Shape-Based Computer-Aided Detection of Lung Nodules in Thoracic CT Images

1810 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 56, NO. 7, JULY 2009

Shape-Based Computer-Aided Detection of LungNodules in Thoracic CT Images

Xujiong Ye∗, Xinyu Lin, Jamshid Dehmeshki, Member, IEEE, Greg Slabaugh, Senior Member, IEEE,and Gareth Beddoe, Member, IEEE

Abstract—In this paper, a new computer tomography (CT) lungnodule computer-aided detection (CAD) method is proposed fordetecting both solid nodules and ground-glass opacity (GGO) nod-ules (part solid and nonsolid). This method consists of several steps.First, the lung region is segmented from the CT data using a fuzzythresholding method. Then, the volumetric shape index map, whichis based on local Gaussian and mean curvatures, and the “dot”map, which is based on the eigenvalues of a Hessian matrix, arecalculated for each voxel within the lungs to enhance objects ofa specific shape with high spherical elements (such as nodule ob-jects). The combination of the shape index (local shape informa-tion) and “dot” features (local intensity dispersion information)provides a good structure descriptor for the initial nodule candi-dates generation. Antigeometric diffusion, which diffuses acrossthe image edges, is used as a preprocessing step. The smoothnessof image edges enables the accurate calculation of voxel-based geo-metric features. Adaptive thresholding and modified expectation–maximization methods are employed to segment potential noduleobjects. Rule-based filtering is first used to remove easily dismis-sible nonnodule objects. This is followed by a weighted supportvector machine (SVM) classification to further reduce the num-ber of false positive (FP) objects. The proposed method has beentrained and validated on a clinical dataset of 108 thoracic CT scansusing a wide range of tube dose levels that contain 220 nodules (185solid nodules and 35 GGO nodules) determined by a ground truthreading process. The data were randomly split into training andtesting datasets. The experimental results using the independentdataset indicate an average detection rate of 90.2%, with approx-imately 8.2 FP/scan. Some challenging nodules such as nonspheri-cal nodules and low-contrast part-solid and nonsolid nodules wereidentified, while most tissues such as blood vessels were excluded.The method’s high detection rate, fast computation, and applica-bility to different imaging conditions and nodule types shows muchpromise for clinical applications.

Index Terms—Antigeometric diffusion, computer-aided detec-tion (CAD), CT, expectation–maximization, lung nodule, shapeanalysis.

I. INTRODUCTION

THERE has been growing interest in the development ofcomputer tomography (CT) as a tool for detecting lung

cancer. Lung nodules can be classified into two categories:solid nodules characterized by their high-contrast and ground-

Manuscript received September 16, 2008; revised December 13, 2008.Current version published June 12, 2009. Asterisk indicates correspondingauthor.

*X. Ye is with the Medicsight PLC, London W14 8UD, U.K. (e-mail:[email protected]).

X. Lin, G. Slabaugh, and G. Beddoe are with the Medicsight PLC, LondonW14 8UD, U.K.

J. Dehmeshki was with the Medicsight PLC, London W14 8UD, U.K. He isnow with the Digital Imaging Research Centre, Kingston University, London,U.K.

Digital Object Identifier 10.1109/TBME.2009.2017027

glass opacity (GGO) nodules with faint contrast and fuzzy mar-gins [1]. Generally speaking, nodules with GGO characteris-tics are either part solid (consisting of solid components andGGO components) or nonsolid (pure GGO). GGO nodules aremore likely to be malignant than solid nodules [2]. Studies onlung nodule computer-aided detection (CAD) are reported fre-quently in the literature [3]–[17]. However, most attention hasbeen given to solid nodule detection. As pointed by Sluimeret al. in a review of computer analysis of CT lung scans [11],research leading to improved detection of GGO nodules shouldhave top priority. Recently, there are a number of papers that de-scribe GGO nodule detection. But most of the work focuses ondetection with high-dose CT imaging. As discussed in [2], lungcancer screening using low-dose CT (LDCT) has been reportedto be effective at detecting lung cancer. This paper describes anew CT lung CAD method that aims to detect both solid nodulesand GGO (part solid or nonsolid) nodules using a range of tubedose levels.

A. Previous Work on Nodule Detection

Existing approaches in the literature for detecting potentialnodules can be roughly categorized into intensity- and model-based detection methods. Intensity-based detection methods areusually based on the assumption that lung nodules have rela-tively higher intensity than those of lung parenchyma and em-ploy techniques such as multiple thresholding [3]; clustering [4];artificial neural networks [5]; and mathematical morphology [6],to identify nodules in the lung area.

For model-based detection methods, techniques such astemplate-matching [7], [8], object-based deformation [9], andthe anatomy-based generic model [10] have been proposed toseparate spherical shaped nodules from elongated structuressuch as blood vessels. Lee et al. [7] proposed a genetic algo-rithm (GA) template matching (GATM) technique for detectingnodules within the lung area. Shape and gradient features ruleswere used to reduce false positives (FPs). They achieved 72%sensitivity with 31 FP/scan. Farag et al. [8] proposed a similarGATM approach based on Gaussian templates, while the Gaus-sian parameters were automatically estimated from the givendata. They achieved the detection rate of 82.3% with the FP rateof 9.2%.

Recently, several approaches to lung CAD that combine geo-metric and intensity models to enhance local anatomical struc-ture (e.g., spherical objects) have been proposed. Paik et al. [13]proposed surface normal overlap (SNO) method to capture theconcentration of normals by calculating derivatives of intensityimages. They report results on eight chest datasets with 90%

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YE et al.: SHAPE-BASED COMPUTER-AIDED DETECTION OF LUNG NODULES IN THORACIC CT IMAGES 1811

sensitivity and 5.6 FP/scan for solid nodules. Zhang et al. [14]integrated surface curvature features into the voting procedure ofnormal overlap. They tested on 42 thoracic CT cases and showedimprovement compared to the original SNO method, with sen-sitivity of 92% at the same FP rate. Mendonca et al. [15] alsoanalyzed surface curvature by using the eigen analysis of thecurvature tensor to detect nodules, which achieved a sensitiv-ity of 67.5% at 9.3 FP/scan (for nodules above 4 mm) on 50low-dose images. Pereira et al. [16] extracted a set of rotationinvariant features from a multiscale and multiorientation filterbank and those features were then used in a multiclassifier forthe FP reduction.

