Two Methods of Haustral Fold Detection from Computed Tomographic Virtual Colonoscopy Images Ananda S. Chowdhury1, Sovira Tan, Jianhua Yao, Marius G. Linguraru and Ronald M. Summers2 Department of Radiology and Imaging Sciences, National Institutes of Health Clinical Center Building 10, Room 1C368X, Bethesda, MD 20892- 1182, USA. ABSTRACT Virtual colonoscopy (VC) has gained popularity as a new colon diagnostic method over the last decade. VC is a new, less invasive alternative to the usually practiced optical colonoscopy for colorectal polyp and cancer screening, the second major cause of cancer related deaths in industrial nations. Haustral (colonic) folds serve as important landmarks for virtual endoscopic navigation in the existing computer-aided-diagnosis (CAD) system. In this paper, we propose and compare two different methods of haustral fold detection from volumetric computed tomographic virtual colonoscopy images. The colon lumen is segmented from the input using modified region growing and fuzzy connectedness. The first method for fold detection uses a level set that evolves on a mesh representation of the colon surface. The colon surface is obtained from the segmented colon lumen using the Marching Cubes algorithm. The second method for fold detection, based on a combination of heat diffusion and fuzzy c-means algorithm, is employed on the segmented colon volume. Folds obtained on the colon volume using this method are then transferred to the corresponding colon surface. After experimentation with different datasets, results are found to be promising. The results also demonstrate that the first method has a tendency of slight under-segmentation while the second method tends to slightly over-segment the folds. Keywords: Haustral folds, computer-aided-diagnosis, computed tomography, virtual colonoscopy.

1. INTRODUCTION Colon cancer is the second leading cause of cancer-related deaths in industrial nations [1]. Virtual colonoscopy (VC) is a new, less invasive alternative to the usually practiced optical colonoscopy for colorectal polyp and cancer screening [2]. The purpose of this work is to robustly detect the haustral folds throughout the entire colon to enhance the effectiveness of the existing computer-aided-diagnosis (CAD) system for VC. Proper identification of haustral folds [3-4] can be used for many subsequent important tasks like prone-supine registration, better colonic polyp detection and tenia coli extraction [5-7]. In this work, two different methods for fold detection are presented. The first method (henceforth denoted as method I) employs level sets to detect the hasutral folds on colon surface. The second method (henceforth denoted as method II) uses a combination of heat diffusion and Fuzzy C-Means (FCM) clustering to locate the haustral folds on colon volume. The folds are then mapped on the corresponding colon surface. We then qualitatively and quantitatively compare the fold detection results on colon surface for the two proposed methods. The rest of the paper is organized in the following way: in section 2, we describe the two proposed methods for fold detection. In section 3, we discuss the experimental results. The paper is concluded in section 4 with an outline of future research directions.

2. METHODS In this section, we describe the two proposed methods in some details. In the first sub-section, we briefly explain the image preprocessing. In the second sub-section, we describe fold detection based on evolution of level sets. In the third sub-section, we depict how a combination of heat diffusion and FCM can be employed for fold detection.

1 2

E-mail: [email protected] E-mail: [email protected] Medical Imaging 2009: Computer-Aided Diagnosis, edited by Nico Karssemeijer, Maryellen L. Giger Proc. of SPIE Vol. 7260, 72602U · © 2009 SPIE · CCC code: 1605-7422/09/$18 · doi: 10.1117/12.811031

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2.1 Preprocessing The input to our problem is volumetric computed tomographic virtual colonoscopy images. The colon lumen is first segmented from the input. The segmentation is performed using modified region growing and fuzzy connectedness [8]. The centerline of the colon is extracted using level sets [9]. The centerline is later used for flattening the colon surface. The flattening facilitates better visualization of folds compared to that on the unflattened surface. 2.2 Fold detection using level sets The segmented colon is further processed to extract its surface using the Marching Cubes algorithm. The surface represented as a triangular mesh is smoothed using a Laplacian method. A level set technique (Geodesic Active Contour) capable of evolving on a 3D mesh [10] is then applied on the smoothed colon surface. The level set we chose to implement is the Geodesic Active Contour (GAC) which evolves according to [11]:

dψ = αgc ∇ψ + βgκ ∇ψ + γ∇g∇ψ dt

(1)

r

The evolving contour is encoded as the zero level set of the distance function ψ ( x, t ) . The first term on the right-hand side of the Equation (1) is the propagation term that makes the contour move with velocity c. The second is the curvature term which controls the smoothness of the contour using the mean curvature κ . The third term, the advection term, was

introduced by Caselles et al. [11] to lock the contour to the boundary. The parameters α , β and γ weight the importance of each term. For the segmentation of haustral fold ridges, an appropriate speed function, based on the Shape Index (SI) and curvedness (CV) features [12], is designed. Mathematically, the speed function can be written as a combination of two sigmoids:

g (V ) = g SI (V )g CV (V )

