c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

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Metal artifact reduction in dental CT images using polarmathematical morphology

Valery Naranjo ∗, Roberto Lloréns, Mariano Alcaniz, Fernando López-MirInstituto Interuniversitario de Investigación en Bioingeniería y Tecnología Orientada al Ser Humano, Universidad Politécnica de Valencia,Camino de Vera s/n, 46022 Valencia, Spain

a r t i c l e i n f o

Article history:

Received 31 July 2009

Received in revised form

27 October 2010

Accepted 18 November 2010

Keywords:

Dental CT

Artifact reduction

a b s t r a c t

Most dental implant planning systems use a 3D representation of the CT scan of the patient

under study as it provides a more intuitive view of the human jaw. The presence of metallic

objects in human jaws, such as amalgam or gold fillings, provokes several artifacts like

streaking and beam hardening which makes the reconstruction process difficult. In order

to reduce these artifacts, several methods have been proposed using the raw data, directly

obtained from the tomographs, in different ways. However, in DICOM-based applications

this information is not available, and thus the need of a new method that handles this

task in the DICOM domain. The presented method performs a morphological filtering in

the polar domain yielding output images less affected by artifacts (even in cases of multiple

Polar morphology metallic objects) without causing significant smoothing of the anatomic structures, which

allows a great improvement in the 3D reconstruction. The algorithm has been automated

er im

and compared to oth

1. Introduction

The 3D representation of CT scans is widely used in medicalapplications such as virtual endoscopy, plastic reconstructivesurgery, dental implant planning systems and more. This rep-resentation is built thresholding the axial CT slices whichconstitute the volume of the CT scan.

Metallic objects present in CT scans cause strong artifactslike beam hardening and streaking, strongly noticeable in axialimages after being reconstructed by means of filtered backprojection algorithm (FBP), as shown in Fig. 1. Metal artifactscomplicate to a large extent the 3D reconstruction (Fig. 15).

FBP is the most extended method to reconstruct imagesfrom projections. The algorithm assumes that the tomography

data is the Radon transform of the attenuation coefficients ofthe scanned objects. This assumption is plausible if the den-sity of the objects is similar. But when objects with different

∗ Corresponding author. Tel.: +34 963877518x6718; fax: +34 96 387 95 10E-mail address: vnaranjo@labhuman.i3bh.es (V. Naranjo).

0169-2607/$ – see front matter © 2010 Elsevier Ireland Ltd. All rights resdoi:10.1016/j.cmpb.2010.11.009

age denoising methods with successful results.

© 2010 Elsevier Ireland Ltd. All rights reserved.

densities, such as cavities (∼200 HU), bones (∼1200–1800 HU),teeth (∼2000 HU) and dental fillings (temporary fillings:∼6000–8500 HU, composite fillings: ∼4500–17000 HU and amal-gam and gold >30700 HU), are present at the same time, thereconstructed images have perceptible artifacts as streaking(high level rays emerging from metallic objects), beam harden-ing (shadows cast over the areas surrounding the object) andsome other effects. Fig. 1 shows a CT image of a jaw clearlyaffected by the previously described artifacts. Consequently,several research studies have tried to reduce these artifacts,and have approached the problem in different ways.

Most metal artifact reduction (MAR) research focuses onthe development of methods which use raw CT scan data. Allthese studies can be classified into two categories: methods

.

which use the filtered back projection algorithm to reconstructthe image and others which try to avoid this technique so asnot to obtain artifacted images caused by its drawbacks. Wewill now consider some of these studies.

erved.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n

F

tMpjfistt[uriuitaioAwlsa

eaertcmetbi

d

ig. 1 – Example of MAR artifacts in a CT image from a jaw.