Most of the above algorithms have been developed for solidnodules. For detection of GGO nodules, Kim et al. [12] usedtexture features and a three-layered neural network to detectGGOs. They tested on 14 scans with tube dose from 200 to400 mA and achieved a sensitivity of 94.3%. Zhou et al. [17]developed a boosting k-NN classifier for automatic detection ofGGO. The detected GGO region was then automatically seg-mented by analyzing the texture likelihood map. They appliedtheir method to chest CT with 10 GGOs. The method detectedall of the ten nodules with only 1 FP.

Despite much effort being devoted to the computer-aided nod-ule detection problem, lung CAD systems remain an ongoingresearch topic [18]. One of the major difficulties is the detec-tion of GGO nodules with low-dose thin-slice CT screening.Another two difficulties are the detection of nodules that areadjacent to vessels or the chest wall when they have very simi-lar intensity; and the detection of nodules that are nonsphericalin shape. In such cases, intensity thresholding or model-basedmethods might fail to identify those nodules.

B. Our Approach

This paper proposes a new and effective approach to lungCAD by calculating 3-D local geometry and statistical intensityfeatures for potential solid and GGO nodule detection. It aims tobuild a unified lung CAD framework with clinically acceptableperformance for the detection both of solid and GGO nodulesusing a wide range of tube dose levels. The main contributionsof the paper are summarized below:

1) A unified lung CAD framework for the detection of solidand GGO nodules using a wide range of tube dose level(e.g., 30–250 mA). Incorporating GGO detection intoa lung CAD framework has great potential for clinicalapplication.

2) The components of our algorithm utilize some existingmethods in new ways. In particular, new efforts have beenmade to adapt the methods into our lung CAD frameworkas follows:

a) An adaptive fuzzy thresholding method is presentedfor the segmentation of the lung region.

b) The application of antigeometric diffusion [19] tothe image prior to computing geometric features.The smoothness of the edges generated by antigeo-metric diffusion is better suited to the accurate cal-

Fig. 1. Block diagram of the proposed nodule detection system.

culation of the voxel-based features (such as shapeindex features).

c) The combination of features is well suited to de-tect solid and GGO nodules. In particular, the shapeindex [20] (local shape information) and “dot” fea-tures [21] (local intensity dispersion information)provide a good structure descriptor that can detectmost of the nodules.

d) The accurate segmentation of the nodule object isvery important for the extraction of features. Oursolution to efficiently segment the potential noduleobject involves two steps: i) an adaptive threshold-ing for a coarse segmentation and ii) a modifiedexpectation–maximization (MEM) algorithm for ac-curate segmentation.

The proposed method has been evaluated on a clinical datasetof 108 thoracic CT scans with tube range from 30 to 250 mA.The experimental results demonstrate the high performance ofthe proposed method, with an overall detection rate of 90.2% (in-cluding solid and GGO nodules), FPs at approximately 8.2/scan.

II. METHODOLOGY

Fig. 1 gives an overview of our proposed lung nodule detec-tion scheme. In the following sections, each stage is describedin detail.

A. Lung Segmentation

Due to the different scanning protocols, it is challenging tochoose a threshold for lung image segmentation. Vinhais andCampilho. [22] presented a fully automated method for ex-tracting the lung region based on material decomposition. Theyapplied the method on 30 thoracic CT images, and it provideda reproducible set of thresholds for accurate extraction of thelungs. Hu et al. [23] used optimal thresholding to automaticallysegment lungs.

In this paper, a two-step segmentation method is proposedfor lung extraction. First, a 3-D adaptive fuzzy thresholding


Fig. 2. Lung segmentation based on a fuzzy-thresholding method; processinggoes from left to right. (a) Original CT lung image; (b) lung mask extractionfrom fuzzy thresholding; (c) segmented concave regions (an attached noduleand other attached tissues) based on critical points; (d) final segmented lungmask formed by adding the (b) and (c) to produce the final lung mask.

[24] is used to obtain the initial lung mask; then a 2-D-basedpostrefinement process on the lung contour chain code is appliedto obtain a complete lung mask; both described below.

Let Tlow (i) and Mlow (i) denote the cumulative histogramand first moment starting from the minimum intensity Imin ofthe image, respectively, while Thigh(i) and Mhigh(i) startingfrom the maximum intensity Imax . In this paper, to exclude thevoxels outside the thorax, a simple thresholding (e.g., –1000HU) is first applied on the whole image to produce a processingmask image. Imin and Imax are then the minimum and maximumgray level of the original image over the voxels in the mask.

Given a particular gray level i, the histogram can be dividedinto two regions. For each of the two regions, the mean valuecan be calculated as

µlow (i) =Mlow (i)Tlow (i)

, µhigh(i) =Mhigh(i)Thigh(i)

. (1)

In order to determine an optimum threshold, a cost functionis calculated at each gray level i [24],

Ci =L−1∑t=0

[mi (t) ∗ (1.0 − mi (t))]2 (2)

where mi (t) is a membership measurement at each gray levelt to one of two regions separated in the histogram by the graylevel i. The closer the data point (t) is to the mean of its region,the higher its membership value. The gray level I0 that providesa minimum cost function is chosen as a threshold for 3-D lungimage segmentation.

Based on the threshold I0 , the initial thorax object is identifiedfrom the original CT image. A morphological flood fill operation[25] is then used to obtain a hole-free lung mask. Fig. 2 (b) showsan example of the initial segmented lung mask from the first stepof the lung extraction. It is noted that a nodule attached to thelung wall and some other attached tissues such as vessels areinitially excluded from the lung mask at this step.

