A Novel Method for Removing Image Staircase Artifacts

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1 Vol.139 (SIP 016, pp A Novel Method for Removing Image Stairae Artifat Zhong Chen 1,, Zhiwei Hou 1, Yuegang Xing, Xiaobing Chen 1 1 Jiangu Key Laboratory of Advaned Manufaturing Tehnology, Huaiyin Intitute of Tehnology, Huaian 3003, China Department of Orthodonti Surgery, Huaiyin Hopital of Huaian City, Huaian 3300, China. zhonghenn19@163.om Abtrat. Due to limited reolution fator, triangle mehe extrated from medial CT image often ontain tairae artifat. In order to remove tairae artifat during meh generation and obtain a mooth model from medial image, a novel removing tairae artifat method i preented. Firtly, we extrat ontour by uing image egmentation and onvert a tak of ontour into point loud. Etimating the normal of point loud and diard outlier by a weighted ovariane analyi, and then remove noie by bilateral filtering. Denoiing point are fitted by the quadri error funtion, and then ontrut triangle mehe by adaptive pherial over. The reulting triangle mehe are evaluated regarding urfae moothne, volume preervation, geometri auray. The experimental reult how that the propoed approah an reate a mooth, high- quality urfae model from medial image. Keyword: Medial CT; Point loud; Triangle mehe; Stairae artifat 1 Introdution In medial imaging uh a CT an, produing aniotropi data in whih the lie reolution in the z diretion i ommonly lower than the imaging reolution in the x-y plane i poible. In other word, in-plane reolution i only aurate to the pixel, wherea lie an be apart by more than one pixel. A ommon problem i the appearane of tairae artifat when triangle mehe from medial image are generated. Uually, medial urfae mehe are generated through the marhing ube (MC algorithm [1] (ee Figure 1, in whih aniotropi voxel ize i mm. Stairae artifat affet 3D printing and finite element (FE imulation. In uh appliation, mooth, high-quality triangle mehe are eential. ISSN: ASTL Copyright 016 SERSC

2 Vol.139 (SIP 016 Stairae artifat an be removed after meh generation (by meh moothing or during meh generation (by urfae reontrution. Thee two method are deribed a follow. (1 By meh moothing: a variety of meh moothing method have been propoed to improve moothne. Smoothing method only allow to redue tairae artifat after meh generation (e.g. Laplaian moothing [], Taubin moothing [3] and Mean Curvature Flow [4]. Thee method an remove tairae artifat, but often aue lo of feature and volume hrinkage. Reently, feature-preerving moothing [5-8] wa propoed, thee method an remove the noie while retaining original feature. However, tairae artifat are retained a feature when uing thee feature-preerving moothing method. Thu, Moenh et al. [9] propoed ontext-aware meh moothing, whih an be adaptively moothed the artifat area and preerve feature in non-artifat area, but thi method wa generated many low-quality mehe. Contrained Elati Surfae Net (CESN moothing method [10] redued tairae artifat partly but retaining ome feature, and ome obviou tairae may till remain on the urfae. ( By urfae reontrution: Impliit urfae reontrution i an ative reearh field in Digital Geometry Proeing (DGP. The following method an generate urfae mehe from point loud diretly. Hoppe et al. [11] propoed an impliit reontrution approah, whih produed urfae mehe from point loud by uing a igned ditane funtion. Levin [1] and Alexa et al. [13] approximated point loud with polynomial by moving leat quare (MLS. The Multi-level partition of unity impliit wa preented by Ohtake et al. [14]. Bade et al.[15] reontruted vaular urfae model by uing the MPU method baed on point loud from binary egmentation mak. Zhao et al. [16] ontruted urfae model from point loud by level et method [17]. Thee method an generate mooth urfae, but the tairae artifat are not entirely removed. Ohtake et al. [18] propoed an integrating approah to mehing point loud. Thi method i baed on the Garland-Hekbert [19] loal quadri error minimization trategy. High-quality mehe an be reated from point diretly by mean of adaptive pherial over. However, noie and outlier produe a failed urfae reontrution in Ref. [18]. (b (a ( Copyright 016 SERSC 57

