Liver Segmentation in CT Data: A SegmentationRefinement Approach

Reinhard Beichel12, Christian Bauer3??, Alexander Bornik3, Erich Sorantin4,and Horst Bischof3

1 Dept. of Electrical and Computer Engineering, The University of Iowa, USA,2 Dept. of Internal Medicine, The University of Iowa, USA,

reinhard-beichel@uiowa.edu,3 Inst. for Computer Graphics and Vision, Graz University of Technology, Austria,

4 Department of Radiology, Medical University Graz.

Abstract. Liver segmentation is an important prerequisite for planningof surgical interventions like liver tumor resections. For clinical applica-bility, the segmentation approach must be able to cope with the highvariation in shape and gray-value appearance of the liver. In this pa-per we present a novel segmentation scheme based on a true 3D seg-mentation refinement concept utilizing a hybrid desktop/virtual realityuser interface. The method consists of two main stages. First, an initialsegmentation is generated using graph cuts. Second, an interactive seg-mentation refinement step allows a user to fix arbitrary segmentationerrors. We demonstrate the robustness of our method on ten contrastenhanced liver CT scans. Our segmentation approach copes successfullywith the high variation found in patient data sets and allows to producesegmentations in a time-efficient manner.

1 Introduction

Liver cancer is one of the four most common deadly malignant neoplasms in theworld, causing approximately 618,000 deaths in 2002, according to the WorldHealth Organization5. Tomographic imaging modalities like X-ray computed to-mography (CT) play an important role in diagnosis and treatment of liver dis-eases like hepatocellular carcinoma (HCC). Deriving a digital geometric modelof hepatic (patho)anatomy from preoperative image data facilitates treatmentplanning [1]. Thus, methods for liver segmentation in volume data are neededwhich are applicable in clinical routine. In this context, several problems have tobe addressed: (a) high shape variation due to natural anatomical variation,disease (e.g., cirrhosis), or previous surgical interventions (e.g., liver segment re-section), (b) inhomogeneous gray-value appearance caused by tumors ormetastasis, and (c) low contrast to neighboring structures/organs like colon or

?? Cristian Bauer was supported by the doctoral program Confluence of Vision andGraphics W1209.

5 http://www.who.int/whr/2004/en

T. Heimann, M. Styner, B. van Ginneken (Eds.): 3D Segmentation in The Clinic:A Grand Challenge, pp. 235-245, 2007.

stomach. For practical application, segmentation must be capable of handlingall possible cases in a time-efficient manner.

Several approaches to liver segmentation have been developed so far (see[2–6] for examples). However, in summary, basic bottom-up segmentation al-gorithms frequently fail, especially in more complex cases like livers with largetumors. In addition, solely model-based approaches are problematic, because ofthe high shape variability of the liver. Very few approaches provide methods forthe refinement or editing of segmentation results.

In general, segmentation refinement approaches are very rare. For example,a tool is reported in [7] and [8] where Rational Gaussian (RaG) Surfaces areused to represent segmented objects. Segmentation errors can be corrected bymanipulation control points using a 2D desktop setup. Another tool for datadriven editing of pre-segmented images/volumes based on graph cuts or alterna-tively random walker algorithms was proposed in [9]. All approaches mentionedso far are based on 2D interaction and monoscopic desktop-based visualizationtechniques, despite the fact that 3D objects are targeted. Usually, 2D interactionmethods are not sufficient for refinement of 3D models extracted from volumetricdata sets, which is inherently a 3D task [10].

We propose a novel refinement approach to 3D liver segmentation. Based onan initial highly automated graph cut segmentation, refinement tools allow tomanipulate the segmentation result in 3D, and thus, to correct possible errors.Segmentation refinement is facilitated by a hybrid user interface, combining aconventional desktop setup with a virtual reality (VR) system. The segmentationapproach was developed for clinical application. In addition, our concept can beutilized for other segmentation tasks.

2 Methods

The proposed approach to liver segmentation consists of two main stages: ini-tial segmentation and interactive segmentation refinement. As input for the firststage, a CT volume and one or more start regions, marking liver tissue, areused. The segmentation is then generated using a graph cut approach6. In addi-tion, a partitioning of the segmentation and the background into volume chunksis derived from edge/surface features calculated from CT volume. These twotypes of output are passed on to the second stage which allows for the correc-tion/refinement of segmentation errors remaining after the first stage. Refine-ment takes place in two steps. First, volume chunks can be added or removed.This step is usually very fast, and the majority of segmentation errors occurringin practice can be fixed or at least significantly reduced. Second, after conversionof the binary segmentation to a simplex mesh, arbitrary errors can be addressedby deforming the mesh using various tools. Each of the refinement steps is fa-cilitated using interactive VR-enabled tools for true 3D segmentation inspectionand refinement, allowing for stereoscopic viewing and true 3D interaction. Since6 Note that graph cut segmentation is not used interactively, as proposed by Boykov

et al. in [11], since the behavior of graph cuts is not always intuitive.