In the first category, Rohlfing et al. [1] compare some ofhese techniques and discuss the problematic issues aroundAR. Watzke and Kallender [2] combine two MAR methods

reviously proposed: linear interpolation (LI) of the repro-ection of metallic objects and multi-dimensional adaptiveltering (MAF) of the raw data. The LI algorithm [3] con-ists of reconstructing a preliminary image, reprojecting thehreshold-segmented metallic objects, linear interpolating inhe raw data domain and reconstructing. The MAF algorithm4] consists of filtering the significant raw data (sinogram val-es above a threshold selected by the user). This algorithmeduces artifact noise but has no effect on beam harden-ng. Therefore, a distance dependent merging technique issed for these algorithms. Yu et al. [5] propose a method

nspired by Kalender’s work, which includes a mean-shiftechnique to improve accuracy in the segmentation processnd an iterative feedback-based interpolation method. Shiy-ng et al. [6] proposed a wavelet method for MAR. It consistsf estimating the metallic set by threshold-segmentation.fter this, the scan data can be defined by its scaling andavelet coefficients and a wavelet multiresolution interpo-

ation can be applied to design an appropriate weightingcheme in order to recover the information affected by thertifact.

In the second category, avoiding the FBP algorithm, Wangt al. [7], consider the CT scan as a deblurring problemnd try to solve it by using two iterative approaches: thexpectation maximization formula (EM) and the algebraiceconstruction technique (ART). The method minimizes itera-ively the discrepancy between the measured raw data and theomputationally synthesized data to obtain iterative improve-ents in the retroprojected image. In a similar way, Murphy

t al. [8] use an alternating minimization (AM) algorithmo minimize the I-divergence (to maximize the similarity)

etween the data and its estimation in order to form the

mage.All the results of the aforementioned methods are either

erived from the raw data obtained from the tomograph, or

b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74 65

use it in some way to replace the FBP data. But in mostapplications, as ours (an intelligent system for designing,simulating and flexible manufacturing of implant-supporteddental prostheses), the raw data is not available and expertsmust infer conclusions from the artifacted FBP images. A newpoint of view is needed to improve the image quality in thiscontext.

With this consideration in mind, Sohmura et al. [9] replacethe artifacted teeth with the CT representation of a dentalcast previously registered. It implies having a patient’s accu-rate cast, CT scan with the markers used for the registrationand high accuracy at the registration process. As well withthe aim of 3D reconstruction, Tognola et al. [10] segment themandibular surface after enhancing the image. This processconsists of a histogram equalization followed by a threshold-ing. Naranjo et al. [11] transform the image into the polardomain before the processing step. This way, the radial patternof the artifact is reshaped to a vertical pattern, which makespossible applying a morphological filter. However, the studyrequires further testing, automation and more extensive vali-dation. This paper extends this study and tries to overcome itslacks.

Regarding automation, the focus of the transformation isestimated without human interaction even in cases of mul-tiple artifact sources. Regarding the processing, the currentpaper discusses different morphological filters and, in addi-tion, the size of the structuring elements used are estimateddepending on the distance to the artifact origin. Finally, anew validation which compares the processed images witha groundtruth set is presented.

Hence, our aim is to describe a new approach in MAR tech-niques always oriented to 3D reconstruction, which starts withFBP images stored in DICOM files and tries to make medi-cal examination easier and more accurate without additionalinformation.

2. Method

2.1. Morphological filtering

Mathematical morphology is a theory based on minimumand maximum operations [12,13], constructed from two basicoperators. The dilation (Eq. (1)) computes the maximum graylevel of a neighborhood determined by a structuring ele-ment (SE). On the contrary, the erosion (Eq. (2)) computes theminimum gray level of a neighborhood determined by thetransposed structuring element.

ıB(f ) = sup{fb, b ∈ B} (1)

εB(f ) = inf{fb, b ∈ B�} (2)

Combining the dilation and erosion it is possible to define twonew operations. The morphological opening (Eq. (3)), consists ofan erosion followed by a dilation. The opening of a grayscale

image f with the structuring element B, �B(f), removes clearareas in the image where the structuring element does not fit.On the other hand, the closing (Eq. (4)) consists of a dilationfollowed by an erosion. In the same way, the closing removes

66 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

E wi

blurred the image results. Since the rays are thicker at the

Fig. 2 – (a) Original image. (b) Opening with horizontal S

those dark image areas where the structuring element doesnot fit.

