Nuclear Instruments and Methods in Physics Research A 652 (2011) 602–605

Contents lists available at ScienceDirect

Nuclear Instruments and Methods inPhysics Research A

0168-90

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/nima

Metal artifact reduction algorithm based on model images andspatial information

Jay Wu a, Cheng-Ting Shih b, Shu-Jun Chang c, Tzung-Chi Huang d, Jing-Yi Sun a, Tung-Hsin Wu e,n

a Institute of Radiological Science, Central Taiwan University of Science and Technology, Taichung, Taiwan, ROCb Department of Biomedical Engineering and Environmental Sciences, National Tsing-Hua University, Hsinchu, Taiwan, ROCc Health Physics Division, Institute of Nuclear Energy Research, Taoyuan, Taiwan, ROCd Department of Biomedical Imaging and Radiological Science, China Medical University, Taichung, Taiwan, ROCe Department of Biomedical Imaging and Radiological Sciences, National Yang-Ming University, No.155, Sec. 2, Linong Street, Taipei 112, Taiwan, ROC

a r t i c l e i n f o

Available online 25 January 2011

Keywords:

Computed tomography

Metal artifact

k-means clustering

02/$ - see front matter & 2011 Elsevier B.V. A

016/j.nima.2011.01.041

esponding author. Tel.: +886 2 28267061.

ail address: tung@ym.edu.tw (T.-H. Wu).

a b s t r a c t

Computed tomography (CT) has become one of the most favorable choices for diagnosis of trauma.

However, high-density metal implants can induce metal artifacts in CT images, compromising image

quality. In this study, we proposed a model-based metal artifact reduction (MAR) algorithm. First, we

built a model image using the k-means clustering technique with spatial information and calculated the

difference between the original image and the model image. Then, the projection data of these two

images were combined using an exponential weighting function. At last, the corrected image was

reconstructed using the filter back-projection algorithm. Two metal-artifact contaminated images were

studied. For the cylindrical water phantom image, the metal artifact was effectively removed. The mean

CT number of water was improved from �28.95797.97 to �4.7674.28. For the clinical pelvic

CT image, the dark band and the metal line were removed, and the continuity and uniformity of the soft

tissue were recovered as well. These results indicate that the proposed MAR algorithm is useful for

reducing metal artifact and could improve the diagnostic value of metal-artifact contaminated

CT images.

& 2011 Elsevier B.V. All rights reserved.

1. Introduction

Computed tomography (CT) provides high resolution cross-sectional images and has become a daily clinical routine indiagnostic radiology. However, metal objects with high attenua-tion coefficients in the human body greatly absorb low energyX-ray, causing severe beam hardening and loss of projection datain sinogram. Streak artifacts eventually appear in the recon-structed images, reducing image quality and uniformity [1].

Several metal artifact reduction (MAR) algorithms have beenproposed in the last decade. They can be concluded into threecategories: interpolation-based sinogram corrections [2], iterativeimage reconstructions [3,4], and adaptive filtering methods [5].For the first category, the projection data of the metal objects arereplaced by linear [6] or polynomial [1] interpolation of surround-ing data in the sinogram. The major drawback is the incompleteartifact correction or even producing secondary artifacts [7]. Forthe second category, the iterative reconstruction methods usuallyprovide good correction results when the metal objects do not

ll rights reserved.

stop all X-rays [8]. However, the relatively high computationalcomplexity of these approaches makes it impractical for clinicalpractice. As for the third category, adaptive filtering can smoothstreak artifacts and reduce image noise, but the adjustment offilter parameters must consider the strength of the artifact, whichvaries in each case.

In this study, we proposed a MAR algorithm based on themodel image built by the k-means clustering with spatial infor-mation. Forward projections of the model image and the originalimage were summed together by a weighting function. This MARalgorithm has the advantages of fast computation and simpleimplementation, and no original sinogram is required.

