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This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 2. Unlimited M3 segmentation our method can perform Pednekar et al 18 proposed an intensity based affinity esti. segmentation across multi modality chamber subject mation for LV region and perform segmentation by contour. Free view segmentation the segmentation is not limited fitting Ben Ayed et al 19 followed the level set approach. to specific regulated image views arbitrary image views and using overlap LV priors as global constrains to obtain. can be accepted for the segmentation LV segmentation Strong shape priors are also frequently. Automatic heart localization Our groupwise segmenta used in LV or RV segmentation Zhang et al 20 used a. tion method naturally provides a heart region localization combined active shape and appearance model ASM AAM. It can be directly performed on raw image scans without for segmentation of 4D MR images Mahapatra et al 21. manually cropping the heart ROIs utilized the geometric relation between LV and RV learned. Incremental segmentation Our new groupwise segmen from training sets to obtain segmentation of both regions. tation can propagate the M3 segmentation from a small Regulated Image Views Besides the regulated segmenta. image subset to the whole large image set tion target regions cardiac segmentation are often restricted. on the four chamber long axis view and two chamber short. II R ELATED W ORK axis view 3D models are intensively used for synthesizing. multiple image views but each view still requires a view. The existing cardiac segmentation are often performed dependent segmentation algorithm Lelieveldt et al 22 trained. under regulated settings Images from freeviews and or other each standard view separately with an Active Appearance. non regulated M3 settings can easily fail in these methods models AAM to obtain multi view cardiac segmentation. Unsupervised v s Supervised Segmentation Supervised Lotjonen et al 23 constructed a 3D statistical shape model of. learning methods are intensively used in most existing car heart using images from both long axis and short axis views. diac segmentation methods For example level set with prior Sermesant et al 24 proposed a deformable model approach. shape knowledge 3 4 5 Marginal Space Learning MSL for 4D segmentation by fitting a manually created tetrahedral. 6 for learning the heart shapes multi atlas approaches 7 mesh heart model to the MRI SPECT images Lorenzo Valdes. 8 9 10 for transferring reference segmentation labels et al 7 used the stack of MR images from short axis. to target images are popular supervised methods in cardiac view to construct the 3D heart model and then provided the. segmentation However for large cardiac datasets pre selected 4D segmentation model via model fitting These 3D models. training sets will be insufficient to cover all the changes of should be constructed from regulated two four chamber views. modality regions views and should be associated to the same subject. Groupwise v s Single Segmentation Most existing seg. mentation methods focus on single image segmentation other. III M ETHOD OVERVIEW, than joint segmentation over a set of images Despite their. success in LV RV segmentation single image segmentation Our segmentation is fully data driven and unsupervised As. is not efficient for batch analysis i e a group of images illustrated in Fig 1 groups of M3 images from an arbitrary. from a cardiac cycle Instead groupwise approach conducts view are segmented automatically and simultaneously by fol. the segmentation simultaneously to all input images and lowing the four steps below. automatically coordinates their segment labels A groupwise 1 Spectral Decomposition Fig 1 Step 1 Sec IV Each. segmentation significantly simplify the labeling coordinating input image is decomposed into Spectral Bases in this. work and provide joint analysis to the segmentations and can step to obtain a set of robust modality independent and. be easily incorporated with existing groupwise registration or characteristic preserving feature representations The spectral. groupwise analysis i e 11 12 methods bases are the principal components major eigenvectors of. Regulated Modality Segmentation Due to the differences a Spectral Matrix whose elements are the pairwise pixel. between the intensity features of MR and CT the segmentation similarities of the images a N pixel image will have a N N. of MR CT were separately done in the previous studies matrix The spectral matrix constitutes a graph structure over. Zheng et al 6 applied marginal space learning techniques the image called Spectral Graph 25 26 The spectral. for warping prior control points specific for CT volumes to base representation depends on pairwise pixel similarities oth. perform the model based segmentation Isgum et al 8 took er than absolute values thus are independent of the intensity. the multi atlas approach and perform cardiac and aortic CT changes across modalities As Fig 1 and 2 show smooth. segmentation using local label fusion Jolly 13 proposed regions and boundaries in images are extracted in the spectral. a separated MR and CT heart localization steps and used a bases converted to 2D regardless of the original modalities. unified deformation step to combine the two modality results which simplifies the segmentation as direct clustering. Ecabert et al 14 developed a deformable model based multi 2 Spectral Synchronization Fig 1 Step 2 Sec V Spec. chamber segmentation for 2D CT images and the similar tral bases from a group of images are correlated in this. method was shown successful in MR by Peters et al 15 step obtaining a uniform feature representation Similar heart. Regulated Chamber Segmentation As reviewed in 16 features i e chamber regions are thus uniformly matched. many cardiac segmentation algorithms focused on LV segmen across images which enables a groupwise analysis over all. tation only Among the LV segmentation in recent studies images The unification is done by shuffling and recombining. Cousty et al 17 used watershed cut algorithm and incorpo the spectral bases under a minimization Spectral Synchroniza. rated spatio temporal representation for cardiac segmentation tion thus the new Synchronized Spectral Bases are obtained. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 3. Fig 1 The overview of our free view groupwise segmentation The M3 images from different views are decomposed and then synchronized using our. spectral synchronization network SSN The generated synchronized superpixels immediately provide multi chamber segmentation. Fig 2 Invariant spectral graphs and their spectral bases that are shared across MR and CT images The values of Edist Einten EESP show different. modality images can have similar self similarity measures Thus adjacent matrixes of both graphs are similar which can be used for cross modality image. matching The full matrixes W shown at last are constructed by the same self similarity over the whole MR CT image. with minimum 2D appearance differences This provides an Spectral decomposition is the building block of our SSN. implicit matching for all images without explicit registration model. 3 Synchronized Superpixels Fig 1 Step 3 Sec VI A and. B The group of synchronized spectral bases are clustered into A Spectral Graph by Image Self similarity. superpixels in this step to achieve groupwise oversegmentation. with superpixel superpixel correspondences across all images The spectral graph is a graph structure for the self. Unlike traditional superpixels which are obtained by spectral similarities among all pixels within an image The graph is. clustering of one image e g 26 our synchronized super represented as a Spectral Matrix whereas each element is a. pixel representation is obtained by groupwise clustering over similarity value for a pixel pair The same image structures. the synchronized spectral bases from all images Synchronized from different modalities will have similar spectral matrixes. superpixels not only enhance the clustering robustness but also so that cross modality matching becomes possible. correlate all labeled regions across images as Fig 6 shows For an image I with total N pixels we construct spectral. 4 Segmentation Sec VI C The chamber regions of the graph G V E such that V N V is the pixel set. input images can be easily identified from the synchronized and each edge e E connects two arbitrary pixels i j in the. superpixels This is done by stacking the superpixel maps image Each e for i j is weighted by W i j and W is a. and locating the largest superpixels around the centers The N N spectral matrix for I W i j is the combination of. identified superpixels are extracted as the segmentation result three self similarity measures. Edist i j Einten i j EESP i j,W i j exp 1,IV S PECTRAL D ECOMPOSITION FOR I MAGES x I E. Unsupervised segmentation of M3 cardiac images requires where the terms Edist Einten EESP are the Euclidean dis. a modality independent feature representation for all images tance intensity difference and the Edge Stopping Penalty. that capture their common image structural information Im ESP see Fig 3 Fig 4 respectively which are defined as. age spectral bases only depend on image self similarities Edist i j xi xj. pairwise pixel similarity and can be used for modality. Einten i j Ii Ij 2, independent representation These bases are obtained by the.
