Sequential Monte Carlo Tracking for Marginal Artery Segmentation on CT Angiography by Multiple Cue Fusion

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1 Sequenial Mone Carlo Tracking for Marginal Arery Segmenaion on CT Angiography by Muliple Cue Fusion Shijun Wang, Brandon Peplinski, Le Lu, Weidong Zhang, Jianfei Liu, Zhuoshi Wei, and Ronald M. Summers Imaging Biomarkers and Compuer-Aided Diagnosis Laboraory, Radiology and Imaging Sciences, Naional Insiues of Healh Clinical Cener, Behesda, MD, , U.S. Absrac. In his work we formulae vessel segmenaion on conras-enhanced CT angiogram images as a Bayesian racking problem. To obain poserior probabiliy esimaion of vessel locaion, we employ sequenial Mone Carlo racking and propose a new vessel segmenaion mehod by fusing muliple cues exraced from CT images. These cues include inensiy, vesselness, organ deecion, and bridge informaion for poorly enhanced segmens from global pah minimizaion. By fusing local and global informaion for vessel racking, we achieved high accuracy and robusness, wih significanly improved precision compared o a radiional segmenaion mehod (p= Our mehod was applied o he segmenaion of he marginal arery of he colon, a small bore vessel of poenial imporance for colon segmenaion and CT colonography. Experimenal resuls indicae he effeciveness of he proposed mehod. Keywords: Sequenial Mone Carlo racking, muliple cues, paricle filering, marginal arery, CT angiography. 1 Inroducion The marginal arery is a small blood vessel locaed wihin he abdominal mesenery which ravels parallel o he colon, and communicaes beween he inferior and superior meseneric areries (IMA and SMA. Segmenaion of he marginal arery can improve supine-prone colonic polyp regisraion and help connec collapsed colonic segmens in CT colonography (CTC. The purpose of his pilo sudy is o auomaically deec he marginal arery on high-resoluion abdominal CT angiograms (CTA using a sequenial Mone Carlo (SMC racking mehod. Vessel enhancemen filering, region-growing, acive conours, cenerline exracion, and sochasic framework are five major approaches o 3D vessel segmenaion [1]. Among hese mehods, SMC racking, or paricle filering (PF, has been widely used for is accuracy, robusness, and compuaional feasibiliy. Florin e al. proposed a PF-based approach for segmenaion of coronary areries [2]. In heir model, sae variables include posiion, orienaion, shape, and vessel appearance. Laer, Schaap e adfa, p. 1, Springer-Verlag Berlin Heidelberg 2011

2 al. presened a Bayesian racking framework for ubular srucures such as vessels [3]. The key conribuion of heir work is a novel observaion model designed for ubelike objecs. Lacose e al. employed Markov marked poin processes for segmenaion of coronary areries on 2D angiograms [4]. More recenly, Friman proposed a muliple hypohesis emplae racking scheme for small 3D vessel srucures [5]. SMC has also been used in compuer vision o handle ahlee or vehicle racking in video sequences. The collecion and uilizaion of more arge and background informaion will ypically improve accuracy and robusness for a given noise level. In recen years, incorporaing muliple cues in he Bayesian racking framework has been a major research direcion. Wu and Huang proposed a facorized graphical model o inegrae muliple cues for Bayesian racking [6]. Brasne e al. proposed visual cues including color, edge, and exure for objec racking in video sequences [7]. The work of Moreno-Noguer e al. [8] focused on inegraing dependen muliple cues for robus racking. In his work, we propose a new Bayesian vessel segmenaion mehod by fusing muliple cues exraced from CT images o auomaically deec he marginal arery on high-resoluion abdominal CT angiograms. The remainder of his paper is organized as follows: in Sec. 2 we inroduce our SMC racking framework wih muliple cues; in Sec. 3 we show experimenal resuls on a CTA daase of 7 paiens. We conclude our findings in Sec. 4 wih a shor discussion. 2 Sequenial Mone Carlo Tracking by Muliple Cue Fusion 2.1 Bayesian Tracking Framework Firs we will inroduce he SMC racking framework and noaion. Observaions my y ; N, y R are ypically capured in a sequenial order. Each observaion has mx an associaed hidden variable x ; N, x R which generally corresponds o he locaion of he arge and speed a ime poin. For each, he observaion y is only condiionally dependen on x, i.e. p 1: 1, 1: p y y x y x, where 1: 1 represens all observaions from ime poin 1 o ime poin -1 and x represens all hidden variables from ime poin 1 o ime poin. We also assume ha he ime sequence x, =1,2, T has a Markov propery of order one: p 1: 1 p 1 y x x x x. The dynamics of he Markov chain can be described by he following wo seps: 1 Predicion sep: px y1: 1 px x 1 px 1 y1: 1 dx 1 (1 2 Updae sep: py x px y1: 1 px y1: (2 p y 1:

3 In our implemenaion, he sae variable x was composed by x x, x', y, y ', z, z ' he vessel during he dynamic racking process., corresponding o he curren locaion and moving speed of 2.2 Mixure Dynamic Model Combined wih Vecor Field Considering ha he majoriy of vessel segmens are smooh in 3D space and exhibi a ube srucure, we chose a consan velociy model o capure ranslaional moion: x Fx d 1, d ~ N 0, d, (3 where marix F conrols he speed a which he arge (vessel segmenaion can proceed during he racking process. d follows a zero-mean Gaussian disribuion whose covariance marix was deermined empirically based on he raining se. Fig. 1. 3D vecor field plo obained from Hessian analysis and eigenvecor decomposiion. Eigenvecors wih he lowes magniude eigenvalue correspond o he direcion of smalles curvaure and hus poin in he direcion of vessel flow. Vecors were used o creae accurae predicion seps for paricle filering. Some vessel segmens change direcion abruply and canno be capured by he ranslaional moion model, especially a vessel bifurcaion poins. To rack his movemen we employed a vecor field model for moion predicion. A vecor field was produced by eigenvecor decomposiion of he Hessian marix. The eigenvecor associaed wih he lowes magniude eigenvalue indicaes he direcion of leas curvaure, corresponding o he direcion of vessel flow. The algorihm swiches from ranslaional moion model o vecor field moion model in he presence of a srong vecor signal. Such uilizaion of Hessian eigenvecors for moion predicion is novel o he medical image analysis field. Fig. 1 shows he vecor field on a shor segmen of he arery.

4 2.3 Likelihood Models Combined wih Muliple Cues In previous paricle filering vessel segmenaion work on CT [2, 3], inensiy is used as he dominan informaion. Upon inspecion of CT images for vessel segmenaion, radiologiss no only check inensiy informaion, bu also uilize anaomical informaion such as organ locaion, regional vesselness, and fa and muscle issue. Thus human vision combines muliple cues during vessel racking. Inspired by radiologiss, we propose a new likelihood model for vessel segmenaion by fusing muliple cues. Fig. 2 shows four racking domains used o produce cues on an axial slice CT image. Fig. 2. Four paricle filering domains used o generae vessel racking cues. A Vesselness response from Hessian analysis, wih a mask generaed by hresholding and pos-processing. B A minimum spanning ree algorihm was applied o inensiy and vesselness feaures o connec hin, low conras segmens of he arery. C A MIP mask was used o amplify vessel signal in hin, low conras segmens. D Global, unhresholded vesselness response o Hessian analysis. Inensiy Cue. As wih radiional vessel segmenaion mehods, inensiy is he mos imporan informaion for vessel racking on CT. For a paricle x a ime poin, i 1,..., N, where N is he oal number of paricles, we exraced a spherical search region and summed he inensiies of all voxels wihin he sphere as our inensiy cue for racking. The single voxel paricle inensiy was used as an addiional cue. Vesselness Cue. Because he majoriy of vessel segmens exhibi ube srucure, a vesselness cue is essenial o differeniae rue vessels from noisy, brigh, blob-like areas. We employed Li s muliscale vessel enhancemen filering [9] o provide his vesselness cue. Spaial scale sandard deviaions from 0.5 voxels o 2 voxels wih 0.25 voxel incremenal seps were used for muli-scale analysis. Three vesselness cues were uilized: single voxel paricle vesselness, vesselness sum wihin he spherical search region, and a binary vessel mask produced by hresholding vesselness response and applying ray casing and conneced componen analysis pos-processing. i