3 Vol.139 (SIP 016 Fig. 1. (a Medial CT image lie of the firt ervial vertebrae (C1 for hort. (bsurfae rendering by the marhing ube algorithm. (C Mean urvature viualization. In order to remove tairae artifat during meh generation, we have introdued the adaptive pherial over method into biomedial engineering and modified thi method in our work. Our method improve the anti-noie ability and loalization auray baed on the impliit approah. 1.1 Approah Overview An overview of our preented approah to triangle meh reontrution i illutrated in Figure. The input data derive from medial CT image lie. The proe begin with a tak of ontour proeed by image egmentation (ee Setion.1. We onvert a tak of ontour into a et of point loud in a three-dimenional pae (ee Setion.. We then ontrut a data truture of the CT point loud and query the neighbor by mean of the kd-tree. The k-nearet neighbor of medial CT point loud are ontruted and the normal are etimated by mean of a weighted ovariane analyi (ee Setion.3, and then redue the noie from point loud through bilateral filtering (ee Setion.4. Point loud are fitted by uing the quadri error funtion, and then ontrut triangle mehe by the adaptive pherial over (ee Setion.5. Fig.. Overview of the preented meh generation approah. A tak of loed ontour by image egmentation. Point loud extrat from a et of ontour. Dividing point loud by kd-tree, etimate the normal and redue the noie. Contruting triangle mehe by the modified adaptive pherial over. 58 Copyright 016 SERSC

4 Vol.139 (SIP 016 Surfae Reontrution.1 Contour Extration of CT Image Medial image ued in our tudy were egmented by an ative ontour without edge algorithm [0]. The algorithm ha ertain advantage: (1 it i robut againt noie; ( a loed ontour urve by image egmentation under any ondition an be obtained. The main obetive of the algorithm i to evolve an interfae, whih divide the image into two homogeneou region. Thi i the olution to minimize the energy funtional F( 1,, C, defined by: 1 1 inide ( 1 F (,, C Length( C Area( inidec u ( x, y dxdy (, outide ( u x y dxdy (1 u ( x, y where C orrepond to the loed urve, orrepond to the image, and the average intenity of inide and outide of C, repetively. Additionally,,,, are fixed parameter. In thi paper, we et the parameter a: 1 1, 7 (bone and , 0, V t 0.01 ( i the time tep, 10 iteration u ( x, y Vt 1 are. Point Cloud Extration To ontrut bone mehe by mean of impliit urfae reontrution, obtaining point loud of bone image i firtly required. We extrat bone ontour from CT image equene and et a ingle pixel of the preie ontour in a D plane a x, y oordinate, baed on the loation in whih the profile alulated the Z oordinate. Finally, we obtain 3D point oordinate and the ontour tranlate into point loud. Point loud are only available for 3D oordinate information. No topologial information exit and the point loud of every point of differential geometry information (i.e., normal vetor, urvature an only be alulated through the neighbor of a point. Therefore, etablihing topologial relation in point i neeary and we an eaily query the k-nearet neighbor for eah point. At preent, three k-nearet neighbor querie are ommonly ued: otree, grid, and kd-tree method [1-]. The firt two method are laified by a bounding box, and the third approah i to earh for the nearet two point. In thi tudy, we adopted the kd-tree method in order to ontrut the data truture of the CT point loud and query the neighbor..3 Normal Etimation Point loud frequently ontain noie derived from anning and tranformation proee. CT point loud that ommonly exhibit artifat of irregular ampling (e.g., Copyright 016 SERSC 59