2. Materials and methods

2.1. Model-based image

k-means clustering [9] was used to produce an initial modelimage by classifying all pixels into several clusters. After inputtingthe contaminated image and choosing the cluster number, theinitial center of the cluster was randomly assigned. The pixelclassification was based on the Euclidean distance between the

J. Wu et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 602–605 603

pixel value and each cluster center. The sum of square error (SSE)between the cluster center and its membership was calculatedby:

SSE¼Xk

j ¼ 0

Xn

xACj

Jxi�viJ2, i¼ 1,. . .,n; j¼ 1,. . .,k ð1Þ

vi ¼

Pni ¼ 1 mðCj9xiÞxiPn

i ¼ 1 mðCj9xiÞ, j¼ 1,. . .,k ð2Þ

where xi is the ith pixel value that belongs to the cluster j and vj isthe jth cluster center. m(x) denotes the membership function, Cj isthe jth cluster, k is the cluster number, and n is the total pixelnumber. The iteration was terminated when the change in SSE fellbelow 0.02. Six clusters were defined, including air, fat, soft tissue,mineral bone, cortical bone, and metal objects. After imageclustering, the pixel value was transformed from the original CTnumber to the value of the cluster center, to which the pixelbelonged.

2.2. Spatial information

The region severely influenced by streak lines may causewrong classification during k-means clustering. Therefore, thespatial information of the original image was incorporated [10].The spatial information was calculated by

Ci ¼ argfmaxð9P \ Cj9Þg, j¼ 1,. . .,k ð3Þ

where P denotes a set of pixels covered by a 9�9 mask centeredat the pixel i. 9.9 means the number of elements in the set. Thisprocedure reassigns the pixel i to the cluster Cj with the mostmembers within the mask. By the method, a noise-free andartifact-free model image can be constructed.

Original image(Io)

Model image(Im)

k-means clustering

Spatialinformation

Difference image(Id)

Radon transform

Po

Pd

PmPd*

Weighting function

Correctedsinogram

FBP

Corrected image(Ic)

Fig. 1. The flowchart of the proposed MAR algorithm. The k-means clustering with

spatial information is applied to the original image (Io) to produce the artifact-free

model image (Im). The difference image (Id), model image, and original image are

then forward projected to the sinogram space. The corrected sinogram (Pc) is

summed by the original sinogram (Po) and the model sinogram (Pm) with an

exponential weighting function. Finally, the corrected image (Ic) is reconstructed

from the Pc by the filtered back-projection algorithm.

2.3. Weighting of sinogram

After creating the model image, the difference image (Id) wasobtained by subtracting the model image (Im) from the original

Fig. 2. (a) Original image of the cylindrical water phantom with a 1 cm-radius

lead rod inserted at the center, (b) the model image built by the k-means

clustering with spatial information, and (c) the final corrected image.

J. Wu et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 602–605604

image (Io). The sinograms of these three images were forwardprojected by the Radon transform. Then, the corrected sinogram(Pc) was obtained by the weighted combination of the originalsinogram (Po) and the model sinogram (Pm):

Pcði,jÞ ¼wði,jÞ � Poði,jÞþ½1�wði,jÞ� � Pmði,jÞ ð4Þ

where w(i,j) denotes the pixel-based weighting factor thatdepends on the local value of the difference sinogram (Pd) forwardprojected from the difference image. The weighting factor isdefined as:

wði,jÞ ¼ e�mP�dði,jÞ ð5Þ

where P�d is the normalized version of Pd, and m is the weightingparameter that controls the shape of the exponential function andthe preservation of details in structure. Subsequently, the cor-rected image (Ic) was reconstructed from the Pc by the filteredback-projection algorithm. Fig. 1 shows the flowchart of theproposed MAR method.