eigen decomposition for the Spectral Graph over each image EESP i j max Edge x. x line i j, 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 4. Fig 3 Typical cases of edge stopping penalty EESP Left the line i j. is intersected by the image contour Green versus Right no intersection of. contours The similarity between pixel i j on left is lower than that on right. Fig 4 Spectral bases with without edge stopping effect The artificial image. top left is decomposed into spectral bases under first row without EEPS. xi xj are the location of the pixels i j and the Ii Ij are their in Eqn 2 second row with ESP term The spectral bases obtained via ESP. intensities respectively Edge x represents an edge detector have sharper boundaries than those without it. i e Canny detector in location x x I E are constants. that will be assigned empirically In practice W i j will only SSN which enables the groupwise analysis of all images. be computed in k nearest neighbors thus W is a sparse matrix Fig 5 and Fig 6 show the overall idea of constructing. Fig 2 shows an illustrative example of a spectral graph synchronized spectral network using spectral synchronizations. which contains three pixels over a MR and a CT image. The weight values of each modality invariant self similarity. measure Edist Einten EESP are shown as normalized his A Spectral Synchronization for Graphs. tograms It is easy to see from Fig 2 that the spectral graph Spectral synchronization is the searching of a new set of. structure is invariant to MR CT modality spectral bases for the input images so that the common 2D. A self explained example of edge stopping penalty is illus spectral features are enhanced and correlated across images. trated in Fig 3 Term EESP in 2 is a penalty cost function Once the spectral bases are synchronized the related image. developed in 26 for measuring the contour intervention features regions edges they represented are matched accord. between two pixels Unlike other measures such as intensity ingly and can be simultaneously segmented. similarity the second term in 2 or gradient similarity e g Our synchronization are applied to the whole group of. Ii Ij the edge stopping penalty only consider the 2D spectral maps using Joint Laplacian Diagonalization with. intensity changes along line segment line i j of pixel i j Fourier coupling 27 2 Suppose Lm is the Laplacian. matrixes for Im I we aim to obtain a new set of generalized. B Spectral Bases on Graph quasi eigenvectors Ym ym 1 ym K RN K which. Spectral bases are the eigenvectors of the matrix represen X. tation W for the spectral graph We obtain the eigen vectors YmT Lm Ym m 2F. from the graph Laplacian instead of direct decomposition of. W Let D be the diagonal matrix whose elements are the row for m diag 1 Gm K Gm and 0 is small. summations of W We can have the Laplacian matrix In addition different quasi eigenvectors Ym and Yl should be. L Id D 1 2 W D 1 2 3 matched in a feature space such that for a linear non linear. feature mapping F RN RNF we have, The eigenvectors of L are unsynchronized spectral bases such X. that L can be approximated by the K smallest eigenvectors F Ym F Yl 2 5. m l I m6 l, L k k kT 4 where mapping F is determined according to different appli. k 1 cations The complete joint diagonalization problem can be. where k and k are the eigenvalue and its associated eigen formulated by the following optimization problem. vector respectively These spectral bases preserve the self X X. similarity information described by 2 As spectral bases are min YmT Lm Ym m 2F F Ym F Yl 2. obtained by independent eigen decompositions bases from 6. different images are to be synchronized for a more uniform The optimized results Y1 YM. are the demanded syn, representation chronized spectral basis The resulting vectors not only serve.
