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about 5 minutes for a single CT scan of 512 × 512 × 440 on. Pentium IV 2.6 GHz PC. 2. METHODS. Variational method based deformable model is a break-.

ACCURATE AND FAST 3D COLON SEGMENTATION IN CT COLONOGRAPHY Dongqing Chen1 , Rachid Fahmi1 , Aly A. Farag1 , Robert L. Falk2 , and Gerald W. Dryden3 1

Computer Vision & Image Processing (CVIP) Laboratory Department of Electrical and Computer Engineering University of Louisville, Louisville, KY, 40292 2 Department of Medical Imaging Jewish Hospital & St Mary’s Healthcare Louisville, KY, 40202 3 Division of Gastroenterology/Hepatology Department of Medicine University of Louisville, Louisville, KY, 40202

ABSTRACT This paper introduces an adaptive level set method for 3D segmentation of colon tissue in CT colonography filled with air and opacified fluid. First, most of the opacified liquid is removed by a threshold value. The closed contours are propagated toward the desired 3D region boundaries through the iterative evolution of the adaptive level sets function. The proposed method has been tested on 22 real CT colonography datasets with various pathologies, and the segmentation accuracy has achieved 98.40%. Index Terms— Colorectal cancer, CT colonography, 3D colon segmentation, adaptive level sets 1. INTRODUCTION Colorectal cancer is the second leading cause of death among cancers and the third most common form of cancer in the United States [1]. The computer aided diagnosis (CAD) for colorectal cancer screening normally consists of colon segmentation, 3D colon object reconstruction and visualization, polyp detection, feature extraction and benign/malignant polyp classification [2, 3, 4, 5]. Accurate and reliable 3D colon segmentation are important, since any incorrect segmentation, for example, missing colonic segments, containing non-colon tissue (e.g. small bowel) or reconstructing colon wall of poor quality, impairs interpretation of 3D visualization. Moreover, inaccurate 3D colon segmentation and visualization diminish the perception of polyp detection, classification and the whole performance of CAD system. The 3D colon segmentation in CT colonography (CTC), normally suffers from the following difficulties. First, CTC sometimes contains disconnected regions of the colon because collapsed segments result from different reasons such

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as colon spasm, insufficient distension, etc. Second, in clinical practice, oral contrast agent may be given to patients for CTC, however, oral contrast in colon can cause leakage into small bowel. Third, opacified liquid is generated by ingesting iodine and barium of the oral contrast, then some polyps may submerge under the liquid, which causes hard colonic polyp detection. Fourth, the segmentation accuracy and speed are greatly affected by the complicated colon structure and topology. There are several sophisticated image segmentation procedures introduced in literatures. They were mainly based on two concepts: thresholding and connectivity [6]. In tagged CT colonography, the opacified liquid is generated when iodine and barium finally enters colon and tags residual fluid. Electronic cleansing [7, 8] was a very useful technique to balance CT values in fluid-filled lumen parts and others filled with air, and to remove the contrast fluid. However, some artifacts were generated to affect image interpretation. Yoshida and N¨appi [9] designed a CAD framework to detect and classify the colonic polyps by using shape index and curvedness. The first stage of their CAD system was colon segmentation. It mainly consisted of two major steps: 1) anatomy based extraction and 2) colon based analysis. Summers et al. [6] proposed an entire framework for hybrid segmentation of colon tissue in CT colonoscopy. It achieved good segmentation results, however it consisted of eight different steps, so the average processing time was very long. For a single CT scan 512 × 512 × 400, it took 18 minutes on 1.8 GHz PC (even without I/O operations). This paper assumes a bi-model model, which classifies the colon as foreground and non-colon tissue as background. An accurate and fast 3D colon segmentation algorithm is introduced. The proposed method has been tested on 22 real CT colonography datasets, 9,621 slices in total. The average segmentation accuracy has achieved 98.40%, and it just takes

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about 5 minutes for a single CT scan of 512 × 512 × 440 on Pentium IV 2.6 GHz PC. 2. METHODS Variational method based deformable model is a breakthrough of image processing, especially in image segmentation. A famous application of curve or surface evolution is the deformable model which mainly includes the explicit deformable models (e.g. snake [10], balloon force model [11], and gradient vector flow (GVF) model [12]) and the implicit deformable models (e.g. level sets [13]). 2.1. Basic Level Sets

(a)

(b)

(c)

Fig. 1. (a) An original CTC slice, (b) after liquid removal in the middle, and (c) initial seeds selection inside the colon.  Hα (Φi )dX (6) πi = 2   Hα (Φi )dX i=1

Given a curve Γ, it can be embedded into a higher dimension function Φ as Γ = {X : Φ(X) = 0}. Then the curve is defined as the zero level of the implicit function. If we add time t to the function, curves (fronts) evolution function is changed to Φ = Φ(X, t). The surface function Φ evolves with time and then the evolution front is always represented as the zero level, so we can write the following equation as a general description:

where, X = (x, y, z) is a 3D voxel, and Hα (•) is the Heaviside step function as a smoothed differentiable version of the 2  unit step function. πi = 1.

Φ(X, t) = 0

For further details, please refer the previous work from our lab in [14].

