Relational and Spatial 3D Visualisation with Dental Cone Beam CT Images. Ma Tengfei 1, Ong Sim Heng 2

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1 Relational and Spatial 3D Visualisation with Dental Cone Beam CT Images Ma Tengfei 1, Ong Sim Heng 2 Department of Electrical & Computer Engineering National University of Singapore, 10 Kent Ridge Crescent, Singapore ABSTRACT Clinicians can scroll through regions of 2D anatomy in three visual planes at 90 degrees to one another using viewing software. Different degrees of tissue transparency may be used to display surface and internal anatomy. However, the problem is that the spatial relationship of internal anatomic air spaces bone cannot be visualized in 3D. In this project, we present a level set algorithm to segment the maxillary sinuses (left and right) from cone beam computed tomography (CBCT) images and use the segmented slices to reconstruct the 3D volume images. BACKGROUND The maxillary sinuses are located beneath the cheeks, above the teeth and on either sides of the nose. The maxillary sinuses (Fig. 1) drain into the nose through a hole located about half way up the side of the sinus wall. Cone beam computed tomography (CBCT) images can be used to view the sinuses. Segmentation of the sinuses followed by 3D visualization will assist the clinician in diagnosis and treatment planning. APPROACH Region Growing: We attempted to segment the slices using region growing. The following algorithm is used. First, construct the image of the same size containing only 1 s and 0 s. As there are only two regions to grow, there are initially only two 1 s and the other pixels are labelled 0. Second, construct two arrays of the same size as the image. One is for pixels that have already been grouped in the region while the other is for border information. In region 1, assign the border value of 1. In region 2, assign the border value of 2. Third, scan the entire image and update the information for the mean, sum and the number of pixels in the region. Finally, add a pixel (using 8-connectivity) to the region if it satisfies the criterion mean pixel value threshold value. It is obvious from Fig. 2 that the boundaries are not smooth using region-growing. When applied to the image with greater noise, the segmentation result is worse. Region growing is not stable when the image is noisy inside or at the boundaries. It also results in boundaries that are not smooth. The criteria used in the region growing is not adaptive. A global threshold value for determing whether regions to grow or not is also not reliable. 1 Student 2 Associate Professor 1

2 Fig.1: (a) maxillary sinus anatomy; one slice of through the maxillary sinus. (a) (c) (d) Fig.2: (a) Segmentation result using region growing on less noisy image; segmentation result using region growing on noisy image; (c) zoomed-in view on maxillary sinus region in (a); (d) zoomed-in view on maxillary sinus region in. 2

3 Level Set Method Geometric active contours have been proposed by Kass et al. [1] and Xu and Prince [2]. In implementing the traditional level set methods, it is necessary to keep the evolving level set function close to a signed distance function: φ = sign ( φ 0 )(1 φ ) (1) t In Li et al. s approach [3] the level set algorithm without re-initialization solves this difficult task and it involves the energy aspect. That energy functional consists of internal energy and external energy terms. The internal energy item penalizes the deviation of the level set function from a signed distance function, whereas the external energy term drives the motion of the zero level set to the desired image features such as object boundaries. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. In the project, we followed [3] in implementing the level set function: εg, λν,( φ) = λlg( φ) + νag( φ) (2) where ε is the external energy, λ > 0 and ν are constants, L ( φ ) is the length term, A ( φ ) is the area term, g is the edge indicator, and φ φ φ = μ [ Δφ div( )] + λδ ( φ ) div g + ν g ( ) t φ φ δ φ (3) When implementing Eq. (3), we should consider the Neumann boundary condition that the normal component of the gradient is specified at each point of the boundary. Comparison Between Level Set and Region Growing To clearly see why we choose the level set instead of region growing, we concentrate on two major aspects: the smoothness of the curve and the robustness. Comparing Figs. 3(a) and, we see the boundaries of the result obtained using the level set method are smoother. Comparing Figs. 3(c) and (d), region growing fails to segment when there is much noise present in the image. The main reason is that level set always evolves in the energy-minimizing direction. Though noise is present, it should not affect much of the result. RESULTS AND DISSCUSION Different Parameters in Level Set Time step: A larger time-step can make the evolution faster but may give rise to a false location of the curve. Increasing the time step can reduce the number of iterations but result in less accurate boundaries. It is always applicable to choose time step less than 10 and bigger than 1 to most images. Weighted length term λ : λ cannot be made so large since it significantly determines the shape (the length) in the curve evolution. To see this result clearly, use λ =6 and λ =16 for comparing. Weighted area term ν : The larger the value of ν, the faster it grows towards the actual shape. A negative value means that the curve is expanding while a positive value means that the curve is shrinking. If ν is small, the curve is not fully expanded; if ν is too big, the curve bends inward and incorrectly traces the boundaries. g g 3