The aim of the second step of the lung extraction process isto obtain those attached objects. For each 2-D slice of the seg-mented lung object, a chain code [25] is employed to representthe initial lung contour. Alternatively, each code can be consid-ered as an angular direction, in multiples of 45◦. 1-D Gaussiansmoothing is then applied to the chain codes to remove the noisefrom the initial lung contour. By specifying a threshold valueon the smoothed angle code (e.g., 180), each point can be clas-sified as a concave point (above 180), or a convex point (below180), or a smooth point (180). A concave section is specified

Fig. 3. Lung postprocessing based on critical points.

by its critical points (such as A and B in Fig. 3). These pointsare detected by examining the chain code and identifying eachtransition point for which the angle increases [26]. By usingthis chain code representation, the pairs of critical points arethen detected on each segmented lung slice. The next step ofthe lung contour refinement is to join corresponding pairs ofcritical points and fill in the resulting polygons formed by allthe points in the contour in between the pair of critical points,which are end points of a concave region. Fig. 2(d) shows thefinal segmented lung image. The subsequent nodule detectionis calculated within the segmented lung mask.

B. Potential Lung Nodule Concentrations Extraction

The volumetric shape index [20] is a measure of local shapecharacteristics. Given the fact that a nodule is generally eitherspherical or has local spherical elements, while a blood vesselis usually oblong, the volumetric shape index, which identifiesspherical elements, can be used as the first step to detect po-tential nodule candidates. It is noted that, compared to solidnodules, GGO nodules have irregular shapes and vague bound-aries. In this paper, it is assumed that there are some spher-ical elements embedded in those irregular shapes. We definespherical elements as a local grouping of voxels recognized byhigh-volumetric shape index values. For example, while a GGOnodule may not be entirely spherical, it can still be detectedby identifying small spherical elements concentrated within theGGO object. The goal in this section is to detect the potentialnodules based on these spherical elements. In the next section,we will address the complete segmentation of potential nodules.An example of pure GGO using spherical elements concentratedin parts of the object is given in Fig. 7.

In this section, an antigeometric diffusion model, proposedby Manay and Yezzi. [19] is used prior to the shape index calcu-lation. This model differs from Gaussian smoothing suggestedin [27] or geometric diffusion models (including anisotropic dif-fusion) introduced by Perona and Malik [28] for image smooth-ing and denoising. The antigeometric diffusion model diffusesacross image edges. The advantages of diffusing across imageedge include better localization, less sensitivity to noise, andbetter connectivity of the shape index map.

1) Preprocessing Using Antigeometric Diffusion: The anti-geometric diffusion model was introduced in the context ofadaptive thresholding and fast segmentation [19]. A brief de-scription of this method is as below.

Given the isointensity contours of an image I(x, y, z),let η and ξ denote the gradient and the tangent directions,respectively. Recall that the linear heat equation is described as


Fig. 4. Shape index map with a nodule attached to a vessel. (a) Original CTimage; (b) shape index map; shape index map values for (c) the nodule and(d) the blood vessel.

∂I∂ t = ∇ · ∇I = Iζ ζ + Iηη . In the case of antigeometric diffu-sion, the tangential diffusion is excluded and only the normaldiffusion is applied, the antigeometric diffusion is defined as

∂I

∂t= Iηη =

I2x Ixx + 2IxIy Ixy + I2

y Iyy

I2x + I2

y

(3)

where, Ix and Iy are the first derivatives along x and y.The result of diffusion in the normal direction is that the

image edges are smeared. The smoothness of the edge is veryimportant for accurate voxel-based geometry feature calculation(such as shape index). This will be discussed in the next section,where examples of shape index calculation on one GGO nodulewith different diffusion models are also given for comparison.

2) Shape Index (A 3-D Geometric Feature): The volumetricshape index (SI) at voxel p(x, y, z) can be defined as [20], [27]:

SI (p) =12− 1

πarctan

k1 (p) + k2 (p)k1 (p) − k2 (p)

(4)

where k1 (p) and k2 (p) are principal curvatures at voxel p.Every distinct shape, except for the plane, corresponds to a

unique shape index [20]. Five well-known shape classes have thefollowing shape index values: cup (0.0), rut (0.25), saddle (0.5),ridge (0.75), and cap (1.0). For example, the shape index valueis 1.0 indicates a sphere-like shape that represents a “cap”, and0.75 indicates a cylinder-like shape that represents a “ridge.”Volumetric shape index directly characterizes the topologicalshape of an isosurface in the vicinity of each voxel.

To illustrate the characteristics of the shape index, Fig. 4(a)shows an example of one small lung nodule attached to a bloodvessel. It is noted that different shape index values between thesphere-like nodule and the cylinder-like blood vessel at eachvoxel are obtained; the average of shape index values for thenodule is higher than that for the blood vessel.

Fig. 5 demonstrates the influence of the different diffusionmodels on the shape index calculation of a GGO nodule. It canbe seen that, by using the antigeometric diffusion, the averageshape index value at voxels close to nodule edge are higherthan that of geometric diffusion or Gaussian smoothing. Thisis because the antigeometric diffusion smears the image edge,providing better localization and connectivity of the shape indexat nodule edges. Later, in Section III of this paper, we willpresent results showing that the use of antigeometric diffusion

Fig. 5. Shape index maps produced using different diffusion models.(a) One slice of a GGO nodule; shape index map with (b) Gaussian smoothing(σ = 1.0); (c) geometric diffusion (∆t = 1.0); and (d) antigeometric diffusion(∆t = 1.0); (e)–(g) example of corresponding shape index values at the samevoxels adjacent to the nodule edge.

Fig. 6. Example of solid nodule regions extraction. (a) shape index map;(b) high sphericity regions; (c) low sphericity regions; (d) detected potentialnodule candidates from step (3).

in the overall CAD system yields better performance than theuse of Gaussian smoothing as a preprocessing step.

3) Potential Nodule Candidates Detection Based on theShape Index Feature: A sphericity region is defined as a re-gion for which, for ∀i, j ∈ �s , (i, j are 3-D connected voxels)we have

SI(i) ≥ ϑ1 , SI(j) ≥ ϑ1 (5)

where ϑ1 is a high shape index threshold chosen experimentally.In this paper, we refer to clusters of spherical elements as poten-tial nodule concentration regions, which can be extracted usingthe following steps:

1) Based on the calculated shape index map using (4), all thehigh sphericity regions (∪�sh ) that satisfy the conditionset in (5) are identified, with ϑ1 ∈ [0.9, 1]. The size ofeach �sh is set to be larger than δ1 voxels. Fig. 6(b) isthe detected high sphericity concentration regions with ϑ1and δ1chosen to be 0.92 and 3, respectively.