�B(f ) = ıB(εB(f )) (3)

ϕB(f ) = εB(ıB(f )) (4)

Morphological filtering is a kind of non linear filtering widelyused in image noise reduction and artifact elimination [14].The effects produced by these filters depend on the natureof the filter and on the shape and size of the SE, which fixthe analysis surroundings. A wide family of morphological fil-ters has been developed combining the opening and closingoperators [15].

Fig. 2 shows the effects of the opening of an image usingdifferent SEs (horizontal in Fig. 2b and vertical in Fig. 2c). Theclear areas where the SE does not fit are erased (horizontalnarrower areas than the SE in Fig. 2b, and vertical narrower inFig. 2c).

2.1.1. Types of morphological filtersThe aim of this study is to reduce the noisy artifacts while pre-serving, as much as possible, the original image structures tofacilitate the 3D reconstruction. In order to achieve this goal,different morphological filters have been tested to select thebest option to restore the original image. These filters are:Opening–Closing filter: the opening of the original image fol-lowed by a closing operation. Analytically:

OC�(f ) = ϕB� �B� (f ),

where � is the SE size.Closing–Opening filter: the dual operator of the previous

one. Here the operations are implemented in inverse order.

CO�(f ) = �B� ϕB� (f ).

Alternating sequential filter: concatenation of opening andclosing operators where the size of the SE increases from 2to �. Two different filters can be obtained depending on thefirst operator:

- Starting by opening

ASFO� = ϕB� �B� ϕB�−1�B�−1 . . . ϕB2 �B2 (f ).

- Starting by closing

ASFC� = �B� ϕB� �B�−1ϕB�−1 . . . �B2 ϕB2 (f ).

th size = 15. (c) Opening with a vertical SE with size = 15.

Closing–Opening Average: the average of the results of theclosing and opening operators:

COA� = �B� (f ) + ϕB� (f )2

In Section 3 a comparison of these morphological filters ispresented (Fig. 10). In accordance with the results obtainedfor a test set, consisting of 52 axial CT slices from 20 differentpatients, the filter with the best performance is implementedin the algorithm.

2.1.2. Structuring element topologyThe results of the morphological filters are associated not onlywith the type of filter but also with the correct selection of theshape and size of SE.

As it is shown in Fig. 2, in order to remove objects with aparticular orientation, it is necessary to apply the morpholog-ical opening of the image with a SE orthogonally oriented tothem. In the case of streaking artifacts (rays emerging frommetallic objects), a set of SE orthogonally oriented to each rayshould be used. This fact makes the process mostly unattain-able and for this reason it is necessary to find another way totackle the problem.

Our approach is based on converting the image from theCartesian into the polar domain, using the artifact source asthe focus of the transformation. With this approach, the radialartifacts go along the angular axis with the same orientation,that is, the streaking rays are transformed into vertical raysand therefore, it is possible to use a single orientation for theSEs for the whole image, orthogonally oriented to the verti-cal rays [16]. In Section 2.2 the geometrical transformation toconvert the image into the polar domain is described.

Fig. 5 shows the image in Fig. 1 in the polar domain. Asshown, the streaking artifacts are converted into vertical rays,easily removable using a morphological filter with a horizontalSE.

The size of the SE is critical. A large SE will remove signifi-cant artifacts but will also blur the image. The larger the SE is,the wider the streaking artifacts it can reduce, but the more

metallic object surroundings and become thinner with the dis-tance, a distance adaptive variation of the SE size is proposedand shown in Fig. 3.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74 67

Fig. 3 – Function of SE size variability.

F

2

IdtTats

rpp

2Ldsi

Dici

d

structures are extracted and refined.The strategy is conceptually based on multiple sieves which

progressively filter out different parts of the original image. Inour case, these sieves are morphological operators with well-

ig. 4 – Rectangular-polar coordinate system relationship.