4 (c) (d) Fig.3 : (a) Region growing on an image with less noise; level set on image with less noise; (c) region growing on noisy image; (d) level set segmentation result on noisy image. Robust Parameter Set From the experiment, we confined our test within the following limits: for 4 ν 1, step = 0.3; for 2 ν 7, step = 0.5. We applied the algorithm and plotted the area and length with respect to the two parameters. For the purpose of comparsion, we used a standard template (i.e., the parameters we used to achieve the best result; with ν = 1.5, λ = 5, the area of the best segmentated result was 9005 and the perimeter was 520. The results are shown in Figs. 4 to 6. We than tried different parameter combinations on segmentating the same slice and plotted the area and perimeter to obtain the plots in Figs. 7 and 8. The error here is defined as the absolute difference between the experimented one and the standard value chosen earlier. From the experiment, we located the following robust parameter set ( λ, ν ) is (-1.5:-1.3, 3.5:5) and (-3.4:1.6, 6:7), but the result is only suitable for the particular slice set we want to segment. In other words, given another slice set, if we do not change the time step and iteration, the stable set here may not be appropriate because different slice sets differ in the noise level. The final result is based on the segmented slices, and the 3D volume is constructed. To help the viewer see more clearly, we cut the volume in the x, y, z directions and use the overlay function to display the segmented result (Fig. 9). 4

5 Fig. 4: (a) Segmentation result using time step 2, iteration 600, λ =5, ν =-1.5; Segmentation result using time step 20, iteration 200, λ =5, ν =-1.5. (a) Fig. 5: (a) Segmentation result using time step 2, iteration 200, λ =16, ν =-1.5; Segmentation result using time step 2, iteration 200, λ =6, ν =-1.5. (a) Fig. 6: (a) Segmentation results using time step 2, iteration 200, λ =6, ν =-5; Segmentation result using time step 2, iteration 200, λ =6, ν =

6 (c) (d) Fig. 7: (a) Plot of object area and ν ( λ =5); plot of total perimeter and ν ( λ =5), (c) plot of object area and λ ( ν =-1.5); (d) plot of total perimeter and λ ( ν =-1.5). In all the experiments, number of iteration=1000, time step=2. (a) Fig. 8: (a) Area error with respect to both λ and ν ; Perimeter error with respect to λ and ν. 6

7 (c) (d) (e) (f) Fig. 9: (a) z cut of the final visualization; x cut of the final visualization; (c) y cut of the final visualization; (d) front view of the reconstructed result; (e) top view of the reconstructed result; (f) back view of the reconstructed result. 7

8 CONCLUSION Using level set methods to segment is more robust than using region growing methods. It is expressed in energy functional that consists of an internal energy term and an external energy term respectively. The internal energy item penalizes the deviation of the level set function from a signed distance function, whereas the external energy term drives the motion of the zero level set to the desired image features. The resulting evolution of the level set function is the gradient flow that minimizes the overall energy functional. λ, ν which are the coefficient of the length and the area term of the level set, respectively, play an important role on the evolution of the curve and therefore determines the segmentation result. Using the 200 segmented slices, we are able to build the 3D volume which has enabled the clinician to visualize the spatial relationship of internal anatomic air spaces bounded by internal bone with the external bone surface within the maxillary bone. References [1] M Kass, AWitkin, and D Terzopoulos, Snakes: active contour models, Int. J. Comp. Vis., vol. 1, pp , [2] C Xu and J Prince, Snakes, shapes, and gradient vector flow, IEEE Trans. Image Proc., vol. 7, pp , [3] CM Li, C Xu, CF Cui, MD Fox, Level set evolution without re-initialization: A New Variational Formulation, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition [4] L Evans, Partial Differential Equations, Providence: American Mathematical Society,

Level Set Evolution Without Re-initialization: A New Variational Formulation

Level Set Evolution Without Re-initialization: A New Variational Formulation Chunming Li 1, Chenyang Xu 2, Changfeng Gui 3, and Martin D. Fox 1 1 Department of Electrical and 2 Department of Imaging 3