sare required to register a pair of volumes with matrix sizes of 256 × 256 × 60 on the GPU. In addition to exceptional time efficiency via its GPU implementation, this methodology provides a clinically informative method for the mapping and evaluation of anatomical changes in TBI.
McDannold N, Zhang Y-Z, Power C, Jolesz F, Vykhodtseva N. Nonthermal ablation with microbubble-enhanced focused ultrasound close to the optic tract without affecting nerve function. J Neurosurg. 2013;119 (5) :1208-20.Abstract
OBJECT: Tumors at the skull base are challenging for both resection and radiosurgery given the presence of critical adjacent structures, such as cranial nerves, blood vessels, and brainstem. Magnetic resonance imaging-guided thermal ablation via laser or other methods has been evaluated as a minimally invasive alternative to these techniques in the brain. Focused ultrasound (FUS) offers a noninvasive method of thermal ablation; however, skull heating limits currently available technology to ablation at regions distant from the skull bone. Here, the authors evaluated a method that circumvents this problem by combining the FUS exposures with injected microbubble-based ultrasound contrast agent. These microbubbles concentrate the ultrasound-induced effects on the vasculature, enabling an ablation method that does not cause significant heating of the brain or skull. METHODS: In 29 rats, a 525-kHz FUS transducer was used to ablate tissue structures at the skull base that were centered on or adjacent to the optic tract or chiasm. Low-intensity, low-duty-cycle ultrasound exposures (sonications) were applied for 5 minutes after intravenous injection of an ultrasound contrast agent (Definity, Lantheus Medical Imaging Inc.). Using histological analysis and visual evoked potential (VEP) measurements, the authors determined whether structural or functional damage was induced in the optic tract or chiasm. RESULTS: Overall, while the sonications produced a well-defined lesion in the gray matter targets, the adjacent tract and chiasm had comparatively little or no damage. No significant changes (p > 0.05) were found in the magnitude or latency of the VEP recordings, either immediately after sonication or at later times up to 4 weeks after sonication, and no delayed effects were evident in the histological features of the optic nerve and retina. CONCLUSIONS: This technique, which selectively targets the intravascular microbubbles, appears to be a promising method of noninvasively producing sharply demarcated lesions in deep brain structures while preserving function in adjacent nerves. Because of low vascularity--and thus a low microbubble concentration--some large white matter tracts appear to have some natural resistance to this type of ablation compared with gray matter. While future work is needed to develop methods of monitoring the procedure and establishing its safety at deep brain targets, the technique does appear to be a potential solution that allows FUS ablation of deep brain targets while sparing adjacent nerve structures.
Lee J, Sandhu R, Tannenbaum A. Particle Filters and Occlusion Handling for Rigid 2D-3D Pose Tracking. Comput Vis Image Underst. 2013;117 (8) :922-33.Abstract
In this paper, we address the problem of 2D-3D pose estimation. Specifically, we propose an approach to jointly track a rigid object in a 2D image sequence and to estimate its pose (position and orientation) in 3D space. We revisit a joint 2D segmentation/3D pose estimation technique, and then extend the framework by incorporating a particle filter to robustly track the object in a challenging environment, and by developing an occlusion detection and handling scheme to continuously track the object in the presence of occlusions. In particular, we focus on partial occlusions that prevent the tracker from extracting an exact region properties of the object, which plays a pivotal role for region-based tracking methods in maintaining the track. To this end, a dynamical choice of how to invoke the objective functional is performed online based on the degree of dependencies between predictions and measurements of the system in accordance with the degree of occlusion and the variation of the object's pose. This scheme provides the robustness to deal with occlusions of an obstacle with different statistical properties from that of the object of interest. Experimental results demonstrate the practical applicability and robustness of the proposed method in several challenging scenarios.
Rios Velazquez E, Parmar C, Jermoumi M, Mak RH, van Baardwijk A, Fennessy FM, Lewis JH, De Ruysscher D, Kikinis R, Lambin P, et al. Volumetric CT-based segmentation of NSCLC using 3D-Slicer. Sci Rep. 2013;3 :3529.Abstract
Accurate volumetric assessment in non-small cell lung cancer (NSCLC) is critical for adequately informing treatments. In this study we assessed the clinical relevance of a semiautomatic computed tomography (CT)-based segmentation method using the competitive region-growing based algorithm, implemented in the free and public available 3D-Slicer software platform. We compared the 3D-Slicer segmented volumes by three independent observers, who segmented the primary tumour of 20 NSCLC patients twice, to manual slice-by-slice delineations of five physicians. Furthermore, we compared all tumour contours to the macroscopic diameter of the tumour in pathology, considered as the "gold standard". The 3D-Slicer segmented volumes demonstrated high agreement (overlap fractions > 0.90), lower volume variability (p = 0.0003) and smaller uncertainty areas (p = 0.0002), compared to manual slice-by-slice delineations. Furthermore, 3D-Slicer segmentations showed a strong correlation to pathology (r = 0.89, 95%CI, 0.81-0.94). Our results show that semiautomatic 3D-Slicer segmentations can be used for accurate contouring and are more stable than manual delineations. Therefore, 3D-Slicer can be employed as a starting point for treatment decisions or for high-throughput data mining research, such as Radiomics, where manual delineating often represent a time-consuming bottleneck.
Savadjiev P, Rathi Y, Bouix S, Smith AR, Schultz RT, Verma R, Westin C-F. Combining Surface and Fiber Geometry: An Integrated Approach to Brain Morphology. Med Image Comput Comput Assist Interv. 2013;16 (Pt 1) :50-7.Abstract
Despite the fact that several theories link cortical development and function to the development of white matter and its geometrical structure, the relationship between gray and white matter morphology has not been widely researched. In this paper, we propose a novel framework for investigating this relationship. Given a set of fiber tracts which connect to a particular cortical region, the key idea is to compute two scalar fields that represent geometrical characteristics of the white matter and of the surface of the cortical region. The distributions of these scalar values are then linked via Mutual Information, which results in a quantitative marker that can be used in the study of normal and pathological brain structure and development. We apply this framework to a population study on autism spectrum disorder in children.
Wassermann D, Makris N, Rathi Y, Shenton M, Kikinis R, Kubicki M, Westin C-F. On Describing Human White Matter Anatomy: The White Matter Query Language. Med Image Comput Comput Assist Interv. 2013;16 (Pt 1) :647-54.Abstract