(2)

where g (V ) is the function which attributes a speed value at each vertex V . The terms g SI (V ) and g CV (V )

respectively denote the contribution of shape index and curvedness. In g SI (V ) the sigmoid function is employed to attribute maximum speed to ridge-like vertices. We make the level set stop at the fold/colon wall boundary (saddle/rut shape) by having the sigmoid function progressively attribute lower speed values to the SI corresponding to saddle and rut. Because haustral fold ridges are more curved than the colon wall, the sigmoid in g CV (V ) is made to assign higher speed to vertices with higher CV values. The method requires correct initial seeds to evolve the contour. The seeds are selected from prior clustering of ridge-like vertices based on a simple blob-labeling technique. However a size threshold (50 vertices) needs to be chosen to avoid putting seeds in noisy non-fold areas. 2.3 Fold detection using diffusion-FCM For the second method, the haustral folds are detected on the segmented colon volume. A combination of heat diffusion and FCM algorithm is employed for this purpose. Any voxel inside the segmented colon is treated as a ‘hot’ voxel and any voxel outside the segmented colon is treated as a ‘cold’ voxel. The segmented colon is set to a constant temperature (= 1) and the background is set to a constant temperature (= 0). This segmented colon is then allowed to cool down [13]. The temperature diffuses across the colon boundary and fills in the fold spaces after certain time. Perona-Malik’s gradient anisotropic diffusion is employed [14] to generate such candidate voxels for folds, which also includes voxels surrounding the edges. The heat diffusion equation is given by:

∂θ (r , t ) ∂t = ∇ ⋅ D∇θ (r , t ) where

θ (r , t ) represents the temperature at position r = r ( x, y, z )

(3)

and time t and D is the diffusion coefficient.

FCM algorithm [15] is applied next to classify the set of voxels into folds and non-folds. This voxel classification is done in the two-dimensional feature space, constituted by the number of ‘hot’ (having temperature > 0.9) and the number of ‘cold’ (having temperature < 0.0001) neighbors. Number of clusters C for the present problem is 2; one corresponds to

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the fold and the other to the non-fold. Let uij ∈ [0,1] be the membership of a voxel vj to belong to cluster ci. Then, uij is given by [16]:

(

⎛ C uij = ⎜ ∑ v j − ci ⎝ k =1

v j − ck

)

2 /( m −1)

⎞ ⎟ ⎠

−1

(4)

where 1 < i < C and 1 < j < Q. Let U be the fuzzy partition matrix and V be the cluster center vector. Label filtering, based on concept of connected pixels labeling, is employed next to isolate some misclassified voxels to further improve the above clustering process [17]. Finally, folds detected on colon volume are transferred to the corresponding surface for the purpose of comparison. We use over-segmentation (criterion: >25% of the area between two folds is detected) and under-segmentation (criterion: <75% of a fold area is detected) to evaluate the performance of the proposed fold-detection methods.

3. EXPERIMENTAL RESULTS We have experimented with six different datasets with varying image dimensions as well as different image resolutions. As mentioned earlier in the paper, all the inputs are volumetric computed tomographic virtual colonoscopy images. The values of different parameters for the discussed methods are chosen experimentally. These values, once properly selected, are kept the same for all the datasets. This level set technique is run for 60 iterations. The values of the three

β

γ

and in equation (1) are chosen as 1.0, 1.0 and 2.0 respectively. For the diffusion part, the parameters α , conductance parameter and time step are selected as 3.0 and 0.0625 respectively in the ITK implementation [18]. The numbers of iterations used for the diffusion are 15 and 17. The FCM algorithm is executed until the fuzzy membership difference for all voxels under consideration falls below 0.1 in two successive iterations. We first present the images of fold detection on three of the six datasets. Folds detected using method I are shown in figures 1(A), 2(A) and 3(A) respectively. Folds obtained from method II, for the same three datasets are shown in figures 1(B), 2(B) and 3(B) respectively. Note that all the processing is done on the original 3D colon space. The results in all the figures 1, 2 and 3 are presented on the 2D colon space for better visualization purpose. The colon unfolding is achieved by employing a chord length parameterization approach [19].

(A)

(B) Fig. 1. Results of haustral fold detection (shown in blue) on a flattened colon surface (shown in red) using two different methods for dataset 6. (A) Level Set-based method, (B) Gradient Anisotropic Diffusion-FCM based method (no. of iterations for diffusion = 15).

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(A)

(B) Fig. 2. Results of haustral fold detection (shown in blue) on a flattened colon surface (shown in red) using two different methods for dataset 5. (A) Level Set-based method, (B) Gradient Anisotropic Diffusion-FCM based method (no. of iterations for diffusion = 15).