as ordinary eigenvectors of each spectral graph but are also. V S PECTRAL S YNCHRONIZATION ACROSS I MAGES matched in pairwise fashion under feature transform F. A groupwise synchronization is applied to unify similar In practice each quasi eigenvector ym k can be considered. chamber regions boundaries representations among the spec as the linear combination of k Gm K k 1 This assumption. tral bases so that these image parts can be jointly correlated resolves the ambiguity of Ym and simplifies the optimization. across images Group of spectral bases are synchronized via We first let Ym Um Am where Am is a K K 0 matrix. an optimization computation to obtain the new Synchronized variable for K 0 K and Um 1 Gm K Gm We. Spectral Bases The spectral graphs are then correlated by also adopt the Fourier coupling 27 in diagonalization and let. these new bases forming a Synchronized Spectral Network F be the matrix of discrete Fourier bases a N 0 N matrix. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 5. Fig 5 Uniform feature correlation from spectral graphs to synchronized. spectral network Spectral graphs from independent images are correlated. by spectral synchronization Spectral graph correlates the pixels pairs while. spectral synchronization correlates the graph bases. which contains N 0 vectorized discrete 2D Fourier bases Let Fig 6 The comparison between unsynchronized and synchronized spectral. m diag 1 Gm K 0 Gm Eqn 6 is modified as bases the unsynchronized and the synchronized superpixels The MR CT. X images are expanded to the unsynchronized spectral bases using the self. min ATm m Am m 2F similarity defined in Eqn 2 The synchronized spectral bases are obtained by. A1 AM Eqn 7 with the unsynchronized bases The superpixels obtained accordingly. X from both types of bases show that the synchronized one can provide part part. F Um Am F Ul Al 2 correspondences between images, subject to ATm Am Id for all m I in long axis view with only one or two simple drawings. 7 The drawings on one image will propagate to all image. The above optimization problem can be effectively computed group under incremental synchronization thus this separation. by the constrained programming solvers in Matlab Fig 6 can be achieved simultaneously for the whole image group. shows a toy example of spectral synchronization using 7 This significantly improves the existing manual segmentation. over two images with different modalities In this example methods on four chamber images. the corresponding anatomic structures in different images are. forced to match by their similar spectral features VI S YNCHRONIZED S UPERPIXELS FOR H EART. L OCALIZATION AND S EGMENTATION, B Incremental Spectral Synchronization The groupwise clustering of all synchronized spectral bases. We propose the incremental spectral synchronization for immediately leads to a set of synchronized superpixels Cham. reducing the complexity of large groupwise synchronization ber regions are segmented by these superpixels within each. and avoiding frequent re synchronization for newly added image and superpixel superpixel correspondences are obtained. data As defined in Eqn 7 the spectral synchronization needs across all images in the group As heart regions of the images. to synchronize all images in the group which will not be are groupwisely correlated heart locations can thus be jointly. efficient for large dataset or frequent data updates Instead identified from the correlated central superpixels. of complete re synchronization for the data the incremental. method adaptively adopt the previously synchronized bases to. A Single scale Synchronized Superpixels for Segmentation. build the new spectral bases obtained from the new images. Similar to 6 for a new input image Iw we construct The synchronized superpixels are directly obtained from the. Laplacian Lw and the re synchronized spectral bases Yw by K means clustering of synchronized spectral bases Unlike the. X classical single image superpixel approach we conduct K. min YwT Lw Yw w 2F F Ym F Yw 2 8 means clustering for all synchronized spectral bases in the. m I group to obtain uniform superpixel labeling The resulting. where I I1 IM is the set of images already superpixels not only provide oversegmentation for each image. correlated by SSN I will be fixed during the optimization but also provide the superpixel superpixel correspondences. computation In other words I serves as the training set for across all images which enables correlated groupwise segmen. supervising the spectral synchronization of Iw The resulting tation Let Sn m denotes the nth superpixel on image Im the. Yw can be calculated using the same fast computation method synchronized superpixels Sn 1 Sn M are correlated. in 7 For a large dataset the computation complexity of 8 and assigned to the same label Corresponding image regions. will remain linear as Yw can be computed one by one for each in I1 IM are matched accordingly The generation of. w in the dataset single scale SSP can be summarized as Algorithm 1. The incremental method also provide great flexibility for In practice additional contour refinement is applied for. practical applications For example in four chamber segmen each extracted segmentation regions The refinement is done. tation chambers in the long axis view are not naturally by first applying the automatic shape adjustment 28 29. separated in the images By using our incremental region over the extracted heart region superpixels then smoothing the. correspondences users can still easily separate these chambers superpixel contours by classical Fourier descriptor method. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 6. Algorithm 1 Single scale Synchronized Superpixels Gen. eration SSSG,Input of SSP N of spectral bases K K 0 image.
Output Superpixels S1 m Sn m M m 1,1 Construct spectral graph Gm for each Im. 2 Set m diag 1 Gm K Gm,m diag 1 Gm K 0 Gm,Um 1 Gm K Gm for all m 1 M. 3 Compute optimization 7 using m m Um M m 1,obtaining Ym Um Am for m 1 M. 4 Stack matrixes Y Y1 Y2 YM,5 Cluster rows of Y into N clusters using K means. 6 For all m 1 M partition Im to,S1 m Sn m according to the row clusters of Y.
Fig 8 The multi scale hierarchical SSN decomposition The synchronized. superpixels scale 1 can be sub decomposed into finer synchronized super. pixels scale 2 and even finer scales scale 3 4, synchronized superpixels For each synchronized superpixel. S the corresponding image regions forms a set of subgraphs. out of the original input images We then apply the spectral. Fig 7 The effect of superpixel granularity The increase of superpixel number decomposition and synchronization to these subgraphs obtain. N in Algorithm 1 does not affect the flat regions eg LV RV it only ing a new set of synchronized superpixels Scale 2 The sub. increases the split of non flat regions, decomposition can be carried out to even finer scales Scale 3. 4 etc to obtain smaller synchronized superpixels for refined. Synchronized v s Unsynchronized Superpixels Synchro part part correspondences At each scale the single scale SSP. nized superpixels are more robust for within image segmenta algorithm Algorithm 1 can be directly used for the generation. tion and allow cross image correlations As shown in Fig 6 of the SSP at that scale The algorithmic form of the complete. traditional superpixels are independently obtained for each multi scale SSP generation is presented as Algorithm 2. image by K means clustering of its spectral bases No cross. image correspondences are available from the resulting super Algorithm 2 Multi scale Synchronized Superpixels Gen. pixels In contrast synchronized superpixels are groupwisely eration MSSG. determined by clustering of all synchronized spectral bases Input Scale L of SSP at each scale N1 NL. Regions with common spectral representations are enhanced Image set I1 IM. and uniformly labeled in the groupwise clustering This label Output Multiscale Superpixels. ing provides part part correspondences across images Snl l n1 m l 1 L m 1 M n 1 N. Superpixel Granularity The increase of number N in 1 Initialize N0 1 l 0 let S 0 m Im for all. Algorithm 1 will lead to smaller superpixels Because of the m 1 M. edge stopping effect in Eqn 2 the smooth regions and major 2 For each n 1 Nl collect superpixels in group. boundaries will be preserved even if the number increases l. Sn n Sn n l l,l 1 n1 l 1 n1 l 1 n1, The additional superpixels generated will appear in non flat for all nl 1 1 Nl 1 n1 1 N1. regions of the images As Fig 7 shows the flat regions LV RV 3 For each Sn n l. generate Nl 1 superpixels, regions are insensitive to the increase of superpixel number l 1. S1 n nl 1 n1 1 SN l 1,l n nl 1 n1,S1 n nl 1 n1 M SN l n nl 1 n1.