.2. Polar coordinate system

mages obtained by FBP of CT scan data often show someegree of symmetry since the image is derived from the scat-ering values of the X-ray beam rotating around the object.herefore, it is intuitive to define any point in terms of anglesnd distance, which implies using trigonometric formulae inhe rectangular coordinate system. Easier expressions are pos-ible in the polar coordinate system.

The polar coordinate system determines each point by itsadial and angular coordinates denoting the distance from theole, the origin of symmetry, and the angle defined with theolar axis. Fig. 4 shows this relationship.

.2.1. Definitionet P be a point in a two-dimensional coordinate system. Weenote P(x, y) to refer to it in rectangular (or Euclidean or Carte-ian) coordinates. The transformation into polar coordinatess defined by the following equations:

� =√

(x − xc)2 + (y − yc)

2, 0 ≤ � ≤ �max

� = arctan(y − yc

x − xc), 0 ≤ � ≤ 2�

(5)

efining (xc, yc) as the origin of the streaking rays, that is, tak-ng the streaking source as the focus of the transformation, the

onversion of the artifacted image results in the polar imagen Fig. 5.

In order to automate the whole process, a method toetect the transformation center, (xc, yc), using granulome-

Fig. 5 – Image of Fig. 1 in the polar domain.

try, has been developed and is explained in the followingsection.

2.2.2. Automated streaking origin detectionGranulometry is a geologic term adopted in textured imageprocessing to refer to the extraction of sets of elementswith some specific properties in an image [12]. The imageis processed by a filtering scheme so that in each step some

Fig. 6 – Block diagram of the proposed MAR method.

68 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

Fig. 7 – (a, d, g): Resulting overdetermined system. (b, e, h): The overdetermined system after refinement. (c, f, i): Results

over the original image.

known properties, so the design of the granulometry processconsists of finding the correct operators to extract the targetstructures of the image.

Analytically, let B be a convex structuring element and r,sscalar parameters with r > s > 0.

Consider the opening of a binary image A by B with differentsizes.

It follows that:

A ◦ rB ⊆ A ◦ sB (6)

Then, the granulometry of generator B is a family of morpho-logical operations, B

t for t ≥ 1

Bt (A) = A ◦ tB (7)

It is the set of operators which extract image objects withsome desired features, combining different SEs (B) and their

sizes (t). Our aim is to detect the streaking source, whichintuitively can be defined as the intersection of the fam-ily of functions described by the set of streaking lines.So, to deduce these functions, the streaking lines must be

extracted, and the scheme shown in Fig. 6 is designed for thispurpose.

First of all, the image is thresholded to extract the binaryobjects (blobs), which matches the streaking rays. The top-hatopenings extract the blobs nearly perpendicular to the struc-turing elements (SE orientations of 45 ◦ and −45 ◦); that is,those objects with 135 and 225 degrees orientation, respec-tively. Then, the area, eccentricity and orientation values arecomputed for all the blobs in the resulting images, and are con-strained to reach some values. To sum up, a blob is consideredto be a line structure if:

• Area ≥20• Eccentricity ≥0.96

• Orientation ∈{

[105◦, 165◦] , if∠SE = 45◦

[195◦, 255◦] , if∠SE = −45◦

Once these geometrical properties are evaluated and the blobs

are filtered, we proceed to the curve fitting step. We use a firstdegree polynomial equation to fit the lines, so we arrive to asystem with many more equations than unknowns, that is, anoverdetermined system which can be easily solved by the least

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74 69

F nedi

s

y

w

p

ig. 8 – (a): Selected origins. (b and c): Resulting overdetermimage.

quares method in the following way:

= Ax + b (8)

⎛a1

⎞ ⎛b1

⎞

here A =

⎜⎜⎝a2

...an

⎟⎟⎠ and b =⎜⎜⎝

b2

...bn

⎟⎟⎠ are the coefficients of the

olynomial expressions of the family of n lines. Consequently,

Fig. 9 – Block diagram of the

systems for both origins. (d): Results over the original

the solution of the system denoted by Ax = b is given by leastsquares

x = (AtA)−1

Atb (9)

Finally, we carry out a refinement of the data to improve theaccuracy of the results. As the first approach is satisfactorydue to the previous geometrical filtering, we can remove theoutliers of the distribution simply determining if the distance

proposed MAR method.