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the last stage of the refinement procedure is mesh-based, a voxelization methodis used to generate a labeled volume [12].

2.1 Graph-Cut-based initial segmentation

An initial segmentation is generated using a graph cut [11] approach. Fromimage data, a graph G = (V,E) is built, where nodes are denoted by V andundirected edges by E. Nodes V of the graph are formed by data elements(voxels), and two additional terminal nodes, a source node s and sink nodet. Edge weights allow to model different relations between nodes (see [11] fordetails). Let P denote the set of voxels from the input volume data set V—toreduce computing time, only voxels with density values above −600 HounsfieldUnits (HU) are considered as potentially belonging to the liver. The partitionA = (A1, . . . , Ap, . . . , A|P |) with Ap ∈ {”obj”, ”bkg”} can be used to representthe segmentation of P into object (“obj”) and background (“bkg”) voxels. Let Nbe the set of unordered neighboring pairs {p, q} in set P according to the usedneighborhood relation. In our case, a 6-neighborhood relation is used to savememory. The cost of a given graph cut segmentation A is defined as E(A) =B(A)+λR(A) where R(A) =

∑p∈P Rp(Ap) takes region properties into account

and B(A) =∑

{p,q}∈N Bp,qδAp 6=Aq, with δAp 6=Aq

equaling 1 if Ap 6= Aq and 0if Ap = Aq, being boundary properties. The parameter λ with λ ≥ 0 allows totradeoff the influence of both cost terms. Using the s-t cut algorithm, a partitionA can be found which globally minimizes E(A). However, in practice a refinementof this segmentation result might be necessary to be useful for a given clinicalapplication.

Region term The region term R(A) specifies the costs of assigning a voxelto a label based on its gray-value similarity to object and backgroundregions. For this purpose, user defined seed regions are utilized. Fol-lowing the approach proposed in [13], region cost Rp(·) for a givenvoxel p is defined for labels “obj” and “bkg” as negative log-likelihoodsRp(”obj”) = −ln(Pr(Ip|”obj”)) and Rp(”bkg”) = −ln(Pr(Ip|”bkg”)) withPr(Ip|”obj”) = e−(Ip−mobj)

2/(2σ2obj) and Pr(Ip|”bkg”) = 1 − Pr(Ip|”obj”),

respectively. From a object seed region placed inside the liver, the mean mobj

and standard deviation σobj are calculated. Clearly, in the above outlined ap-proach, a simplification is made since liver gray-value appearance is usuallynot homogeneous. However, this simplification works quite well in practicein combination with the other processing steps. Further, the specified objectseeds are incorporated as hard constraints, and the boundary of the scene isused as background seeds.

Boundary term The basic idea is to utilize a surfaceness measure as boundaryterm which is calculated in four steps:1. Gradient tensor calculation: First, to reduce the effect of unrelated struc-

tures on the gradient, the gray value range of the image is adapted:

If = κ(If ) =

vlow if If < tlow

vhigh if If > thigh

If otherwise.

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Second, a gradient vector ∇f = (fx, fy, fz)T is calculated for each voxelf on the with κ gray-vale transformed data volume V by means of Gaus-

sian derivatives with the kernel gσ = 1/(2πσ2)32 e−

x2+y2+z2

2σ2 and standarddeviation σ. The gradient tensor S = ∇f∇fT is calculated for each voxelafter gray-value transformation.

2. Spatial non-linear filtering: To enhance weak edges and to reduce falseresponses, a spatial non-linear averaging of gradient tensors is applied.The non-linear filter kernel consists of a Gaussian kernel which is modu-lated by the local gradient vector ∇f . Given a vector x that points fromthe center of the kernel to any neighboring voxel, the weight for this voxel

is calculated as: hσ′,ρ(x,∇f) =

1N e−

r2σ′2 e

− tan(φ)2

2ρ2 if φ 6= π2

0 if φ = π2 and r = 0

1N otherwise

,

with r = xT x and φ = π2 − | arccos(∇fT x/(|∇f ||x|))| . Parameter ρ de-

termines the strength of orientedness, and σ′ determines the strengthof punishment depending on the distance. N is a normalization factorthat makes the kernel integrate to unity. The resulting structure tensoris denoted as W.