2) Find all the low sphericity regions (∪�sl) that satisfy (5)with ϑ1 ∈ [0.8, 0.9). The size of each �sl is set to belarger than δ2 voxels. Fig. 6(c) is the detected low spheric-ity regions with ϑ1 and δ1 chosen to be 0.82 and 20,respectively.

3) The region �sl is regarded as a potential nodule region ifthe region �sl contains at least one high sphericity region�sh as �sh ⊂ �sl . Fig. 6(d) shows an example of thedetected potential nodule regions.

Figs. 6 and 7 are the examples of potential nodule concentra-tion extraction based on the shape index for both solid and GGOnodules. Compared to the nodule concentration in Fig. 6(d) forthe solid nodule that the spherical elements covers most of thenodule object, the high spherical elements shown in Fig. 7(d)only cover a small part of the GGO. This demonstrates that


Fig. 7. Example of pure GGO nodule regions extraction. (a) GGO subimage;(b) shape index map of the GGO; (c) high sphericity regions; (d) detectedpotential nodule candidates from step (3).

although the GGO nodules have irregular shapes and vagueboundaries, they still contain small spherical elements that canbe detected by the shape feature.

4) Multiscale Dot Enhancement Filtering: The dot enhance-ment (DE) algorithm can be used to enhance the objects of aspecific shape (such as dot-like nodule objects). For each voxel,the dot value is defined as [21]

Zdot (λ1 , λ2 , λ3) =

{ |λ3 |2/|λ1 | if λ1 < 0, λ2 < 0, λ3 < 0

0 Otherwise(6)

where λ1 , λ2 , and λ3 (|λ1 | ≥ |λ2 | ≥ |λ3 |) are three eigenvaluesof the Hessian matrix calculated from second derivatives ofimage.

To reduce the effect of the noise and also to take into accountdifferent object sizes, Gaussian image smoothing with a varietyof scales is performed prior to the calculation of the secondderivatives. Assuming that the diameters of nodule objects to beenhanced are in a range [d0 , d1 ] (e.g., [2 mm, 20 mm]), the Ndiscrete smoothing scales (σN ) in the range of [d0/4, d1/4] canbe calculated as

σ1 =d0

4, σ2 = rσ1 , . . . , σN =rN −1 σ1 =

d1

4(7)

where r = (d1/d0)1/(N −1) . It is noted that image resolution

is considered in the calculation of Gaussian smoothing withdifferent scales and each of the enhancement filters enhancesobjects with a specific scale. The maximum dot value calculatedusing (6) among the different scales (7) is chosen to be the finaldot value for each voxel in the dot map.

In this paper, the dot map is calculated on each CT subimage,which contains one potential nodule region �sl . Three Gaussianscales are used to remove the noise. The region is kept as apotential nodule candidate if the number of voxels whose dotvalues are larger than a predefined threshold. By using the dotfiltering, most of the FP regions (e.g., joint of vessel) with highspherical elements can be removed from the nodule candidates.

C. 3-D Potential Nodule Segmentation

In this section, two methods are proposed to segment thepotential nodule objects: 1) Segmentation based on an adaptivethresholding; 2) segmentation based on a MEM algorithm. Theformer is an intensity-based method for fast segmentation ofpotential nodule objects (referred to as a coarse segmentation),especially for low-contrast nodules such as GGOs, while the

Fig. 8. Potential nodule segmentation based on adaptive thresholding; (a) One2-D cross-section of 3-D original nodule image; (b) potential nodule concentra-tion �s l from shape index map; (c) segmented nodule region.

latter is used to segment the potential nodule objects consideringthe neighboring intensities (referred to as a fine segmentation).

1) Adaptive Thresholding-Based Segmentation: An adap-tive thresholding method is applied to the extracted subimagefrom the potential nodule concentration (�sl) to segment thepotential nodule objects. The high- and low-intensity thresholdscan be calculated as follows:

fT L = fM − |fmin − fM | ∗ 0.1,

fT H = fmax + |fmin − fmax | ∗ 0.1 (8)

where fM and fmax are the mean and maximum intensities inthe region �sl , respectively. fmin is the minimum intensity inthe subimage. Fig. 8 shows a segmented potential GGO nod-ule based on the adaptive thresholding. A 3-D region labelingtechnique [25] is applied on the segmented image and the 3-Dconnected region that has the largest overlap with the concentra-tion mask is used as the final segmented nodule object as shownin Fig. 8(c).

The adaptive thresholding is a fast segmentation method.Based on (8), the low threshold (fT L ) for the nodule segmenta-tion is mainly estimated based on the intensity statistics (suchas mean intensity) of the region concentration �sl . Therefore,the algorithm can provide a better object boundary when theseintensity statistics are similar to that of the segmented nodule.As discussed in the previous section, the region �sl representslower sphericity concentration that is obtained from shape in-dex map. It usually covers the core part of the segmented object.This is the main reason why this adaptive algorithm can seg-ment most of the potential nodules that have smaller intensityvariance within the nodule objects (e.g., most low-contrast nod-ules). However, in the case of some potential nodules that haverelatively larger intensity variance, the algorithm fails to prop-erly identify the object boundary. An example can be seen inFig. 10(b), which shows underestimation of nodule boundary.To solve this problem, a MEM-based segmentation method isdiscussed below.

2) MEM-Based Segmentation: To properly segment the po-tential nodule object, a mixed statistical model taking into con-sideration spatial properties is used. This method is based onthe combination of a Markov Random Field (MRF) and anexpectation–maximization (EM) algorithm to iteratively esti-mate the model parameters and then calculate the probabilitythat each voxel represents the object (potential nodule) [29]. Abrief description of this method and how it is applicable to thenodule segmentation are given below.