5 Organ Cue by Ray Casing. Nearby organs are a major source of false posiives, including he bowel, liver, and kidneys. Tracking pahs can be araced o organ boundaries having line or curve characer. To avoid hese paricle racks, a ray casing echnique was applied a each paricle. Rays are cased in 26 spaial direcions, and hal a eiher low inensiy or a maximum disance, boh deermined heurisically. Maximum Inensiy Projecion Cue. Maximum inensiy projecion (MIP provides a mehod o amplify inensiy signal in a seleced direcion. This is an informaive cue for noisy daa and hin, peripheral vessel segmens wih poor conras enhancemen. MIP was applied in pre-processing o he volumeric daa based on several pre-seleced direcions. We hen projec he 2D deecions back o 3D space o creae a binary mask. Missing Vessel Cue. Vessel enhancemen is generally no uniform on abdominal CT angiograms. Due o non-uniform blood flow or vessel consricion, some segmens may have paricularly low enhancemen. Thus, some segmens are no well disinguished by inensiy and vesselness cues alone, which necessiaes global conex informaion o rack hese difficul areas. We employed a minimum spanning ree o connec segmens wih very high vesselness response, and generaed a missing vessel cue mask prior o racking. The use of a minimum spanning ree as a racking cue is also novel o he medical image analysis field. We used a binary variable B for each voxel o indicae wheher he voxel lies on a pah connecing wo curves in he 3D CT image wih high vesselness response. Fusing of Muliple Cues. The eigh racking cues are fused as a produc of likelihoods: L y x L y x L y x L y x L y x L y x, (4 I ( V ( O( M ( B( s where he five likelihood funcions correspond o inensiy, vesselness, organ, MIP and bridge cues. In he fusion process, each cue is reaed independenly and uniformly regarding is weigh. Cues were aken o be independen, which is a common assumpion used in compuer vision for a Naïve Bayes mehodology [7, 8]. For each cue, a kernel densiy esimaor (KDE was leveraged o learn he arge disribuion based on a 10 paien raining se. During racking, cue observaions for each paricle were weighed probabilisically using he respecive KDE s o updae he vessel locaion. Fig. 3 shows he kernel densiy esimaion for each cue. The inensiy and vesselness cues above conain 2 and 3 independen sub-cues, respecively. 2.4 Auomaic Bifurcaion Deecion The marginal arery is composed of several large loops ha frequenly bifurcae ino anasomoses, presening a challenge o a local racking mehod. To solve his, we implemened a robus auomaic bifurcaion deecion sysem using a spherical shell search region. A each sep, he shell was checked for high inensiy voxels in he enhanced vessel range. A single vessel enering and leaving he shell produced wo high inensiy paches, bu a a bifurcaion he shell idenified hree paches indicaing hree pahs leaving he sphere. In his case, muliple parallel pahs were iniialized o complee he vessel ree.

6 Fig. 3. Kernel densiy esimaion from raining se for each cue. A Inensiy sum in spherical search region. B Single voxel inensiy. C Hessian vesselness sum in spherical search region. D Single voxel Hessian vesselness response. E Number of posiive voxels from binary hresholded vessel mask wih pos-processing. F Number of posiive voxels from MIP mask. G Single voxel ray casing score o idenify organ. H Number of posiive voxels from binary minimum spanning ree mask. 3 Daase and Experimenal Resuls Our daase conained 17 paiens wih high-resoluion conras-enhanced CT angiograms, 10 for KDE raining and 7 for validaion. Daa acquisiion and analysis were conduced under an Insiuional Review Board (IRB approved proocol. CT scans were acquired following oral adminisraion of 3 boles Volumen and inravenous adminisraion of 130 ml Isovue-300 wih 5 ml/sec injecion rae and 30 second delay. The scanning parameers were secion collimaion 1.0-mm, reconsrucion inerval 0.5 mm, 512x512 marix and in-plane pixel dimensions of 0.82 mm o 0.94 mm depending on he paricipan s body size. A major inclusion crierion for he esing se was high levels of visceral fa conen for good spaial separaion of he arery. The proposed mehod was evaluaed on he wo larges and ypically bes enhanced segmens of he marginal arery, which run parallel o he ransverse and descending colon. A manual seed poin was designaed a he bifurcaion poin beween hese wo segmens, and he algorihm was allowed o rack in he hree iniial vessel direcions. The racking algorihm required a runime of approximaely one hour per paien. Fig. 4 shows he segmenaion resul on hese branches for one paien. Fig. 5 shows he recall and precision raes for each esing paien. Compared o he radiional baseline Hessian analysis mehod for vessel segmenaion [9], our SMC muliple cue fusion algorihm achieved an average recall of 88.5% while improving he average segmenaion precision o 32.2%. Baseline average recall and precision raes were 91.4% and 7.9%, respecively. Recall was defined as he fracion of ground ruh voxels deeced by he algorihm, and precision was defined as he fracion of deeced voxels ha