The main contribution of this work is the careful syntactical definition of major white matter tracts in the human brain based on a neuroanatomist's expert knowledge. We present a technique to formally describe white matter tracts and to automatically extract them from diffusion MRI data. The framework is based on a novel query language with a near-to-English textual syntax. This query language allows us to construct a dictionary of anatomical definitions describing white matter tracts. The definitions include adjacent gray and white matter regions, and rules for spatial relations. This enables automated coherent labeling of white matter anatomy across subjects. We use our method to encode anatomical knowledge in human white matter describing 10 association and 8 projection tracts per hemisphere and 7 commissural tracts. The technique is shown to be comparable in accuracy to manual labeling. We present results applying this framework to create a white matter atlas from 77 healthy subjects, and we use this atlas in a proof-of-concept study to detect tract changes specific to schizophrenia.

Sweet A, Venkataraman A, Stufflebeam SM, Liu H, Tanaka N, Madsen J, Golland P. Detecting Epileptic Regions Based on Global Brain Connectivity Patterns. Med Image Comput Comput Assist Interv. 2013;16 (Pt 1) :98-105.Abstract
We present a method to detect epileptic regions based on functional connectivity differences between individual epilepsy patients and a healthy population. Our model assumes that the global functional characteristics of these differences are shared across patients, but it allows for the epileptic regions to vary between individuals. We evaluate the detection performance against intracranial EEG observations and compare our approach with two baseline methods that use standard statistics. The baseline techniques are sensitive to the choice of thresholds, whereas our algorithm automatically estimates the appropriate model parameters and compares favorably with the best baseline results. This suggests the promise of our approach for pre-surgical planning in epilepsy.
Wassermann D, Ross J, Washko G, Westin C-F, San José Estépar R. Diffeomorphic Point Set Registration using Non-Stationary Mixture Models. Proc IEEE Int Symp Biomed Imaging. 2013.Abstract

This paper investigates a diffeomorphic point-set registration based on non-stationary mixture models. The goal is to improve the non-linear registration of anatomical structures by representing each point as a general non-stationary kernel that provides information about the shape of that point. Our framework generalizes work done by others that use stationary models. We achieve this by integrating the shape at each point when calculating the point-set similarity and transforming it according to the calculated deformation. We also restrict the non-rigid transform to the space of symmetric diffeomorphisms. Our algorithm is validated in synthetic and human datasets in two different applications: fiber bundle and lung airways registration. Our results shows that non-stationary mixture models are superior to Gaussian mixture models and methods that do not take into account the shape of each point.