(A)

(B) Fig. 3. Results of haustral fold detection (shown in blue) on a flattened colon surface (shown in red) using two different methods for dataset 4. (A) Level Set-based method, (B) Gradient Anisotropic Diffusion-FCM based method (no. of iterations for diffusion = 15).

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From the three pairs of images (figures 1, 2 and 3), it is evident that both the methods have detected the haustral folds fairly well. We next present a table (table 1), where we show a quantitative performance evaluation of the two methods in terms of number of over-segmented and number of under-segmented/missed folds. Table. 1. Performance measure for fold detection using method I and method II.

Dataset

No. of undersegmented/missed folds using method I

No. of oversegmented folds using method I

No. of undersegmented/missed folds using method II (# iterations for diffusion = 15)

No. of oversegmented folds using method II (# iterations. for diffusion = 15)

1

8

1

5

5

2

21

3

3

6

3

12

2

9

5

4

29

1

1

12

5

16

1

4

13

6

20

0

6

8

Table 1 demonstrates that method I, on average, under-segments/misses 18 folds and over-segments 2 folds. In contrast, method II, on average, under-segments/misses 5 and over-segments 8 folds. Thus, we notice a definitive pattern in the two fold detection methods. Method I has a tendency of under-segmentation and method II gives an impression of oversegmentation. We now present another table showing the impact of variation of number of iterations for diffusion on fold detection. Table. 2. Impact of variation in iteration for diffusion on fold detection

Dataset

No. of undersegmented/missed folds (# iteration for diffusion = 15)

No. of oversegmented folds (# iteration for diffusion = 15)

No. of undersegmented/missed folds (# iteration for diffusion = 17)

No. of oversegmented folds (# iteration for diffusion = 17)

1

5

5

0

26

2

3

6

2

8

3

9

5

5

9

4

1

12

1

17

5

4

13

2

16

6

6

8

2

15

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With an increase in the number of iterations for diffusion, we see an increase in the over-segmentation and a decrease in the under-segmentation of folds. Particularly, average number of under-segments/misses gets reduced from 5 to 2 folds while average number of over-segmentation gets increased from 8 to 15 folds when the number of iterations for diffusion is increased from 15 to 17. This behavior can be explained in the following manner. With an increase in number of iterations, there is an increase in amount of diffusion. Consequently, more voxels are identified as possible fold candidates and eventually classified as ‘folds’ by the FCM algorithm. We finally present a section of unflattened colon and show the limitations of the proposed methods in an image pair with folds detected using method I (figure 4(A)) and II (figure 4(B)) respectively.

Under-segmented Folds (A)

Over-segmented Folds

(B) Fig. 4. Some limitations of haustral fold detection, on parts of an unflattened colon using the proposed methods. (A) Level Set-based method showing under-segmented folds, (B) Gradient Anisotropic Diffusion-FCM based method showing over-segmented folds.

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The green circle in figure 4(A) shows a fold missed by method I. In contrast, the green circle in figure 4(B) illustrates the same fold over-segmented by method II. We end this section with some explanations on the under-segmentation issue of method I and the over-segmentation issue of method II. A size threshold needs to be chosen for the level setbased method I to avoid putting seeds in noisy non-fold areas. When this threshold is set so that no false folds are seeded some true folds are also missed resulting in under-segmentation. For the method II, the diffusion component generates folds as well as non-fold voxels. The FCM algorithm then properly identifies the true fold voxels. However, it also misclassifies some non-fold voxels as fold voxels, which results in the over-segmentation.

4. CONCLUSION AND FUTURE SCOPE We presented in this paper two different approaches for fold detection in human colon. In method I, a level set technique (Geodesic Active Contour) is applied on the colon surface for detection of haustral folds. A novel speed function, based on shape index and curvedness is designed for that purpose. The second method uses a novel combination of physicsbased modeling (heat diffusion) and a pattern clustering technique (fuzzy c-means algorithm). Both the methods extracted the haustral folds reasonably well. However, it is observed that the level set-based method suffers from the problem of under-segmentation while the “heat diffusion plus fuzzy c-means” -based method has a problem of oversegmentation. As part of a future work, we plan to implement a synergistic combination of the two methods to further improve the fold detection results. Colonic folds can improve the existing CAD system by identifying colonic polyps, registering the prone-supine scans and detecting tenia. Another direction of future research will focus on the application of fold detection for solving these above-mentioned problems.

ACKNOWLEDGEMENT This research was supported by the Intramural Research Program of the NIH Clinical Center. We thank Dr. Perry Pickhardt, Dr. J. Richard Choi, and Dr. William Schindler for providing CT colonography data.

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