Fig. 9. Potential nodule segmentation based on MEM; (a) one 2-D cross-section of 3-D original nodule image; (b) potential nodule concentration �s l

from shape index map; (c) segmented nodule region.

Fig. 10. Comparison of segmentation results of a nonuniform nodule basedon adaptive thresholding and MEM; (a) original nodule image; segmented resultbased (b) on adaptive thresholding and (c) on MEM.

We assume an intensity image Y = {yi, i = 1, 2, . . . ,M}with M voxels of intensity yi and K different classes L ={1, 2, . . . K}. In this paper, a special case of two classes(K = 2): object (potential nodule) and background, is consid-ered. The ranges of image intensities can be modeled as Gaus-sian distributions with parameters φl = (µl, σl), here l = 1, 2:

pl (yi |ϕl ) = G (µl, σl) =1√2πσl

exp

(− (yi − µl)

2

2σ2l

). (9)

According to the Bayesian probability theory, the posteriorprobability p (ϕl |yi ) can be obtained as

p

(ϕl

yi

)=

pl (yi/ϕl) p(ϕl (i)

)∑l

pl (yi/ϕl) p(ϕl(i)

), l = 1, 2. (10)

Here, p(ϕl(i)

)is a spatial prior probability. The spatial con-

straints can be imposed by an MRF and Gibbs Random Field(GRF) [29].

The posterior probability p (ϕl |yi ) in (10) represents theprobability that the given voxel i belongs to one class l ∈ L.In the case of nodule object segmentation, the class l∗i ∈ [1, 2]that maximizes p (ϕl |yi ) is chosen to be the class label for thatvoxel. Namely, l∗i = arg max

lp (ϕl |yi ).

Fig. 9 shows an example of the potential nodule segmentationbased on the MEM algorithm. It can be seen that the potentialnodule boundary can be properly separated from the attachedblood vessel.

Fig. 10 shows the segmentation results of a mixed GGO nod-ule based on the adaptive thresholding and MEM methods. Inthis example, it can be seen that due to the heterogeneity of thenodule, there is a “dark” area surrounding the core part (highcontrast) of the nodule in Fig. 10(a). Using the adaptive thresh-olding, those pixels in the “dark” area are wrongly identified asbackground so that the segmented nodule object is underesti-mated [Fig. 10(b)], while by using the MEM algorithm, thosepixels can be correctly identified as being part of the noduleobject, as seen in Fig. 10(c). This is because the MRF-GRF is

used as a spatial constraint. The segmentation depends not onlyon the intensity but also on the spatial information.

To speed up the overall computation time, we make use ofthe assumption discussed in the previous section that most low-contrast nodules have smaller intensity variance within the nod-ule objects so that the fast adaptive algorithm can properly seg-ment those potential nodules. In this paper, for each potentialnodule region, the adaptive thresholding is firstly applied to ob-tain the initial segmented object. The intensity mean of eachsegmented object is then calculated. For the region that have ahigh-intensity mean (e.g., larger than –500 HU), the MEM isthen employed to properly segment the potential nodule object.

It is worthwhile to emphasize that, in the case of nodules withvasculature attachment, theoretically, the MEM-based method,which takes into account spatial information, provides bettersegmentation results (e.g., this may separate the nodule fromadjoining vessel) compared to the adaptive-based method. How-ever, for the nodule attached to the lung wall (pleural nodule),both the adaptive- and MEM-based methods cannot properlysegment those nodules. In this paper, those nodules are seg-mented in the process of lung segmentation, where the chaincode-based critical point method is used, which is discussed inSection II. An example of segmented attached nodule is shownin Fig. 2(c). Below is the summary of the potential nodule seg-mentation.

For each potential nodule region from Section 2-B:Step 1) (Pleural nodules): If the region overlaps with a critical

point region detected during lung segmentation, the po-tential nodule is considered to be attached to the lungwall. The critical point region is used as the segmentedregion.

Step 2) (Non-pleural nodules): If the nodule is not attached tothe lung wall (not overlaps with a critical point region),segment the region based on the adaptive threshold-ing and calculate the intensity mean of the segmentedregion. If the mean intensity is less than −500 HU,stop; otherwise, refine the segmentation using the MEMmethod.

D. Local 3-D Geometric Features and Rule-Based Classifier

In this step, geometric features are calculated on each seg-mented potential nodule object. A rule-based classifier is thenapplied on each potential nodule object in order to quickly re-move easily dismissible nonnodule objects.

1) 3-D Maximum Distance Based on Distance Transform:For each potential nodule object (�seg ), a 3-D distance mapis calculated based on the Euclidean distance transform [25].Fig. 11 shows an example of the distance transform map;Fig. 11(c) is the corresponding distance map within the seg-mented object. The pixel with the highest gray leveling inFig. 11(c) has the maximum distance to the boundary withinthe object. This maximum distance value can be used as onefeature, which that represents the object thickness. This featurecan be used to remove regions with small maximum distancevalue, which are often vessels. It is noted that, in this paper,


Fig. 11. Example of distance transform map; (a) original subimage; (b) seg-mented object; and (c) gray-level distance transform map.

Fig. 12. Example of a blob-moving object; (a) 3-D view of the object (bloodvessel); (b) 2-D view of each blob on continuous slices (along scan direction).

the distance transform is calculated with consideration of theanisotropy of the image data.

2) 3-D Object Filtering Based on Motion Tracking: Assum-ing that the 3-D potential nodule object contains more than one2-D blob (a blob is a cross-sectional object defined in x-y plane,also referred as scan plane) along the scanning (z) direction,an object is defined as a blob-moving object if its 2-D blobson different continuous slices are moving along the x-y plane.Blob-moving objects are typically indicative of vessels. Fig. 12shows an example of a blob-moving object.

The aim of the rule described in this section is to detect 3-Dblob-moving objects by calculating the overlap kernel (core)regions between the 2-D blobs on consecutive slices. The 2-Dkernel region is calculated based on 2-D distance transform. Let�i

2DKernel the kernel region of the ith 2-D blob, for each pixel pin ith 2-D blob �i

2DBlob , ∀p ∈ Rseg and p ∈ Ri2DBlob , we have,

p ∈ Ri2DKernel if f2DDist p ≥ f2DDistMax ∗ k (11)

Here, f2DDist p is the distance value at the pth pixel in the 2-Ddistance map, while f2DDistMax is the maximum distance valuewithin the 2-D blob in the 2-D distance map, and k is a positiveconstant that controls the size of the core region, k ∈ (0, 1). Inthis paper, k is 0.6, which is determined experimentally. A briefdescription of how to choose an optimal value for parameter kis given in Section II-D (5).