70 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

r; (c

Fig. 10 – (a) Original image; images filtered using (b) OC� filteall cases the size of the SE is � = 9.

in a coordinate, fixing the other coordinate, is greater thana threshold (that is, those lines which are too far from theestimated center) and redefining the system. This is done forboth coordinates. Fig. 7 shows this process.

2.2.3. Multiple metallic objects case

In situations where there are multiple streaking sources due tothe presence of several metallic objects, the human interven-tion is required in order to achieve the same precision. In thesecases, a bounding box must be defined around each origin.

Fig. 11 – (a) Original image; Image 11 filtered using the COA� filtelambda = 25; (e) variable size from �min = 3 to �max = 15; (f) variable

) CO� filter; (d) ASFO� filter; (e) ASFC� filter; (f) COA� filter. In

The boundary fixes the region of interest (ROI) of each systemin such a way that each origin could be processed as a sin-gle source case. Finally, the systems are solved by the leastsquares method to obtain the results shown in Fig. 8.

2.3. The algorithm

The block diagram of the algorithm which synthesizes thewhole process explained above is shown in Fig. 9. The originalimage is converted from the Cartesian into the polar domain

r with (b) fixed lambda = 5; (c) fixed lambda = 15; (d) fixedsize from �min = 3 to �max = 25.

c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74 71

ded.

bfi2ro(ecctti

I

It

Fig. 12 – (a) Original images. (b) Original images threshol

y means of the polar block. After this, the polar image isltered using a morphological filter as described in Section.1, and the result is reconverted into the Cartesian domain,esulting in the filtered image Ifiltered. On the other hand, theriginal image is segmented in order to detect the cavities

Ioriginal < T) using a simple threshold. The threshold block gen-rates a mask (Imsk) where the pixels corresponding to theavities are set to 1 and the rest of the pixels are set to 0. Theavities are also artifacted but due to their low density values,hey are easily reconstructible, hence they are preserved fromhe effects of the filter. The output image is obtained by merg-ng the original and the filtered images in the following way:

output = Ioriginal × Imsk + Ifiltered × (1 − Imsk)

n the multiple origin case the method consists of performinghe same process for every streaking source. That is, perform-

(c) Processed images. d) Processed images thresholded.

ing different transformations (one for each streaking origin),filtering and transforming again the processed images. Finally,Ifiltered is computed averaging all the filtered images.

3. Results

In this section the results of the MAR method presented in thispaper are shown. 52 slices from 20 different patients, whosedata sets have been obtained using different tomographs (GEMEDICAL SYSTEMS HiSpeed QXi and Philips Medical Systems -Philips CT Aura), have been considered in order to evaluate themethod, shaping the test set. In order to analytically evaluate

the performance of the method the test set has been manu-ally segmented by a group of experts, defining the groundtruthset. Hence, the test set has been processed by the presentedmethod and the resulting images have been compared with

72 c o m p u t e r m e t h o d s a n d p r o g r a m s i n b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

Fig. 13 – (a) Original images. (b) Original images thresholded. (c) Processed images. (d) Processed images thresholded.

Table 1 – Mean improvements in JC and DC achievedwith filters (a) OC�; (b) CO�; (c) ASFO�; (d) ASFC�; (e) COA�.

Filter type JC improvement DC improvement

OC� 0.1617 0.1074

Table 2 – Mean improvements in JC and DC achieved bymeans of COA� with (a) � = 5; (b) � = 15; (c) � = 25; (d)�min = 3 to �max = 15; and e) �min = 3 to �max = 25.