B Multi scale Synchronized Superpixels for Segmentation Algorithm 1. Coarse to fine segmentation is required in the analysis of 4 l l 1 and go to step 2 if l L. the multiscale image structures in input data Our spectral syn. chronization network can be conducted iteratively for the input. images to obtain the multiscale hierarchical decomposition In. the multi scale synchronization images are iteratively corre C Groupwise Heart Localization using Multiscale Synchro. lated and segmented obtaining the multiscale synchronized nized Superpixels. superpixels The multi scale SSPs are then progressively ex The synchronized superpixels naturally provide superpixel. tracted as sub images sub sub images for finer segmentation superpixel correspondences for all images in the group which. As illustrated in Fig 8 we first decompose and synchronize can be used for simultaneous localization for similar objects. the spectral bases of the input images Scale 1 generating among the images This property can be employed for locating. the set of synchronized spectral bases and subsequently the the heart regions from the raw cardiac scans. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 7. Fig 10 Multiscale synchronized superpixels two scales for simultaneous heart localization in raw MR CT images Two examples are shown in this figure. Top the example on multiscale decomposition and heart localization in raw axial MR and CT images Bottom the example on sagittal MR and CT images. The heart regions in these examples are simultaneously identified as the largest synchronized superpixels around the centers. are simultaneously identified by stacking superpixels together. and detecting the highest overlapping regions near the center. VII E XPERIMENTS, Our segmentation is tested on one open and two self. collected M3 cardiac datasets covering MR CT modalities. Fig 9 Heart localization by synchronized superpixel maps The heart short axis long axis two four chamber views and various. regions are identified by 1 stitching the two maps together and finding the. overlapping regions that are sharing the same label 2 locating the region. heart sizes poses field of view conditions High dice metric. stack near image center as the heart region stack DM 85 is constantly achieved in almost all tests which. shows our segmentation is a reliable tool for analyzing the. general M3 cardiac images, Fig 9 shows the heart region localization from two synchro. nized superpixels The joint localization can be obtained by. stacking the two superpixel maps with rescaling and finding A Datasets. the overlapped superpixels at the centers Some existing heart The three datasets are organized as follows. localization methods such as maximum discrimination 13 Dataset 1 2 collected 93 subjects with 10300 short. circle fitting 30 Hough transform 31 template matching axis view two chamber and horizontal long axis view four. 32 can provide automatic LV detection but are restricted to chamber MR heart images all manually cropped by experts. short axis view only Our method does not rely on a particular according to their experience All short axis view images are. image view and can be applied to freeview scans with resolution 80 80 obtained from 60 frames out of three. For a group of raw cardiac scans MR CT or both different slice levels from the short axis stacks in a cardiac. the spectral synchronization and synchronized superpixels cycle The four chamber images are of 100 100 manually. correlate the regions among the raw scans As shown in sampled from 25 frames in a cardiac cycle along the long axis. Fig 10 the synchronized superpixels at scale 1 provide part Dataset 2 64 subjects 32 MR 32 CT collected by our. part correspondences for regions in a MR image and a CT supportive hospitals The MR images are all uncropped with. image The correlated regions include the regions of the resolution 192 192 and pixel spacing 1 51 1 51 mm The. hearts spine and lung areas Similarly as shown in previous CT images are uncropped with resolution 512 512 and pixel. examples the synchronized superpixels at scale 2 provide the spacing 0 98 0 98 mm The MR CT in this set are extracted. correspondences between chamber regions All heart regions as upper body raw axial slices. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 8. Fig 11 Spatial Temporal Test Groupwise segmentation for 60 regulated cropped short axis view two chamber MR images from three slice levels base. mid and apex of a whole cardiac cycle The synchronized superpixels automatically correlate chamber regions among the images The LV yellow contour. and RV red contour are automatically identified The total 60 images are jointly segmented using the incremental synchronization Sec V B. Fig 12 Groupwise segmentation for 25 regularly cropped horizontal long axis view four chamber MR images of a cardiac cycle The LV LA yellow. contour and RV RA red contour are automatically identified The total 25 images are jointly segmented using the incremental synchronization Sec V B. Dataset 3 64 subjects 32 MR 32 CT The MR data The accuracy avg DM and robustness std of our seg. in this dataset is from York Cardiac MRI dataset 1 while the mentation are evaluated The resulting Table I shows that. CT data is collected by our group The MR images are with our segmentation can achieve 88 highest DM for cardiac. resolution 256 256 and pixel spacing 0 93 to 1 65 mm while cycle data of 93 subjects This shows the unsupervised SSN. the CT images are extracted from the 512 512 456 volumes segmentation is an accurate and convenient measurement tool. The LV groundtruth of the York MR Dataset is provided by the for multi view cardiac analysis. original dataset and the RV groundtruth is manually obtained As reported in Table I our segmentation obtain average DM. by our supportive expert The MR CT in this set are extracted 88 0 LV and 84 8 RV under short axis two chamber. as upper body sagittal slices views and has 87 6 LV LA and 87 0 RV RA under. long axis four chamber views During the test for each subjec. t all 60 short axis view two chamber images are segmented. B Regularly Cropped Short Long Axis View Images using the incremental segmentation Sec V B Similarly 25. We first test the segmentation in a mostly used spatial four chamber images for each subject are simultaneously seg. temporal temporal diagnostic environment segmentation for mented too The overall performance in both two four chamber. images from one full cardiac cycle in either two or four cham views are close The difference of DM between both views is. ber view In this scenario we use the regularly cropped short less than 3 which proves that our freeview segmentation is. axis long axis view two four chamber MR images from dif insensitive to view changes. ferent cardiac cycles Dataset 1 to form segmentation groups A representative example is shown in Fig 11 which shows. a test for groupwise segmentation for 60 short axis view two. 1 http www cse yorku ca mridataset chamber images one cardiac cycle of temporal resolution. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 9.