3. Surfaceness measure calculation: Let e1W(x) , e2W(x) , e3W(x) be the eigen-vectors and λ1W(x) ≥ λ2W(x) ≥ λ3W(x) the corresponding eigenvalues ofW(x) at position x. If x is located on a plane-like structure, we canobserve that λ1 � 0, λ2 ≈ 0, and λ3 ≈ 0. Thus, we define the surface-ness measure as t(W(x)) =

√λ1W(x) − λ2W(x) and the direction of the

normal vector to the surface is given by e1W(x) .4. Boundary weight calculation: In liver CT images, objects are often sepa-

rated only by weak boundaries, with higher gray level gradients present inclose proximity. To take these circumstances into account, we propose thefollowing boundary cost term Bp,q = min{ξ (t(W(xp))) , ξ (t(W(xq)))}

with the weighting function ξ(t) =

c1 if t < t1c2 if t > t2(t− t1) c2−c1

t2−t1+ c1 otherwise

which

models a uncertainty zone between t1 and t2 (note: t1 < t2 and c1 > c2).Ideally, the graph cut segmentation should follow the ridges of the gra-dient magnitude. Therefore, we punish non-maximal responses in thegradient magnitude volume by adjusted the weighting function as fol-lows: ξnon max(t) = min{ξ(t) + cnm, 1}, where cnm is a constant.

2.2 Chunk-based Segmentation Refinement

After initial segmentation, objects with a similar gray-value range in close prox-imity can appear merged or tumors with different gray-value appearance mightbe missing. Therefore, a refinement may be needed in some cases. The firstrefinement stage is based on volume chunks, which subdivide the graph cut seg-mentation result (object) as well as the background into disjunct subregions.

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(a) (b) (c) (d)

Fig. 1. Mesh-based refinement using a sphere deformation tool. In this case the seg-mentation error is a leak. (a) Marking the region containing the segmentation error.(b) Refinement using the sphere tool. (c) After pushing the mesh surface back to thecorrect location with the sphere tool, the error is fixed. (d) The corrected region inwire frame mode highlighting the mesh contour.

Fig. 2. Initial graph cut (GC) segmentation results. From left to right, a sagittal,coronal and transversal slice from a relatively easy case (1, top), an average case (4,middle), and a relatively difficult case (3, bottom). The outline of the reference standardsegmentation is in red, the outline of the segmentation of the method described in thispaper is in blue. Slices are displayed with a window of 400 and a level of 70.

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Thus, the initial segmentation can be represented by chunks and it can be al-tered by adding or removing chunks.

By thresholding t(W), a binary boundary volume (threshold tb) representingboundary/surfaces parts is generated and merged with the boundary from thegraph cut segmentation by using a logical “or” operation. Then the distancetransformation is calculated. Inverting this distance map results in an image thatcan be interpreted as a height map. To avoid oversegmentation, all small localminima resulting from quantization noise in the distance map are eliminated.

Applying a watershed segmentation to the distance map results in volumechunks. Since boundary voxels are not part of the chunks, they are mergedwith the neighboring chunks containing the most similar adjacent voxels. Sincethe method can handle gaps in the edge scene, the threshold tb can be setvery conservatively to suppress background noise. Refinement can be done veryefficiently, since the user has to select/deselect predefined chunks, which doesnot require a detailed border delineation. This step requires adequate tools forinteractive data inspection and selection methods. For this purpose, a hybriduser interface was developed, which is described in Section 2.4.

2.3 Simplex-Mesh-based Refinement

After the first refinement step, selected chunks are converted to a simplex meshrepresentation. Different tools allow then a deformation of the mesh represen-tation. One example is shown in Fig. 1. More details regarding this mesh-basedrefinement step can be found in [14].

2.4 Hybrid Desktop/Virtual Reality User Interface

To facilitate segmentation refinement, a hybrid user interface consisting of adesktop part and a virtual reality (VR) part was developed (see [10] for details).It allows to solve individual refinement tasks using the best suited interactiontechnique, either in 2D or 3D. The VR system part provides stereoscopic visu-alization on a large screen projection wall, while the desktop part of the systemuses a touch screen for monoscopic visualization.