7 were rue deecions. Paired suden -es comparison beween our algorihm and he baseline mehod showed a p value of for recall, and a precision p value of , indicaing significance in he precision improvemen. Fig. 4. 3D segmenaion of he marginal arery wih pelvis and spine for reference. The arery was racked following he ransverse and descending colon. The porion shown communicaes beween he SMA and IMA. Ground ruh is labeled in green, and SMC deecion is labeled in red. Deecion shown has recall of 94.9% and precision of 58.3%. Fig. 5. Experimenal resuls comparison beween he SMC muliple cue fusion mehod and baseline Hessian vessel analysis. The SMC cue fusion average recall for he 7 esing paiens was 88.5%, compared o he baseline average recall of 91.4%. Average precision for SMC cue fusion was 32.2% compared o he baseline average precision of 7.9%.

8 4 Conclusion and Discussion We have proposed a novel Bayesian racking framework using SMC and muliple cue fusion o auomaically rack and segmen he marginal arery of he colon on conras-enhanced CT angiograms. Such an algorihm was novel o medical image analysis, and advanageous compared o oher vessel racking mehods by incorporaing more informaion for racking robusness. Uilizing his fusion of local and global informaion, we achieved high recall and a significan increase of precision by a facor of 4 compared o he baseline mehod. I is imporan o noe ha he vas majoriy of false posiive deecion occurred on oher segmens of he marginal arery and abdominal vasculaure due o frequen anasomosis and our robus bifurcaion deecor. Thus, an exended sudy evaluaing he algorihm on he complee marginal arery or abdominal vessel ree would likely furher increase precision resuls. References 1. Lesage, D., Angelini, E.D., Bloch, I., Funka-Lea, G.: A review of 3D vessel lumen segmenaion echniques: Models, feaures and exracion schemes. Medical Image Analysis 13, ( Florin, C., Paragios, N., Williams, J.: Paricle filers, a quasi-mone carlo soluion for segmenaion of coronaries. In: Medical Image Compuing and Compuer-Assised Inervenion, pp ( Schaap, M., Manniesing, R., Smal, I., Walsum, T.v., Lug, A.v.d., Niessen, W.: Bayesian racking of ubular srucures and is applicaion o caroid areries in CTA. In: Medical Image Compuing and Compuer-Assised Inervenion, pp ( Lacose, C., Fine, G., Magnin, I.E.: Coronary ree exracion from X-ray angiograms using marked poin processes. In: IEEE Inernaional Symposium on Biomedical Imaging: Nano o Macro ( Friman, O., Hindennach, M., Kuhnel, C., Peigen, H.O.: Muliple hypohesis emplae racking of small 3D vessel srucures. Medical Image Analysis 14, ( Wu, Y., Huang, T.S.: Robus visual racking by inegraing muliple cues based on co-inference learning. Inernaional Journal of Compuer Vision 58, ( Brasne, P., Mihaylova, L., Bull, D., Canagarajah, N.: SequenialMone CarloTracking by Fusing Muliple Cues in Video Sequences. Image and Vision Compuing 25, ( Moreno-Noguer, F., Sanfeliu, A., Samaras, D.: Dependen muliple cue inegraion for robus racking. Ieee Transacions on Paern Analysis and Machine Inelligence 30, ( Li, Q., Sone, S., Doi, K.: Selecive enhancemen filers for nodules, vessels, and airway walls in wo- and hree-dimensional CT scans. Medical Physics 30, (2003