a Scale 1 groupwise segmentation for raw MR scans a Scale 1 groupwise segmentation for raw CT scans. b Scale 2 segmentation for automatically identified sub images from a b Scale 2 segmentation for automatically identified sub images from a. Fig 13 Single Modality Test Groupwise segmentation for raw MR scans Fig 14 Single Modality Test Groupwise segmentation for raw axial cardiac. with different heart poses sizes The scale 1 SSPs successfully segment CT scans with different heart poses sizes The scale 1 SSPs successfully. the heart images while scale 2 SSPs immediately provide heart region segment the heart images while scale 2 SSPs immediately provide heart. segmentation LV yellow contour RV red contour region segmentation LV yellow contour RV red contour. LV LA RV RA All Chambers Representation LV RV All Chambers. Short Axis View 88 0 4 0 84 8 6 0 86 7 5 1 Syn Superpixels SSP 2 89 1 4 1 85 2 5 6 87 1 5 4. Horizontal Long Axis View 87 6 4 6 87 0 6 2 87 4 5 6 SSP Refinement 91 6 3 6 87 6 5 1 90 4 4 7. Q UANTITATIVE COMPARISON DM OF DIFFERENT SEGMENTATION. D ICE METRIC EVALUATIONS OF THE REGULATED VIEW IMAGES 93. REPRESENTATION,SUBJECTS IN DATASET 1, different subjects from Dataset 2 and 30 upper body sagittal. 20 with three slice levels base mid and apex All images. scans 15 MR 15 CT different subjects from Dataset 3. in the test are already manually cropped to short long axis. are used Those images are with different heart sizes poses. views to simulate the regulated clinical condition The LV. institutional protocols and even different field of views During. and RV regions are directly obtained from the superpixels and. this test we rearrange the data into four sets 15 MR axial. quantitative volume estimation is immediately available from. scans 15 CT axial scans 15 MR sagittal scans and 15 CT. Fig 11 Similarly Fig 12 shows a test for groupwise segmen. sagittal scans Each set is further divided into three 5 image. tation for 25 images four chamber images from a cardiac cycle. groups and processed by the groupwise segmentation The. same subject The synchronized superpixels directly provide. overall results for LV LA and RV RA segmentations are. the cardiac segmentation and volume estimation in regulated. reported in Table III and Table IV which shows our segmen. clinical condition, tation can obtain average DM larger than 88 The multiscale. The same regulated configuration can be used to test the. groupwise segmentation provides a convenient coarse to fine. quantitative performance different segmentation properties We. shape volume comparative analysis across subjects directly. test the improvement of the contour refinement of the proposed. from raw scans, method in this paper see Sec VI A and that of the pure. Fig 13 shows a representative example of a 5 MR image. groupwise segmentation the same presented in 2 The test. group from Dataset 3 which contains 5 subjects with differ. is conducted on the York MR Cardiac Dataset now part of. ent sizes poses Using our two scale groupwise segmentation. the Dataset 3 and the results are summarized in Table II As. Algorithm 2 the LV RV regions of the five MR images. shown in the table the SSP refinment has higher accuracy. are automatically extracted achieving average DM 89 2. than the pure SSP segmentation The refinement is applied for. Similarly Fig 14 shows another groupwise segmentation of. all following tests unless stated otherwise,a 5 CT image group with DM 90 1 The segmentation. performance of both examples are insensitive to the changes. C Non regulated Raw Images Single Modality of subject poses and sizes. We then test the segmentation performance under a multi. subject comparative study environment Our segmentation is D Non regulated Raw Images Cross Modality. tested on groups of single modality raw scans from Dataset 2 The segmentation is next tested under the multi subject. and 3 In total 30 upper body axial scans 15 MR 15 CT multi modality comparative study environment We perform. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 10.
a Scale 1 groupwise segmentation for MR CT mixed axial scans. b Scale 2 groupwise segmentation for the MR CT mixed heart sub images automatically identified from a. Fig 15 Cross Modality Test Two scale groupwise segmentation from MR CT mixed raw axial slices a Successful groupwise segmentation for 4 CT 4. MR different subjects under a non regulated axial view b groupwise segmentation for heart regions extracted from a The LV LA yellow contour and. RV RA red contour regions are jointly identified after segmentation. a Scale 1 groupwise segmentation for MR CT mixed sagittal scans. b Scale 2 groupwise segmentation for the MR CT mixed heart sub images automatically identified from a. Fig 16 Cross Modality Test Two scale groupwise segmentation from MR CT mixed raw sagittal slices a Successful groupwise segmentation for 4 CT. 4 MR different subjects under a non regulated sagittal view b groupwise segmentation for heart regions extracted from a The LV yellow contour and. RV red contour regions are jointly identified after segmentation. groupwise segmentation on uncropped images from Dataset in the tests to increase the data variety Uncropped images are. 2 and 3 with varying degrees of MR CT mixtures to sim directly arranged in two originally acquired imaging views. ulate the cross modality conditions As shown in Table V the axial and sagittal views For each view the images are. and Table VI the overall segmentation results LV RV and divided in four groups 2 MR 2 CT 4 MR 4 CT 16 MR. LV RV remain constantly above DM 85 for most of the 16 CT and 32 MR 32 CT to simulate different levels. cases except some rare cases in RV region segmentation of modality mixtures The MR dataset contains a variety of. lower results 83 due to the region fuzziness Thanks to pathology problems including cardiomyopathy aortic regurgi. the spectral features our M3 segmentation is insensitive to tation enlarged ventricles and ischemia as mentioned in 33. the changes of modality subject However no significant segmentation defeats are found during. Particularly all subjects from Dataset 2 and 3 are involved the test which shows our method is insensitive to structural. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 11. 4 image group 8 image group 16 image group 32 image group. LV LA RV RA All Cham LV LA RV RA All Cham LV LA RV RA All Cham LV LA RV RA All Cham. MR 92 8 2 8 91 4 3 0 91 4 2 8 89 8 3 9 90 4 3 2 89 9 3 2 87 8 3 8 88 0 3 9 87 7 4 0 86 2 4 8 85 1 4 7 85 5 5 0. CT 88 7 3 9 86 5 3 3 87 7 3 6 87 0 3 9 87 9 3 8 87 1 4 0 87 1 4 3 85 2 4 9 86 9 4 0 84 2 5 7 82 9 5 2 84 0 5 3. MR CT 91 0 3 7 89 1 3 5 89 3 3 1 87 9 4 0 88 1 3 7 87 2 3 5 87 5 3 9 87 1 4 9 87 0 4 1 85 7 5 1 84 1 5 0 84 5 5 0. AVERAGE DM AND STANDARD DEVIATION ON THE MR CT MIXED RAW AXIAL SCANS SEE EXAMPLES IN F IG 15. 4 image group 8 image group 16 image group 32 image group. LV RV All Cham LV RV All Cham LV RV All Cham LV RV All Cham. MR 91 8 3 2 90 2 3 1 90 4 3 3 88 2 4 2 87 8 4 5 86 8 4 2 86 8 3 8 85 9 4 8 86 4 4 5 85 2 4 9 85 8 4 5 86 0 4 7. CT 89 7 2 9 87 7 3 6 88 2 3 5 86 2 4 6 84 9 4 7 85 8 5 1 86 7 4 9 85 0 5 0 85 9 4 5 86 2 4 7 83 1 5 1 83 8 5 1. MR CT 90 8 3 3 89 8 3 5 89 2 3 2 87 9 4 0 89 1 3 7 87 2 3 9 87 4 4 3 85 1 4 9 86 2 4 1 85 9 5 1 84 6 5 0 84 2 5 2. AVERAGE DM AND STANDARD DEVIATION ON THE MR CT MIXED RAW SAGITTAL SCANS SEE EXAMPLES IN F IG 16. LV RV All Chambers,MR 15 subjects 91 5 2 8 89 0 3 2 90 2 3 1. CT 15 subjects 90 1 2 7 88 3 4 0 89 1 3 8,AVERAGE DM ON SHORT AXIS SINGLE MODALITY DATA. LV LA RV RA All Chambers,MR 15 subjects 90 2 3 2 88 0 3 7 89 2 3 3. CT 15 subjects 89 1 3 7 87 3 4 1 88 2 3 8,AVERAGE DM ON LONG AXIS SINGLE MODALITY DATA.