For each 3-D object �seg , the kernel region of each 2-D blobis calculated based on (11), then the object �seg is kept as anodule candidate if

n−1∑i=1

δ(∣∣∣⋂(

Ri2-D Kernel, R

i+12-D Kernel

)∣∣∣) > 0.5 ∗ n (12)

where n is the total number of the 2-D blobs; the operator ∩ (·)is the AND operation:

δ (x) ={

1 if x > 00 if x = 0 .

That is to say, if the number of the overlap regions is lessthan a preset threshold (e.g., half of total number of 2-D blobs),the region is defined as a 3-D blob-moving object and removedfrom the nodule candidates.

Fig. 13. Receiver operating characteristic curve on 54 training scans by using3-D blob-moving as only one rule with different k values (11). (Here, it isassumed the sensitivity before the rule filtering is 100%).

3) Sphericity: The sphericity is defined as the ratio betweenthe object volume size and the circumscribed (minimum enclos-ing) sphere volume size. The sphericity can be used to removethe 3-D objects that are elongated.

4) Effective Diameter: The effective diameter is defined asthe diameter of a sphere with the same volume of the segmentedobject. This feature is used to remove very small (e.g., 2 mm orless) nodule candidates.

5) Parameter Selection: The above features are used in arule-based classifier to remove easily dismissible nonnoduleobjects. Each feature is associated with one rule. The outputfrom one rule will be employed as the input to a subsequent rule.To determine the threshold for each rule, clinical knowledge,i.e., the size of the region (e.g., 2 mm), the degree of sphericity,and so on, can be considered to obtain the initial thresholdvalue; then the threshold that provides a good cutoff in receiveroperating characteristic (ROC) curve is chosen to minimize theovertraining effect for the rule-based classifier. As an example,we illustrate how to determine k in 11 (Section II-D(2)). Forall the potential nodule objects obtained from Section II-B, 3-Dfiltering based on the detection of the 3-D blob-moving object(Section II-D (2)) is used as one rule to remove FP regions.Fig. 13 shows the ROC curve based on different k values on 54training scans. It can be seen that k = 0.6 gives good detectionperformance with regards to sensitivity and FP.

E. Support Vector Machine (SVM)-Based Classification

The rule-based classifier is employed in order to quickly re-move obvious FP (outliers) so that their influence on the train-ing of the second classifier was eliminated. In this section, aweighted SVM [30] classification method is applied to furtherseparate nodules from nonnodule candidates.

For the feature space in d-dimensions, we are given trainingdataset S = (x1 , y1), . . . , (xl, yl), where xl ∈ d, and the classlabel yl ∈ {+1,−1} (where +1 corresponds to a nodule and −1to a nonnodule). The decision function of the weighted SVM isgiven as [30]:

f(x) = sgn

(l∑

i=1

yia∗i K (x, xi) + b∗

)


TABLE IFEATURES FOR THE CLASSIFICATION

where K (x, y)is a nonlinear kernel function, b ∈ R and a isconstrained as follows: 0 ≤ ai ≤ C+ , for yi = +1, and 0 ≤ai ≤ C−, for yi = −1. Where C+ and C− are penalties forclass +1 and −1, respectively.

In this paper, the LibSVM [31] was used with a radial basisfunction kernel, defined as K (x, x) = exp(−γ ‖x − x′‖2), forγ > 0. The input parameters are determined through fivefoldcross validation via parallel grid search. Each subset is createdbased on subtractive clustering [32].

Fifteen features, which are listed in Table I, are empiricallyused in this study to characterize the remaining nodule candi-dates. All the input features are normalized to [−1, 1].

III. EXPERIMENTAL RESULTS

A database of 108 thoracic CT scans from several differenthospitals was used to evaluate the effectiveness of the proposedmethod. Slice thickness varied from 0.5 to 2.0 mm and thetotal slice number for each scan varied from 79 to 396 with anaverage of 199/scan. The X-ray tube current ranged from 30 to250 mA. Among those 108 scans, 58 scans have 30-mA tubecurrent, 10 scans at 50 mA, and the rest are above 100 mA. Eachscan was read individually by members of a qualified panel andthen a consensual gold standard was defined by the panel. Thisprocess defined ground truth of 220 nodules (185 solid nodulesand 35 GGO nodules). All the GGO nodules are in the scanswith 30-mA tube current.

The whole dataset was processed using the method describedin Section II. Potential nodule candidates were first generatedbased on shape index features, where the high shape indexthreshold ϑ1 in 5 was set to be 0.91 with size threshold δ1 = 3.A ROC curve with different ϑ1 is also given in Fig. 16 in thediscussion section, which indicates ϑ1 = 0.91 provides an op-timal overall performance regarding to the sensitivity and FP.The low shape index threshold in 5 was 0.82 with δ2 = 12; the“dot” filtering was then used to remove FP regions, three-scalesGaussian with σ1 = 0.5 mm, σ2 = 1.6 mm, and σ3 = 5 mm (in7) were used to remove noise. For each region from shape index,if the total number of 3-D-connected voxels with high dot valueare larger than 6, the region is kept as a potential nodule region.By using this dot filtering, in total, 4639 nodule candidates weregenerated at the initial stage (4419 nonnodule regions and 220nodule regions). The dataset was randomly split into trainingand testing datasets with the same number of scans (54 scans

TABLE IIDETECTION PERFORMANCE OF THE TRAINED MODELS (RULE-BASED

FILTERING AND THE WEIGHTED SVM) ON THE TRAINING DATASET (54 SCANS

WITH 98 NODULES)

TABLE IIIDETECTION PERFORMANCE FOR THE RULE-BASED CLASSIFIER ON THE

INDEPENDENT DATASET (54 SCANS WITH 122 NODULES)

each). The latter was used as the independent testing for evalu-ating the performance of the trained classifiers, which has 2393nodule candidates. This includes 122 nodule regions (104 solidnodules and 18 GGO nodules) and 2271 nonnodule regions.