SE size JC improvement DC improvement

� = 5 0.1920 0.0995

comparison of the images obtained using different adaptivesizes for the same example slice is shown in Fig. 11.

Best result is obtained through adaptive size from �min = 3to �max = 25. Table 2 shows the resulting values.

CO� 0.1608 0.1067ASFO� 0.1674 0.1131ASFC� 0.1893 0.1146COA� 0.1927 0.1159

the groundtruth set by means of Jaccard index (JC) and Dice coeffi-cient (DC). The cavities have been segmented using a thresholdparameter T = − 500 HU for the whole evaluation and yield suc-cessful results. It is necessary to emphasize that the cavitiesare easily isolated from beam hardening because this arti-facts appears in the surroundings of the teeth. This sectionshows the justification of the selection of both the filter andthe size of the SE. Once these parameters are fixed, the methodis evaluated.

3.1. Filter selection

The filters in Section 2.1 have been tested, fixing the size ofthe SE, and the results for an example slice are shown inFig. 10. Although the output images are similar, the COA� fil-ter has been proven to give the best results with regard to 3Dreconstruction. Table 1 shows the resulting values. In all cases,the size of the SE has been set to � = 9.

3.2. Structuring element size selection

Once the filter type is selected (COA� filter), the size of the SEneeds to be tested following our objectives of reducing the arti-facts as much as possible (while also preserving the structures)to improve the 3D reconstruction. As shown in Fig. 11, thelarger the SE is, the harder artifacts it can reduce but the moreblurred the image results. In conclusion, a large SE is needed

(� > 20) to reduce streaking in the area surrounding the metal-lic object, but this selection produces significant degradation,mainly in outer tissues. This effect is noticeable in the areashighlighted in Fig. 11). To overcome this problem a distance

� = 15 0.1933 0.1266� = 25 0.2018 0.1345�min = 3 to �max = 15 0.2401 0.1770�min = 3 to �max = 25 0.2649 0.1956

adaptive size of the SE is used, as explained in Section 2.1. A

Fig. 14 – (a) Original image. Image processed by (b)proposed method; (c) DCT-based method (N = 8 and softthreshold); (d) DWT method (Daubechies db2 wavelet andsoft threshold).

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rigin

3

Efibsmfr

ips

iic

ddmfDcsffpSttat

ba0m

crro

Fig. 15 – 3D jaw reconstruction from o

.3. Process evaluation

xperimental results have shown that the configuration COA�

lter with variable � (from �min = 3 to �max = 25) gives theest performance among the tested options. For this rea-on, it is consolidated as the configuration used in the MARethod presented. Figs. 12 and 13 show the results obtained

or different patients with single and multiple origin cases,espectively.

It can be seen that the method reduces significantly streak-ng artifacts and noise, even in cases with heavy degradations,reserving to a great extent teeth, bone, cavities and soft tis-ues.

The resulting images have been analyzed obtaining a meanmprovement in JC and DC of 0.2649 and 0.1956, respectively,n cases with single metallic object, and 0.1966 and 0.1747, inases with multiple metallic objects.

Moreover, the method has been compared with two imageenoising methods: Donoho’s digital wavelet (DWT) [17,18] andiscrete cosine transform (DCT) based methods [19]. In the firstethod, the set of images has been processed using different

amilies of wavelets: Haar, Daubechies, Coiflets and Symlets.aubechies filter (db2) obtained the best results. The coeffi-ient thresholding has been performed using two thresholdchemes: hard and soft threshold. Both have been calculatedrom the image noise variance. The best results were obtainedor the soft threshold. Regarding the DCT-based method, thearameters have been tuned in order to obtain the best results.pecifically, the size of the DCT-block has been set to N = 8 andhe soft threshold option has been chosen for the coefficienthresholding. Fig. 14 shows a comparison between our methodnd the image denoising algorithms described above, usinghe parameters for which the best results have been achieved.