a Scale 1 groupwise segmentation for coronal images of a cardiac cycle. abnormalities Note that one randomly selected subject from. York MR Dataset now Dataset 3 is removed for the equal. pair up of the MR CT joint segmentation The final results are. calculated by taking the average DM over all images in the. same group, A representative example for this test is presented in Fig 15. This example shows a 4 MR 4 CT mixed image group with. different heart poses sizes under the non cardiac axial imaging. view Our unsupervised groupwise segmentation has results. in successful extraction of the LV LA and RV RA regions. in the eight images achieving average DM 88 2 Similarly. Fig 16 presents a successful segmentation on 8 MR CT mixed. raw sagittal scans The full numerical results on axial scans b Scale 2 groupwise segmentation for identified sub images from a. are reported in Table V and Table VI The overall results for. Fig 17 Groupwise segmentation for non diagnostic freely chosen coronal. axial and sagittal scans are insensitive to view and modality MR scans a The scale 1 SSPs successfully segmented and identified the. changes This proves the high versatility of our method in hearts b The LV AO yellow RV red and PA blue are jointly obtained. different clinical conditions by scale 2 SSPs, generates 10 synchronized superpixels The heart locations are. E Non regulated Raw Images Non diagnostic View jointly identified generating 8 new synchronized superpixels. We finally test the segmentation on even less regulated non for the cropped images Then in the scale 2 groupwise segmen. diagnostic view images to evaluate the performance under tation the LV RV and PA regions are jointly identified from. extreme conditions The test images are from Dataset 2 and the synchronized superpixels Segmentation on other views are. 3 under a non diagnostic view A representative example of immediately available by following the same process. this test is shown in Fig 17 Our unsupervised segmentation. can achieve average DM 89 0 in this case which provides F Implementation Details and Computation Time. a highly flexible tool for arbitrary customized scenarios The segmentation is implemented in Matlab and performed. As Fig 17 shows four MR coronal view upper body scans on Intel Core i7 CPU PC for small image group and also the. including the most significant frames of end diatolic and end SHARCNET platform http www sharcnet ca for large im. systolic stages are used in the test Our scale 1 groupwise age group The optimization computation Eqn 7 and Eqn 8. segmentation successfully synchronizes the MR scans and are implemented by the optimization toolbox in Matlab Our. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 12. at multiple scales Specific superpixels can thus be jointly. identified and extracted which provides automatic groupwise. analysis for these target regions, B SSN Groupwise Segmentation v s Existing Cardiac Seg. mentations, Success Failure of Groupwise Segmentation For all the.
Fig 18 The comparison between the computation time of SSN synchroniza tests we conducted no fail cases are found in the groupwise. tion Sec V A and incremental SSN synchronization Sec V B segmentations However one can imagine that when the. groupwise assumption is not met the proposed approach would. unoptimized implementation of SSN synchronization is very fail One extreme case would be the mixture of the test image. efficient as most of the cases will converge in less than 100 group with images from incompatible different views i e. iterations with default settings a short axis view image group mixed with long axis view. Implementation Comparison We also test the implemen images Nevertheless in practice it has no application to put. tation of SSN synchronization Eqn 7 and the incremental different view images in correspondence thus this failure can. synchronization Eqn 8 in Fig 18 For a randomly selected be avoided. group of 60 images sampled from Dataset 1 the incremental M3 Segmentation Compared to the existing cardiac seg. synchronization is initially synchronized with a 4 image set mentation methods 33 6 14 19 20 34 35 36 37. in either two chamber short axis or four chamber long axis 10 our approach is the first to provide groupwise segmen. images The DM accuracies on both implementation are very tation with region correspondences in multi modality multi. close 3 For the same 60 image group the SSN non subject multi chamber situation for different regular non. incremental synchronization will take longer than 40 min regular views The overall comparison is presented in Ta. to converge while incremental synchronization only need ble VII It is clear from the table that after testing the largest. less than 5 2s per image using our matlab implementation datasets 221 subjects so far not only our performance in. Incremental method has linear time growth and thus more LV RV segmentation is very competitive to existing major. suitable for large image set synchronization and segmentation segmentation methods but we also provide a more general. and versatile solution for almost all clinical conditions For the. VIII D ISCUSSION traditional single modality single chamber segmentation. Our spectral synchronization method has many new prop tasks our groupwise segmentation is still among the top per. erties that improve the performances and functionalities of formance methods In Table VIII we present the quantitative. traditional spectral based segmentation methods and existing comparative results of our method and the top ranked meth. cardiac segmentation methods ods on MICCAI LV Segmentation Challenge Dataset 2 The. groupwise setting in this case is similar to those in Sec VII B. A SSN v s Traditional Spectral Segmentations and Sec VII C where a 5 image set out of 20 cardiac cycle. images is first randomly chosen for groupwise segmentation. Enhanced Feature Clustering Traditional spectral based then incrementally propagates to the whole cycle Our method. methods or referred as random walk methods in some litera has the best all phases performance Endo Epi in training set. tures 26 38 utilize the principal decomposition of spectral and is tight to the best method in validation set Illustrative. graph matrix to provide robust image feature clustering and