3 Data and Experimental Setup

For evaluation of the segmentation approach, ten liver CT data sets with undis-closed manual reference segmentation were provided by the workshop organizers.Segmentation results were sent to the organizers, which provided in return evalu-ation results7. For all the experiments, the following parameters have been used:Gaussian derivative kernel: σ = 3.0; non-linear filtering: σ′ = 6.0, ρ = 0.4; graphcut: λ = 0.05; weighting function: t1 = 2.0, t2 = 10.0, c1 = 1.0, c2 = 0.001,ccm = 0.75; Threshold for chunk generation: tb = 10.0; gray-value transforma-tion: tlow = −50, vlow = −150, thigh = 200, and vhigh = 60. To simulate clinical7 See http://mbi.dkfz-heidelberg.de/grand-challenge2007/sites/eval.htm for details.

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work-flow, the initial seed regions were provided manually and the graph cut seg-mentation as well as the chunk generation was calculated automatically. Basedon the initial segmentation, a medical expert was asked to perform: (a) chunk-based (CBR) and (b) mesh-based refinement (MBR). Intermediate results andtask completion times were recorded. Prior to evaluation, the expert was intro-duced to the system by an instructor.

Fig. 3. Chunk-based segmentation refinement (CBR) results. From left to right, a sagit-tal, coronal and transversal slice from a relatively easy case (1, top), an average case (4,middle), and a relatively difficult case (3, bottom). The outline of the reference stan-dard segmentation is in red, the outline of the segmentation of the method describedin this paper is in blue. Slices are displayed with a window of 400 and a level of 70.

4 Results

Table 1 summarizes segmentation metrics and corresponding scores for the initialgraph cut segmentation (Table 1(a)), CBR (Table 1(b)), and MBR (Table 1(c)).The averaged performance measures and scores clearly show the effectiveness

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of the segmentation refinement concept: metrics and scores improve with eachrefinement stage. For example, after the initial graph cut segmentation, fivecases have an overlap error larger than 10 %, and the over-all average is 14.3 %.Using CBR, the average overlap error was reduced to 6.5 %, and reached 5.2 %after the final MBR stage. The average time needed for seed placement is lessthan 30 seconds. For the CBR step 58 seconds were required on average, andthe MBR step took approximately five minutes on average. Despite the low timeconsumption of the CBR step, it is quite effective regarding segmentation qualityimprovement and delivers already a good segmentation result. Computation timefor the graph cut segmentation and chunk generation was approximately 30minutes per data set, which is not critical for our application.

Fig. 4. Mesh-based segmentation refinement (MBR) results. From left to right, a sagit-tal, coronal and transversal slice from a relatively easy case (1, top), an average case (4,middle), and a relatively difficult case (3, bottom). The outline of the reference stan-dard segmentation is in red, the outline of the segmentation of the method describedin this paper is in blue. Slices are displayed with a window of 400 and a level of 70.

In comparison, averages for the performance measures determined from anindependent human segmentation of several test cases yielded: 6.4 % volumetric

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overlap; 4.7 % relative absolute volume difference; 1.0 mm average symmetricabsolute surface distance; 1.8 mm symmetric RMS surface distance; 19 mmmaximum symmetric absolute surface distance8. Thus, our refinement results(CBR and MBR) are within the observed variation range (see Table 1).

Figs. 2, 3, and 4 depict a comparison of reference and actual segmentation forthe initial graph cut, CBR, and MBR for three different data sets. Because of theformulation of the initial graph cut segmentation, larger tumors are not includedin the segmentation result, as shown in the third row of Fig. 2. However, thiscan be easily fixed during the CBR stage (Fig. 3). Remaining errors can then befixed in MBR stage. The examples show that the average maximum symmetricabsolute surface distance of 15.7 mm on average can be explained by differencesin the interpretation of the data in regions where vessels enter or leave the liver.

5 Discussion

For our experiments, we have used a full-blown VR setup which is quite expen-sive. However, a fully functional scaled-down working setup can be built for areasonable price, comparable to the costs of a radiological workstation.

Several experiments with different physicians have shown that the system canbe operated after a short learning phase (typically less that one hour), because ofthe intuitive 3D user interface. The proposed refinement method can also easilybe integrated into clinical work-flow. The CT volume together with the manualgenerated start region is sent by a radiology assistant to a computing node whichperforms the automated segmentation steps. As soon as a result is available, aradiologist is notified that data are ready for further processing. After inspection,possible refinement, and approval of correctness, the segmentation can be usedfor clinical investigations or planning of treatment.