The proposed method has given the best results since it haseen developed in order to reduce this specific noise pattern,chieving an improvement in Jaccard similarity coefficient of.2649 versus 0.1296 and 0.028 obtained by DWT and DCTethods respectively.As it has been commented previously, most of the commer-

ial applications threshold the image to define the structure toeconstruct. Fig. 12 shows the algorithm input images and theesult of thresholding them (with a threshold grayscale valuef 130), and the same for the processed ones.

al (a) and post-processed CT data (b).

The original dental images are remarkably affected by noiseand strong artifacts such as beam hardening and streaking,what makes impossible to isolate hard tissues for 3D recon-struction. The processed images are sensibly less affected bythese effects, so this fact makes the reconstruction easier.For all the studied cases (52 axial CT slices from 20 differentpatients) the algorithm parameters, the size of the SE used inthe morphological filter and the threshold value, have beenset to �min = 3, �max = 25 and T = − 500 HU, respectively.

Resulting images show how the method reduces significa-tively streaking artifacts and noise, not smoothing teeth andpreserving bones and cavities. However, the beam harden-ing surounding the metallic object is not relevantly reducedbecause the suitable size of SE to remove streaking artifacts isnot large enough to erase this other effect. A wider SE wouldover-smooth the rest of the image. To solve this drawbacknew ideas are being studied and future works will featurethis improvement. The processing time of the algorithm onMatLab® has been about 1 s for a 512 × 512 pixel image ina worst-case scenario using an ordinary PC (Pentium IV at2.8 MHz and 1 GB of RAM).

Finally, Fig. 15 shows the improvement of the reconstruc-tion of the CT data after having been processed by thepresented method.

4. Discussion

In this paper a new method for metallic artifact reduction hasbeen presented. This method, based on mathematical mor-phology in the polar domain, has been automated and hasproven to reduce streaking and noise artifacts, while caus-ing very little smoothing of the anatomic structures, even inmultiple origin artifact cases. One of the contributions of thepresented method is the use of CT images as inputs as opposeto most of the MAR methods which use projection data. Thiscondition is crucial in those applications where the raw datais not available.

Our approach achieves these promising results because

takes into account not only the intensities of the artifactedpixels but also the geometry of the artifact in order to removeit. This is a novelty with regard to other image-based MARmethods, such as the proposed in [10], which try to remove

m s i n

r

74 c o m p u t e r m e t h o d s a n d p r o g r a

the artifact based only in the intensities of the artifacted pix-els and have the problem of having anatomical structures withthe same intensities.

The method is particularly efficacious in reducing thestreaking artifacts, which are the major cause of distortion inthe 3D reconstruction, so it is specially suitable for enhancingthese views. In addition, due to its low computational cost, themethod is also suitable for real time applications.

However, the method also presents some weaknesses. Theimprovement achieved is bounded to the quality of the recon-structed CT image and to the morphological filter used. Forthis reason, the method is limited to slightly artifacted images.Its performance decreases when multiple metallic objects arepresent in the same slice, and over all when these objects areclose. Beam hardening is hardly reduced since it presents awide pattern and very low values.

Nevertheless, the method has applicability to a wide rangeof applications, specially in those oriented to 3D reconstruc-tion. Furthermore, the presented algorithm can also be usedas a previous stage for other medical imaging applications orother MAR methods.

Future work will focus on implementing a new method(based on the algorithm described) able to process a fullCT study considering the information of adjacent slices toenhance the 3D reconstruction of the scanned object.

Acknowledgement

This work has been supported by the project MIRACLE(DPI2007-66782-C03-01-AR07) of Spanish Ministerio de Edu-cación y Ciencia.

e f e r e n c e s

[1] T. Rohlfing, D. Zerfowski, J. Beier, N. Hosten, P. Wust, R. Felix,Reduction of metal artifacts in computed tomographies forplanning and simulation of radiation therapy, ComputerAssisted Radiology and Surgery (1998) 57–62.

[2] O. Watzke, W. Kallender, A pragmatic approach to metalartifact reduction in CT: merging of metal artifact reducedimages, European Radiology 14 (2004) 849–856.