examples of this dataset are presented in Fig 19 which shows. image segmentation Compared to these traditional methods a groupwise segmentation with 93 2 DM accuracy. our SSN based method not only preserves the robust spectral Freeview Segmentation As can be observed from Ta. clustering of within image features like contours textures but ble VII unlike our segmentation method all methods ex. automatically builds up the correspondences of these features cept 8 are restricted to the segmentation of well cropped. across images These new correspondences are established by short axis long axis two four chamber views However the. borrowing the spectral clustering of the whole image group method proposed in 8 still requires the manual building of. The SSN correlated spectral clustering in turn enhances the image atlas and has not shown its ability to handle LV RV. feature clustering of each image and finally improves the chamber segmentation Our cross modality whole heart seg. segmentation quality mentation can be done without atlas trainings It makes the. Co segmentation without Explicit Matching In addition complete cardiac segmentation process fully automatic and is. compared to other spectral groupwise segmentation methods more suitable for the segmentation tasks of today s large scale. or referred as co segmentation 43 SSN based image cor M3 image sets. respondences are modality independent and do not require Region to Region Correspondences We propose the novel. exact matching such as alignments of SIFT intensity features unsupervised region to region correspondences between MR. between images This enables our SSN model to perform and CT images in cardiac segmentation in this paper Although. groupwise segmentation across different modalities that have some multi atlas based methods i e 8 10 claimed they. diverse image intensities The cross image correspondence can work on both modalities the image correspondences. also constitutes explicit correlations at multiple superpixel. scales which can be considered as a groupwise registration 2 http smial sri utoronto ca LV Challenge. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 13. Method Modality View Chamber Dataset Performance metric result. Andreopoulos et al MR Short axis LV 33 subjects Endo volumetric error 1 43 0 49 mm. 33 2008 Epi volumetric error 1 51 0 48 mm, Zheng et al 6 2008 CT Horizontal long axis LV LA 137 subjects LA point to mesh 1 13 0 55 mm. RV RA RA point to mesh 1 57 0 48 mm,LV Endo point to mesh 0 98 1 32 mm. LV Epi point to mesh 0 82 1 07 mm,RV point to mesh 0 84 0 94 mm. Ecabert et al 14 CT Horizontal long axis LV LA 108 subjects LA point to surface 0 71 0 88 mm. 2008 RV RA RA point to surface 0 89 0 96 mm,LV Endo point to surface 0 98 1 32 mm.
LV Epi point to surface 0 82 1 07 mm,RV point to surface 0 84 0 94 mm. Ben Ayed et al 19 MR Short axis LV 10 subjects Cavity DM 88 9. 2009 Myocardium DM 81 10, Isgum et al 8 2009 CT Axial view Whole heart 29 subjects Tanimoto Coefficient 0 8847 0 0331. Zhang et al 20 2010 MR Short axis LV RV 50 subjects LV Endo point to surface 1 67 0 3 mm. LV Epi point to surface 1 81 0 4 mm,RV Endo point to surface 2 13 0 39 mm. Ben Ayed et al 34 MR Short axis LV 20 subjects Cavity DM 92 3 1. 2012 Myocardium DM 82 6 1, Nambakhsh et al 35 MR Short axis LV 20 subjects Cavity DM 92 7. 2013 Myocardium DM 80 10, Queiros et al 36 MR Short axis LV 45 subjects Endo DM 93 3.
2014 Epi DM 94 2, Ringenberg et al 37 MR Short axis RV 16 subjects Endo DM 88 11. 2014 Epi DM 90 8, Bai et al 10 MR Short axis LV 83 subjects Method 1 DM 81 2. 2015 Method 2 DM 81 5, Our Method MR CT Freeview LV LA 221 subjects DM 85 for almost all situations. short long axis RV RA 157 MR 64 CT See Table I to VI. axial sagittal views Whole heart, C OMPARISON WITH MAJOR CARDIAC SEGMENTATION METHODS DEVELOPED IN RECENT YEARS. Huang et al Lu et al 39 O Brien et al Jolly 40 Constantinides et al Casta et al Wijnhout et al Ours. 30 41 42 32 31, Training 90 4 Endo 80 Endo 88 1 5 7 Endo 88 4 10 2 Endo 90 8 2 6 All.
15 cases 93 2 Epi 91 3 Epi 93 5 1 4 Epi 92 9 6 5 Epi. Validation 89 4 Endo 89 3 All same as above 87 9 3 2 Endo 92 3 6 1 Endo 92 7 All 89 3 All 92 3 3 8 All. 15 cases 94 1 Epi 93 3 1 8 Epi 92 2 5 0 Epi,TABLE VIII. Q UANTITATIVE COMPARISON OF AVERAGE DM AND STANDARD DEVIATION ON THE MICCAI LV C HALLENGE DATASET. cannot be automatically obtained from the manually built atlas images can be identified simultaneously using synchronized. Instead our method can automatically build up the correspon superpixels and chambers can then be extracted as the segmen. dences and an accurate MR CT registration can also be done tation results Our segmentation has accurate and robust results. by simply aligning the identified chamber regions from our DM 85 for uncropped scans regulated short axis long. synchronized superpixels For single subject study this en axis four chamber images even non regulated images It. ables the cross modality comparative measurement diagnosis provides a general algorithmic framework for today s cardiac. for different cardiac problems For multiple subject study segmentation tasks. particularly in the big data environment this enables a more. comprehensive and non biased statistical analysis for cardiac. data obtained from different modalities and protocols R EFERENCES. 1 Z Wang X Zhen K Tay S Osman W Romano and S Li Regres. IX C ONCLUSIONS sion segmentation for m3 spinal images IEEE TMI 2015. 2 Y Cai A Islam M Bhaduri I Chan and S Li Unsupervised freeview. We proposed an unsupervised groupwise segmentation for groupwise segmentation for m3 cardiac imaged using synchronized. general cardiac images Our method can provide simultaneous spectral network in MICCAI Spinger 2015. segmentation for a group of cardiac images with multiple 3 N Paragios A variational approach for the segmentation of the left. ventricle in cardiac image analysis IJCV vol 50 pp 345 362 2002. modalities multi chamber and multiple subjects images The 4 M Lynch O Ghita and P F Whelan Left ventricle myocardium seg. segmentation is based on the Synchronized Spectral Net mentation using a coupled level set with a priori knowledge Comput. work SSN model which correlates the modality independent Medical Imaging and Graphics vol 30 no 4 pp 255 262 2006. 