(1)

The basic level sets function is given as follows [13]. Φt + F |∇Φ| = 0

i∗ (X) = arg(maxi=1,2 (πi pi (I(X))))

(3)

where, |∇Φ| is the norm of gradient of curve Φ. If F > 0, the original curve shrinks, while it expands when F < 0. And the curve will keep unchanged, if F = 0. Normally, F = ±1 − εκ, where, κ is the curvature, and ε is the parameter controlling the bending of the curve. 2.2. Adaptive Level Sets Technique For the bi-model model in this paper, we use Gaussian distributions for both colon (foreground) and non-colon (background). For each class i(i = 1, 2), the mean μi , variance σi2 , and the prior probability πi are updated during each iteration as follows.  Hα (Φi )I(X)dX (4) μi =  Hα (Φi )dX  Hα (Φi )(μi − I(X))2 dX 2  σi = (5) Hα (Φi )dX

(7)

3. RESULTS AND DISCUSSION

(2)

where, F is the velocity field. Under discrete case, the level sets evolution is governed by Equation 3. Φ(t + Δt) = Φ(t) − F Δt |∇Φ|

i=1

Finally, the classification decision at each pixel X is based on the Bayesian criteria as follows.

We validate the proposed method on 22 CTC datasets. One has been provided by the 3DR Inc., Louisville, KY, and the rest 21 CTC data were received from the Virtual Colonoscopy Center, Walter Reed Army Medical Center, Washington, DC. The patients underwent standard 24-hour colonic preparation by oral administration of 90 ml of sodium phosphate and 10 mg of bisacodyl; then consumed 500 ml of barium (2.1 percent by weight) for solid-stool tagging and 120 ml of Gastrografin to opacify luminal fluid [15]. A four-channel or eightchannel CT scanner was either GE LightSpeed or LightSpeed Ultra. The CT protocol included 1.25 mm to 2.5 mm collimation, 15 mm/second table speed, and 100 mAs and 120 kVp scanner settings. Each dataset contains 400 ∼ 500 slices, and the spatial resolution for is 1.0 × 1.0 × 1.0mm3 . An original CTC slice as shown in Figure 1(a) normally consists of small intestine, bone, colon lumen including air and liquid, which is generated by the high-volume oral contrast to opacify the small bowel in order to maximize imaging accuracy, etc. First, the opacified liquid is removed by using a threshold method and equalize image intensity inside colon as shown in Figure 1(b). Then four initial seeds of the 3D segmentation for the entire CTC dataset are placed totally inside the colon region, which guarantees the segmentation results. The closed contours centered at initial seeds, are propagated toward the desired 3D region boundaries through the

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(a)

(b) Fig. 5. Comparison results of inner surface by the method in [16] on the left and the proposed method on the right.

(c)

(d)

Fig. 2. An example of 3D colon segmentation by the proposed method after (a) 20, (b) 40, (c) 60 iterations, (d) final result

ison results are illustrated on the second row. Figure 5 compares the inner surfaces reconstructed by our previous work in [16], and by the proposed method in this paper. Since the previous colon segmentation was conducted slice by slice on 2D, little spital information of the neighboring slices was incorporated, then resulted in some small holes and coarse surface as shown on the left. On the other hand, the proposed method has generated smooth inner surface without any holes as shown on the right. We also evaluate the segmentation accuracy by computing the overlap between the results by manual and algorithm segmentations in 8. One CTC dataset was manually segmented under guidance of an experienced radiologist. The average accuracy of the whole CTC dataset has achieved 98.40%. η=

Fig. 3. Comparison results by 3D region growing on the left and the proposed method on the right. All the three local surface regions have been improved greatly. iterative evolution of the adaptive functions 4, 5, and 6. During each iteration, information in each region is estimated by the parameters of probability density function (PDF). Figure 2 shows how the 3D segmentation algorithm works. Figure 2 (a) and (b) show the early stage results just after 20 and 40 iterations, respectively. From the segmented results, it is clearly observed that most of the parts have not reached the desired lumen air-tissue boundaries, especially in (a), some of the colon parts are not connected due to the insufficient iterations. Compared with those in (a) and (b), the result in (c) shows that most of the colon parts have achieved the boundaries. Figure 2 (d) shows nice final results with smooth colon surface and clear haustral folders. We have compared the results by the proposed 3D colon segmentation with those by 3D region growing algorithm. From three locally zoomed-in results listed on the right in Figure 3, the colon surface generated by the proposed method has been improved greatly. More results segmented by 3D region growing are shown on the first row of Figure 4, while the corresponding compar-

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Sa ∩ Sm Sa ∪ Sm

(8)

where, Sa and Sm denote the results by manual and algorithm segmentation, respectively. The hybrid segmentation framework in [6] consisted of eight different steps, so the average processing time was very long. For a single CT scan 512×512×400, it took 18 minutes on 1.8 GHz PC (even without I/O operations). The encouraging result of the proposed method is that, on average, it only takes about 5 minutes for 3D colon segmentation for a single CT scan of 512 × 512 × 440 on Pentium IV 2.6 GHz PC. 4. CONCLUSIONS This paper describes an accurate and fast 3D colon segmentation as the basis for detection, visualization and classification of polyp. It mainly relies upon adaptive level sets technique. Compared with the segmentation results by other techniques, the proposed method generates better results with smooth surface, less error, and improved accuracy. Based on this fast segmentation algorithm, we are currently investigating whether polyp architectural features could be analyzed to generate reliable classification into benign or malignant lesion. We must conduct prospective trials to validate the clinical applicability of these methods.

Fig. 4. More comparison results by 3D region growing on the first row and the proposed method on the second row. [9] H. Yoshida and J. N¨appi, “Three-dimensional computeraided diagnosis scheme for detection of colonic polyps,” IEEE TMI, vol. 20, no. 12, pp. 1261–1274, 2001.

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