[3] W. Kalender, R. Hebel, J. Ebersberger, Reduction of CTartifacts caused by metallic implants, Radiology 164 (1987)

576–577.

[4] M. Kachelriess, O. Watzke, W. Kalender, Generalizedmulti-dimensional adaptive filtering (MAF) for conventionaland spiral single-slice, multi-slice and cone-beam CT,Medical Physics 28 (2001) 457–490.

b i o m e d i c i n e 1 0 2 ( 2 0 1 1 ) 64–74

[5] H. Yu, K. Zeng, G. Bharkhada, D. Wang, M. Madsen, O. Saba,B. Policeni, W. Howard, M. Smoker, A segmentation-basedmethod for metal artifact reduction, Academic Radiology 14(4) (2007) 495–504.

[6] Z. Shiying, T. Kyongtae, B. Whiting, G. Wang, A waveletmethod for metal artifact reduction with multiple metallicobjects in the field of view, Journal of X-Ray Science andTechnology 10 (2002) 67–76.

[7] G. Wang, D. Snyder, J. O’Sullivan, M. Vannier, Iterativedeblurring for CT metal artifact reduction, IEEE Transactionson Medical Imaging 15 (5) (1996) 657–664.

[8] R. Murphy, D. Snyder, D. Politte, J. O’Sullivan, Asieve-regularized image reconstruction algorithm with posesearch in transmission tomography, in: SPIE Medical Imaging2003: Image Processing conference, 2003, pp. 1392–1404.

[9] T. Sohmura, H. Hojoh, N. Kusumoto, M. Nishida, K.Wakabayashi, J. Takahashi, A novel method of removingartifacts because of metallic dental restorations in 3-d ctimages of jaw bone, Clinical Oral Implant Research 16 (2005)728–735.

[10] G. Tognola, M. Parazzini, G. Pedretti, P. Ravazzani, F.Grandori, A. Pesatori, M. Norgia, C. Svelto, Novel 3dreconstruction method for mandibular distraction planning,in: International Workshop on Imaging Systems andTechniques, 2006, pp. 82–85.

[11] V. Naranjo, R. Lloréns, P. Paniagua, M. Alcaniz, S. Albalat, Anew approach in metal artifact reduction for ct 3dreconstruction, in: International Work-conference on theInterplay between Natural and Artificial Computation(IWINAC (2)), 2009, pp. 11–19.

[12] J. Serra, Image Analysis and Mathematical Morphology,Academic Press, London, 1982.

[13] J. Serra, Image Analysis and Mathematical Morphology, Vol.II: Theoretical Advances, Academic Press, London, 1988.

[14] V. Naranjo, A. Albiol, J. Mossi, A. Albiol, Morphologicallambda-reconstruction applied to restoration of blotches inold films, in: 4th IASTED International Conference onVisualization, Imaging and Image Processing, 2004, pp.251–257.

[15] J. Serra, L. Vincent, An overview of morphological filtering,Circuits, Systems, and Signal Processing 11 (1) (1992) 47–108.

[16] M. Luengo-Oroz, J. Angulo, G. Flandrin, J. Klossa,Mathematical morphology in polar-logarithmic coordinates.Application to erythrocyte shape analysis, 2th IberianConference on Pattern Recognition and Image Analysis(IbPRIA’2005). Lecture Notes in Computer Science, Vol. LNCS3523 (2005) 199–205.

[17] D. Donoho, Denoising by soft-thresholding, IEEETransactions on Information Theory 41 (3) (1995) 613–627.

[18] B.-J. Yoon, P.P. Vaidyanathan, Wavelet-based denoising bycustomized thresholding, in: Acoustics, Speech, and Signal

Processing, 2004. Proceedings. (ICASSP’04) 2, 2004, pp.925–928.

[19] R. Oktem, L. Yarovslavsky, K. Egiazarian, J. Astola, Transformdomain approaches for image denoising, Journal ofElectronic Imaging 11 (2) (2002) 149–156.