5 Segmentation of the left ventricle of the heart in 3 d t mri data. spectral features across images and clusters the features into using an optimized nonrigid temporal model IEEE TMI vol 27 no 2. synchronized superpixels The heart regions from different pp 195 203 2008. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information. This article has been accepted for publication in a future issue of this journal but has not been fully edited Content may change prior to final publication Citation information DOI 10 1109 TMI 2016 2553153 IEEE. Transactions on Medical Imaging, SUBMITTED TO IEEE TRANSACTION ON MEDICAL IMAGING 14. Fig 19 Examples of groupwise segmentation results 5 image set in MICCAI LV Challenge Dataset Our final contour results yellow contours are very. close to the ground truths green contours The average DM is 93 2 for this image set. 6 Y Zheng A Barbu B Georgescu M Scheuering and D Comaniciu 25 A Y Ng M I Jordan and Y Weiss On spectral clustering Analysis. Four chamber heart modeling and automatic segmentation for 3 d and an algorithm in NIPS 2001. cardiac ct volumes using marginal space learning and steerable features 26 T Cour F Benezit and J Shi Spectral segmentation with multiscale. IEEE TMI vol 27 no 11 pp 1668 1681 2008 graph decomposition in CVPR vol 2 IEEE 2005 pp 1124 1131. 7 M Lorenzo Valde s G I Sanchez Ortiz A G Elkington R H Mohi 27 D Eynard K Glashoff M M Bronstein and A M Bronstein. addin and D Rueckert Segmentation of 4d cardiac mr images using Multimodal diffusion geometry by joint diagnoalization of laplacians. a probabilistic atlas and the em algorithm MedIA vol 8 no 3 pp IEEE TPAMI 2015. 255 265 2004 28 A Tsai A Yezzi Jr W Wells C Tempany D Tucker A Fan W E. 8 I Isgum M Staring A Rutten M Prokop M A Viergever and Grimson and A Willsky A shape based approach to the segmentation. B van Ginneken Multi atlas based segmentation with local decision of medical imagery using level sets IEEE TMI vol 22 no 2 pp. fusionapplication to cardiac and aortic segmentation in ct scans IEEE 137 154 2003. 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Viergever J P Pluim and B van Ginneken Adaptive local multi atlas pp 564 592 2003. segmentation application to the heart and the caudate nucleus MedIA 30 S Huang J Liu L Lee S Venkatesh L Teo C Au and W Nowinski. vol 14 no 1 pp 39 49 2010 Segmentation of the left ventricle from cine mr images using a com. 10 W Bai W Shi C Ledig and D Rueckert Multi atlas segmentation prehensive approach MIDAS J Card MR Left Ventricle Segmentation. with augmented features for cardiac mr images MedIA vol 19 no 1 Challenge 2009. pp 98 109 2015 31 J Wijnhout D Hendriksen H Assen and R der Geest Lv challenge. 11 D Mahapatra Z Li P Schu ffler F Vos and J Buhmann Joint lkeb contribution Fully automated myocardial contour detection The. segmentation and groupwise registration of cardiac dce mri using sparse MIDAS Journal vol 43 p 2 2009. data representations In Proc IEEE ISBI pp 1312 1315 2015 32 C Casta P Clarysse J Schaerer and J Pousin Evaluation of the. 12 K Mcleod C Seiler M Sermesant and X Pennec Spatio temporal dynamic deformable elastic template model for the segmentation of the. dimension reduction of cardiac motion for group wise analysis and heart in mri sequences MIDAS J Card MR Left Ventricle Segmentation. statistical testing in MICCAI Springer 2013 pp 501 508 Challenge 2009. 13 M P Jolly Automatic segmentation of the left ventricle in cardiac mr 33 A Andreopoulos and J K Tsotsos Efficient and generalizable sta. and ct images IJCV vol 70 no 2 pp 151 163 2006 tistical models of shape and appearance for analysis of cardiac mri. 14 O Ecabert J Peters H Schramm C Lorenz J Von Berg M J Medical Image Analysis vol 12 no 3 pp 335 357 2008. 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Trans on Biomed Eng vol 53 no 7 pp 1425 1428 2006 ventricle in short axis cardiac mri Computerized Medical Imaging and. 19 I Ben Ayed S Li and I Ross Embedding overlap priors in variational Graphics vol 38 no 3 pp 190 201 2014. left ventricle tracking IEEE TMI vol 28 no 12 pp 1902 1913 2009 38 L Grady Random walks for image segmentation TPAMI vol 28. 20 H Zhang A Wahle R K Johnson T D Scholz and M Sonka 4 d no 11 pp 1768 1783 2006. cardiac mr image analysis left and right ventricular morphology and 39 Y Lu P Radau K Connelly A Dick and G Wright Automatic. function IEEE TMI vol 29 no 2 pp 350 364 2010 image driven segmentation of left ventricle in cardiac cine mri The. 21 D Mahapatra and J M Buhmann Cardiac lv and rv segmentation MIDAS Journal vol 49 p 2 2009. using mutual context information in Machine Learning in Medical 40 M Jolly Fully automatic left ventricle segmentation in cardiac cine mr. Imaging Springer 2012 pp 201 209 images using registration and minimum surfaces The MIDAS Journal. 22 B P Lelieveldt M U zu mcu R J van der Geest J H Reiber Cardiac MR Left Ventricle Segmentation Challenge vol 4 2009. and M Sonka Multi view active appearance models for consistent 41 S O Brien O Ghita and P F Whelan Segmenting the left ventricle. segmentation of multiple standard views application to long and short in 3d using a coupled asm and a learned non rigid spatial model 2009. axis cardiac mr images in International Congress Series vol 1256 42 C Constantinides Y Chenoune N Kachenoura E Roullot. Elsevier 2003 pp 1141 1146 E Mousseaux A Herment and F Frouin Semi automated cardiac. 23 J Lo tjo nen S Kivisto J Koikkalainen D Smutek and K Lauerma segmentation on cine magnetic resonance images using gvf snake. Statistical shape model of atria ventricles and epicardium from short deformable models The MIDAS Journal Cardiac MR Left Ventricle. and long axis mr images MedIA vol 8 no 3 pp 371 386 2004 Segmentation Challenge 2009. 24 M Sermesant C Forest X Pennec H Delingette and N Ayache 43 M D Collins J Xu L Grady and V Singh Random walks based. Deformable biomechanical models Application to 4d cardiac image multi image segmentation Quasiconvexity results and gpu based solu. analysis MedIA vol 7 no 4 pp 475 488 2003 tions in CVPR IEEE 2012 pp 1656 1663. 0278 0062 c 2015 IEEE Personal use is permitted but republication redistribution requires IEEE permission See http www ieee org publications standards publications rights index html for more information.


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