For the training dataset, the rule-based classifier was firstlyused to remove easily dismissible FP regions. As discussedin the parameter selection Section II-D (5), the parameter foreach rule that provides good cutoff in an ROC curve is chosento minimize the overtraining effect for the rule-based classi-fier. For example, the threshold for the sphericity filtering inSection II-D (3) is set to be 0.8. The threshold for the effectivediameter is chosen to be 2 mm. After the rules filtering, forthe remaining nodule candidates, the weighted SVM was thenemployed to further remove FP regions.

The weighted SVM was trained using the following scheme.Subtractive clustering was used to estimate the number and lo-cation of cluster centers in the training dataset. Fivefold cross-validation (with roughly equal sized folds) was performed basedon the results of the subtractive clustering. Due to the imbal-anced data, and to reduce the computational cost, for each fold,the nonnodule regions (majority class) were randomly down-sampled to five times of the number of the nodule regions(minority class). The model was trained five times, each timeleaving out one of the folds from the training.

Table II shows final nodule detection performance (after rule-based filtering and the weighted SVM) on the training scans. Itcan be seen that 93 (78 solid and 15 GGO nodules) out of thetotal 98 nodules (81 solid and 17 GGO nodules) were detectedby the proposed method, resulting the average detection rate ofabout 95%, with the FP rate of 6.2/scan.

The trained model was tested on the independent data.Table III shows the results of the rule-based classifier appliedto 54 independent testing scans. The first row of the table is thedetection performance for the solid nodules, while the secondrow of the table is for the GGO nodules. The remaining nodulecandidates (1068 regions in total) are then fed into the weightedSVM for the further reduction. Table IV shows the performanceof the trained weighted SVM on independent data. As it canbe seen that, 95 out of 101 solid nodules are detected by theweighted SVM resulting the sensitivity of 94%, while 15 of 17GGO nodules can be found with the sensitivity of 88.2%. 1828nonnodule regions were removed from the candidates, resultingthe final average FP at about 8.2/scan.


TABLE IVDETECTION PERFORMANCE FOR THE WEIGHTED SVM ON THE

INDEPENDENT DATASET (54 SCANS WITH 118 NODULES, INCLUDING 101SOLID AND 17 GGO)

TABLE VSENSITIVITY OF THE PROPOSED METHOD BASED ON THE DIFFERENT NODULE

SIZES ON INDEPENDENT TESTING DATA

TABLE VICOMPARISON OF DETECTION PERFORMANCES WITH GAUSSIAN SMOOTHING

AND ANTIGEOMETRIC DIFFUSION FOLLOWED BY THE RULE-BASED FILTERING

AND THE WEIGHTED SVM ON THE INDEPENDENT DATASET (54 SCANS)CONTAINING 122 NODULES

Fig. 14. Nodules detected by using antigeometric diffusion preprocessing (andmissed with Gaussian smoothing).

Table V shows the final detection sensitivity based on thedifferent nodule size groups for the solid and GGO nodules, byusing the proposed method on the independent testing data.

In the second experiment, the detection performances of dif-ferent preprocessing methods were evaluated (Table VI). Twosmoothing methods were used: Gaussian smoothing and the pro-posed antigeometric diffusion. The first row of the Table showsthe final nodule detection results with using Gaussian smoothingas a preprocessing step on independent testing data (54 scans),where 96 out of the 122 (78.7%) nodules were detected, withan average FP rate of 12.7/scan. For comparison, the secondrow of Table VI gives the results of the whole proposed methodon the same independent testing data. As indicated in Table IV,110 (among which, 95 solid and 15 GGO nodules) of the 122nodules were detected, with the average detection rate of 90.2%.These results demonstrate that by using the antigeometric diffu-sion preprocessing, the sensitivity of the nodule detection rateincreases from 78.7% to 90.2%, while the FP reduces from12.7/scan down to 8.2/scan. Some vascular nodules or pleuralnodules (such as those shown in Fig. 14), were missed whenGaussian preprocessing was used but can be detected with theproposed algorithm.

Fig. 15. Different types of nodules detected with the proposed method.(a)–(c) nonspherical nodules; (d)–(f) nodules attached to vessels with similarintensity.

Fig. 16. Performance evaluation with different high shape index thresholdingvalues ranging from 0.89 to 0.99.

TABLE VIITHE AVERAGE COMPUTATION TIME (IN SECONDS) AT EACH MAJOR STEP

Fig. 15 shows examples of different types of detected nod-ules. Some challenging nodules such as nonspherical noduleswith spherical elements, as shown in Fig. 15(a)–(c), or attachednodules with similar intensity shown in Fig. 15(d)–(f) can bedetected with the proposed shape-based method.

As discussed in Section II, a high spherical concentrationcan be obtained by thresholding the shape index map as in(5). Therefore, different shape index thresholds produce differ-ent nodule detection performances. Fig. 16 shows the detectionperformance curves with regards to the different shape indexthresholds, in which 11 sets of high shape index thresholdingvalues were used, ranging from 0.89 to 0.99. It is noted that, ashape index thresholding value ϑ1 of 0.91 provides an optimaloverall performance with a higher detection rate (about 90.2%)and a relatively smaller FP rate (about 8.2/scan).

The proposed CAD algorithm was tested on the computerwith 2.39 GHz CPU and 2 GB Memory. On average, it takesabout 2.5 min/scan. Table VII shows the average computationtime required for each major step. Since our objective is tobuild a commercial lung CAD system, the fast computationtime is important for the practicality of the method for clinicalapplication.


Fig. 17. Example of nodules missed by the proposed method.