3. Results and discussion

A water phantom image and a pelvic CT image were used toevaluate the performance of the MAR algorithm. Fig. 2(a) showsthe original image of the cylindrical water phantom with a 1 cm-radius lead rod inserted at the center. The water compartmentwas covered with several bright and dark streaks, causing non-uniformity in the pixel values. A 100-pixel region of interest (ROI)was drawn at the dark band above the lead rod. The mean CTnumber was �28.95797.97. Fig. 2(b) shows the model imagebuilt by the k-means clustering with spatial information. Eachregion of the phantom was successfully classified. Fig. 2(c) showsthe corrected image using a weighting parameter m¼40. Thebright and dark streaks were removed and the image uniformitywas improved. The ROI drawn at the same location asin Fig. 2(a) had a mean CT number of �4.7674.28, which wasclose to the CT number of water. Fig. 3 draws the profiles of theoriginal, model, and corrected images of the cylindrical phantom

0 100 200 300 400 500

Position (Pixels)

-300

-200

-100

0

100

200

300

400

500

CT

num

ber

Corrected imageOriginal imageModel image

Fig. 3. Profiles of the original, model, and corrected images of the cylindrical

phantom. The CT values near the center of the phantom had large variance due to

metal artifacts caused by the lead rod.

at the location shown in Fig. 2(b). The large variance of the CTvalues near the lead rod was suppressed after correction.

Fig. 4(a) shows the original CT image of the pelvis with twogold seeds implanted for brachytherapy. Several bright and dark

Fig. 4. (a) Original CT image of the pelvis with two gold seeds, (b) the model

image built by the k-means clustering with spatial information, and (c) the metal-

artifact corrected image with improved uniformity and preserved fine structure.

0 100 200 300 400 500

Position (Pixels)

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

700

CT

num

ber

Corrected imageOriginal imageModel image

Fig. 5. Profiles of the original, model, and corrected images. The CT numbers of the

soft tissue near the gold seeds had large variance ranging from �350 to 600.

Table 1Mean CT values and standard deviations of the four ROIs drawn at different

locations.

Pelvicimage

Mean7std

ROI 1(dark band)

ROI 2 (proximalregion)

ROI 3(bright streak)

ROI 4(distal region)

Originalimage

�61.997215.50 34.64729.62 207.227124.12 �22.69736.75

Correctedimage

51.48720.63 38.9479.28 61.18711.85 23.9974.68

J. Wu et al. / Nuclear Instruments and Methods in Physics Research A 652 (2011) 602–605 605

streaks covered the region of bladder and the surrounding tissue,causing non-uniformity of the soft tissue. Under the dark bandinduced by the two metals, the CT number reached �500 thatwould be classified as air when using the original k-meansmethod. By incorporating the spatial information shownin Fig. 4(b), the streaks and dark bands were classifiedcorrectly. Fig. 4(c) shows the corrected image of the pelvis withm¼7, in that the metal artifacts were removed, the uniformity ofthe bladder and soft-tissue were improved, and the details of thestructure were preserved.

Fig. 5 displays the profiles of the original, model, andcorrected images at the location shown in Fig. 4(b). In the profileof the original image, the maximum and minimum CT numbersof the soft tissue were about 600 and �350 that had recovered tothe CT number of soft-tissue after correction. Table 1 lists thecalculated mean CT values and standard deviations at variouslocations shown in Fig. 4(b). The mean CT values of ROI 1 (darkband) and ROI 3 (bright streak) were �61.99 and 207.22, whichwere fairly discrepant from the CT number of the surroundingsoft tissue. The ROI 2 and ROI 4, representing the proximal anddistal regions of the soft tissue, were also slightly influenced bythe metal artifacts, showing large standard deviations. After

correction, the mean CT numbers of all ROIs approached the CTnumber of soft-tissue, and the standard deviations fellbelow 20%.

4. Conclusion

This study proposed a MAR algorithm based on the modelimage built by k-means clustering with spatial information.Results show that this algorithm is useful for reducing metalartifacts in CT images while preserving the detail structures. Theproposed MAR algorithm has the advantages of fast computationand simple implementation, and no original sinogram is required.Therefore, it could be applied to clinical practice to improve thediagnostic value of the metal-artifact contaminated CT images.

Acknowledgement

This study was financially supported by the National ScienceCouncil of Taiwan (NSC99-2314-B-010 -043-MY3) and (NSC 96-2320-B-166-001).

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