A previous independently performed evaluation with twenty routinely ac-quired CT data sets of potential liver surgery candidates yielded a comparablesegmentation error. However, more time was needed for interactive refinement.This has several reasons: lower data quality (more partial volume effect, motionblur due to cardiac motion, etc.), more severely diseased livers with larger tu-mors or multiple tumors, and more focus on details (e.g., consistently excludingthe inferior vena cava). These observations lead to the following conclusions.First, the used imaging protocol impacts the time needed for segmentation re-finement, and thus, should be optimized. Second, the developed method allowsthe user to adjust the level of detail according to the requirements in trade-offwith interaction time.

6 Conclusion

In this paper we have presented an interactive true 3D segmentation refinementconcept for liver segmentation in contrast-enhanced CT data. The approach con-sists of two stages: initial graph cut segmentation and interactive 3D refinement.8 The values reported were provided by the workshop organizers.

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(a) Graph Cut (GC)

Dataset Overlap Error Volume Diff. Avg. Dist. RMS Dist. Max. Dist. Total[%] Score [%] Score [mm] Score [mm] Score [mm] Score Score

1 17.9 30 10.7 43 4.8 0 10.9 0 67.9 11 172 18.2 29 16.5 12 3.3 19 8.6 0 54.1 29 183 35.2 0 20.3 0 11.2 0 22.2 0 92.3 0 04 8.4 67 1.3 93 1.6 61 3.8 47 43.3 43 625 7.0 73 1.8 90 1.2 69 2.7 62 27.8 63 726 5.7 78 -1.4 92 1.0 76 2.5 65 27.5 64 757 12.2 52 0.7 96 5.3 0 11.3 0 61.6 19 338 7.7 70 -1.6 92 1.6 59 4.3 40 45.9 40 609 7.5 71 -0.0 100 2.2 46 5.4 25 31.9 58 60

10 23.0 10 -17.9 5 3.4 14 7.3 0 39.7 48 15Average 14.3 48 3.1 62 3.6 34 7.9 24 49.2 38 41

(b) Chunk-based Refinement (CBR)

Dataset Overlap Error Volume Diff. Avg. Dist. RMS Dist. Max. Dist. Total[%] Score [%] Score [mm] Score [mm] Score [mm] Score Score

1 8.2 68 2.5 87 2.0 49 5.4 24 47.9 37 532 6.2 76 3.0 84 0.9 78 1.8 75 17.9 76 783 7.1 72 3.2 83 1.6 61 3.5 51 34.7 54 644 6.7 74 -0.5 97 1.2 69 2.5 66 25.2 67 755 6.4 75 1.9 90 1.1 72 2.4 67 21.5 72 756 5.0 80 0.4 98 0.7 81 1.6 78 17.2 77 837 5.4 79 2.2 88 0.8 80 1.5 79 13.0 83 828 7.1 72 -1.2 94 1.1 72 2.5 65 20.2 73 759 5.1 80 2.2 88 0.6 85 1.2 83 16.8 78 83

10 8.0 69 -2.4 87 1.2 71 2.2 69 19.2 75 74Average 6.5 74 1.1 90 1.1 72 2.5 66 23.4 69 74

(c) Mesh-based Refinement (MBR)

Dataset Overlap Error Volume Diff. Avg. Dist. RMS Dist. Max. Dist. Total[%] Score [%] Score [mm] Score [mm] Score [mm] Score Score

1 5.3 79 2.3 88 0.8 80 1.5 79 15.9 79 812 5.5 79 1.9 90 0.8 81 1.4 81 17.9 76 813 4.1 84 1.5 92 0.8 80 1.3 82 14.2 81 844 6.4 75 1.0 95 1.1 72 2.1 70 21.0 72 775 5.4 79 0.1 99 0.9 78 1.7 77 19.2 75 816 4.1 84 -0.9 95 0.6 85 1.1 85 12.6 83 867 4.4 83 2.5 87 0.6 85 1.1 85 12.5 84 858 5.7 78 1.7 91 0.9 77 1.8 76 17.1 77 809 4.2 84 2.4 87 0.5 88 0.8 88 16.8 78 85

10 6.6 74 -2.8 85 0.9 77 1.5 79 9.6 87 80Average 5.2 80 1.0 91 0.8 80 1.4 80 15.7 79 82

Table 1. Results of the comparison metrics and corresponding scores for all ten testcases and processing steps (see Section 4 for details).

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The evaluation of our method on ten test CT data sets shows that a high seg-mentation quality (mean average distance of less than 1 mm) can be achieved byusing this approach. In addition, the interaction time needed for refinement isquite low (approx. 6.5 minutes). Thus, the presented refinement concept is wellsuited for clinical application. The approach is not limited to a specific organor modality, and therefore, it is very promising for other medical segmentationapplications.

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