5 Vol.139 (SIP 016 noie and outlier aue diffiultie in etimating differential urfae attribution. The laial normal etimation i prinipal omponent analyi (PCA [11], whih an be unreliable beaue of outlier and large-ale noie. We deribe a novel normal etimation algorithm, whih i not affeted by unorganized outlier. CT point loud 3 P { p } n ir i 1 with n unorganized point, where the k nearet neighbor of an arbitrary point i denoted by { p } k P 1, k 10, and p i the entroid of the neighbor { p } k P 1. We ue a weighted method [3] to etimate the mot effetive upport for a plane and to eliminate the outlier. We ompute a weighted ovariane matrix for point i given by where g g d exp( / k T ( ( 1 C p p p p g ( p 1 k p k 1 i the weight for point p, If point p i an iolated point, and =1. If point p i an inlier point, then i the mean ditane from the point to all it neighbor p, and d i the ditane from point to it neighbor p. Conider the eigenvetor problem C v v (3 where C i a ymmetri and poitive emidefinite, all eigenvalue are real-valued and the eigenvetor v form an orthogonal frame. The eigenvetor that orrepond to the mallet eigenvalue i onidered a the normal vetor n i of the point..4 Noie Removal Point loud extrated from CT image often ontain undeirable noie, whih an be redued by mean of variou filtering tehnique, uh a low-pa filtering and bilateral filtering. Fleihman et al. [6] have propoed a bilateral filtering method, whih wa modified the bilateral filtering from image denoiing to meh denoiing and ahieve atifatory reult. The bilateral filtering i alo uitable for point loud denoiing. Furthermore, bilateral filtering an not diturb the original hape and truture. We alulate a new poition of a point by mean of equation (4 and (5. d= k 1 W( p p W( p p, n p p, n i i i i i k 1 W( p p W( p p, n i i i W( x x = exp( / (4 60 Copyright 016 SERSC

6 Vol.139 (SIP 016 where d i a igned ditane, = exp( / W( x = exp( x / W( x x i a patial weighting funtion, = exp( / W( x x i a feature-preerving weighting funtion, ditane from a point operator of both ditane vetor to a neighbor p p i p p the, p p, n i a vetor produt and vetor i i tandard deviation, and k i nearet neighbor of.we et Thu we obtain the following point update equation: (5 where point. p ' i p p dn ' i i i i a new point after bilateral filtering, and Finally, we get a new point loud ' P p R ' 3 { } l i i 1 n i (l n of the point 3 n i and i,. i the i a normal vetor at a after bilateral filtering. 4 Conluion In thi tudy, we preented a novel method that remove tairae artifat and reate mooth urfae mehe from medial image. Thi i a multi-tage proe. Firt, we extrat a tak of ontour by mean of image egmentation. The ontour tranlate into point loud. We then ue a weighted ovariane analyi to etimate normal at eah point. A bilateral filtering i applied to remove noie from point loud. Triangle mehe are then ontruted uing an improved adaptive pherial over algorithm. Experimental reult how that the propoed method an effiiently remove tairae artifat and generate high-quality triangle mehe with reaonable auray. Aknowledgment. Thi work i upported by the Natural Siene Foundation of Jiangu Higher Eduation Intitution (No.14KJB46000 and (No.15KJA460003, Huaian Sientifi and Tehnologial Key Proet (No.HAG01503, Jiangu Provine Indutry-Univerity-Reearh Cooperation Propetive Study Proet (No.BY , and Jiangu Key Laboratory of Advaned Manufaturing Tehnology (No.HGDML-104. Referene 1. Lorenen, WE, Cline, HE.: Marhing ube: A high reolution 3D urfae ontrution algorithm. In: ACM SIGGRAPH omputer graphi. ACM; 1987: Nealen A, Igarahi T, Sorkine O, Alexa M.: Laplaian meh optimization. In: Proeeding of the 4th international onferene on Computer graphi and interative tehnique in Autralaia and Southeat Aia. ACM; 006: Copyright 016 SERSC 61

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