IV. DISCUSSION

The result in Fig. 16 shows an optimal detection rate of 90.2%(110 out of total 122 nodules detected including solid and GGOnodules) for the whole proposed method using the independentdataset. Examples of different types of detected nodules areshown in Figs. 14 and 15. As mentioned before, one advantage ofthe local shape feature is that it characterizes the local geometricfeature and favors regions with high spherical elements. This isthe main reason that the proposed algorithm is able to detectnot only spherical nodules but also nonspherical nodules withaspects of high local spherical elements. The second advantageof using the shape index is that, theoretically, it only representsthe local shape feature while being independent of the imageintensity. This is one of the reasons why low-contrast GGOnodules can be detected using the proposed system.

Some examples of nodules missed (false negatives) by theproposed method are shown in Fig. 17. Typically, these nodulesare very low contrast or close to the chest wall. The shape indexfavors regions with high spherical elements. However, nodulescould be missed if they do not include local spherical elementsor if the sizes of the elements are too small.

As mentioned in the beginning of Section III, there are 68scans with low tube current, among which 58 scans are at30 mA and 10 scans are at 50 mA. By using the proposedmethod, for the scans at 30 mA, the average detection sensi-tivity is 91.7% with FP rate of 8.6/scan, while for the scans at50 mA, the average detection sensitivity is 90.6% with FP rate of6.5/scan. For low dose screening, most CAD schemes in the lit-erature are developed for thick-slice CT images, e.g., slice thick-ness 10 mm. There are only a small number of papers that de-scribe the detection with low-dose and thin-slice data. Mendoncaet al. [15] applied the curvature tensor method on 50 low-doseCT scans at 40 mA with reported sensitivity of 67.5% (for thenodules above 4 mm) and FP rate at 9.3 FP/scan. By usingthe same low-dose data, they compared their method with theHessian method proposed by Sato et al. [33], at the same rateof 9.3 FP/scan, the Hessian method achieved a sensitivity of40%. They also applied their method on 192 low-dose scansat 20 mA with sensitivity of 62.9% at 10.3 FP/scan. Althoughthe databases are different, the performance of our proposedmethod on the low-dose data indicates the effectiveness of themethod with low-dose CT screening. We attribute the ability ofour method to handle low-dose data to the antigeometric diffu-sion, which is used as a preprocessing step to remove noise andprovides a good base for the accurate calculation of shape indexfeatures. In addition, the “dot” feature is calculated on multi-ple scales of Gaussian smoothed images. However, very noisyreconstructed images due to very low-dose tube current mightlead to inaccurate calculation of the local shape feature. To fur-

TABLE VIIITHE VARIATION OF NODULE DETECTION PERFORMANCE OVER ALL CASES ON

INDEPENDENCE TESTING DATA BASED ON THE PROPOSED METHOD.([] INDICATES THE NUMBER OF THE DETECTED NODULES AMONG THE TOTAL

NODULES IN ONE SCAN.)

ther improve the detection performance, an adaptive smoothingmethod needs to be further investigated.

By using the proposed method, Table VIII shows the variationin sensitivity and FP rate over all cases on the independenttesting data. As it is known that different imaging parameters(e.g., different slice thickness and different tube currents) mayaffect the nodule detection performance, the proposed methodtries to limit the influence by tuning the model (choosing theoptimal parameters) on a wide range of nodules with differentsizes, slice thickness and radiation. The experimental results onthe independent dataset demonstrate the generalizability of theproposed method.

V. CONCLUSION

This paper proposed a new approach to lung CAD by cal-culating 3-D local geometric and statistical intensity featuresfor potential solid and GGO nodule detection. The method hasbeen built in a commercial lung CAD system. The experimentalresults demonstrate the high nodule detection performance ofthe proposed algorithm, with an overall detection rate of about90.2% (including solid and GGO nodules), and FP at 8.2/scan.Despite some challenging nodules such as nonspherical, low-contrast part solid and nonsolid nodules, the detection sensitiv-ity is high with a low rate of FP regions. Most of the tissues(blood vessels, apical scarring, etc.) can be excluded as nodulecandidates. The method’s high performance for the detectionboth of solid and GGO nodules, applicability to different tubecurrents, and fast computation time shows much promise forclinical applications.

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Xujiong Ye received the Ph.D degree in electricalengineering from Zhejiang University, Hangzhou,China.

She was a Researcher in the Medical VisionLaboratory, Oxford University, Oxford, U.K. She iscurrently a Senior Researcher at Medicsight PLC,London, U.K. Her current research interests includethe area of image processing, computer vision, andmedical imaging in general with a focus on computer-aided detection.

Xinyu Lin received the Ph.D. degree in digital im-age compression from the University of CentralLancashire, Preston, U.K.

He has been working for the R&D Team, Medic-sight PLC, London, U.K., for last six years. Hiscurrent research interests include image process-ing, computer vision, data compression, and medicalimaging.

Jamshid Dehmeshki (M’01) received the Ph.D. de-gree in image processing from The University ofNottingham, Nottingham, U.K., in 1997.

From 2001 to 2006, He was CTO of Medicsight,where he was responsible for developing CAD prod-ucts with FDA clearance. He is currently a Profes-sor of medical image computing in the Faculty ofComputing, Information System and Mathematics,Kingston University, London, U.K. His current re-search interests include CAD and computer-aidedmeasurement (CAM) in medical imaging, which in-

cludes all aspects of image analysis.

Greg Slabaugh (SM’08) received the Ph.D. degreein electrical engineering from Georgia Institute ofTechnology, Atlanta, in 2002.

He has held positions at HP Laboratories andSiemens Corporate Research. He is currently theHead of Research and Development at MedicsightPLC, London, U.K. His research interests includeCAD, image segmentation, registration, computa-tional geometry, multi-view stereo, and partial dif-ferential equations.

Gareth Beddoe (M’06) received the Bachelor’s de-gree in mathematics and computer science and thePh.D. degree in computer science from the Univer-sity of Nottingham, Nottingham, U.K.

He is currently the Vice President for Technol-ogy and Product Development at Medicsight PLC,London, U.K. He is responsible for coordinating thescientific research and product development of imageanalysis tools for medical imaging applications.

Shape-Based Computer-Aided Detection of Lung Nodules in Thoracic CT Images

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Transcript of Shape-Based Computer-Aided Detection of Lung Nodules in Thoracic CT Images