3D Surface Reconstruction of the Brain based on Level Set Method

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1 3D Surface Reconstruction of the Brain based on Level Set Method Shijun Tang, Bill P. Buckles, and Kamesh Namuduri Department of Computer Science & Engineering Department of Electrical Engineering University of North Texas 55 Union Circle # 3366 Denton, TX 763 USA Abstract - In this paper, a new method for 3D surface reconstruction of the brain is presented. The approach is based on the level set method. The 3D visual surface of the brain can be displayed accurately and quickly. Different with 3D model from MC (marching-cubes) algorithm, the results from the proposed method has many specific characteristics, such as direct, convenient and transparent. Keywords: level set method, segmentation, magnetic resonance imaging, 3D surface reconstruction Introduction Computed Tomography (CT) and Magnetic Resonance (MR) have been widely applied to diagnose various diseases. The images (CT and MRI) provide much D information. Yet, 3D visual reconstruction from them offers much more details and is rich in information. Thus, 3D visual reconstruction possesses significant advantages over D rendering when used for diagnosis, treatment planning, and simulation of guiding operation procedures. A classic visualization and surface reconstruction algorithm, the marching-cubes algorithm (MC), has been applied to 3D reconstruction of medical images and data, which builds a geometrical representation of the isosurface defined only by a density threshold []. The main disadvantages of MC include the expensive expenses of computation and the lack of basic volume operations, such as cutting. The number of generated triangles can be extremely large for a high resolution data set []. As the most complex human organ, the brain contains many small tissues corresponding to different functions. An MRI (or CT) contains rich information reflecting these tissues. It is not necessary in all cases to consider all small tissues extracting from the MRI together with their intricate relationships. The images with gray level, such as MRIs, engender great difficulty in doing so. In a specific treatment, for example, the location and analysis of the subthalamic nuclei (STN) for the purpose of deep brain stimulation (DBS), physicians only pay attention to the position of STN and entrance location of treatment on the surface of brain. It will be greatly helpful if the targeted organs and their positions are able to be visualized for the physicians prior to treatment or surgery. In this paper, the proposed method reconstructs the 3D surface of the brain from magnetic resonance images (MRI) based on the level set method which separates the outer boundary of brain from a D MRI. Then, a 3D visual surface of the brain is obtained via superposition of a set of outer boundary slices. Contrasted to traditional methods, the proposed method recovers the 3D surface of the brain to the greatest extent with the least a priori information. Thus, the proposed method is more direct, more effective, and more transparent. Methods The proposed method for 3D reconstruction is composed of two main steps. First, the outer contours of the brain from MRI are separated by using the improved region-based level set method. Then, the 3D transparent skull is reconstructed by putting a series of outer boundaries of the brain from different layers together.. Data We demonstrate the performance of the proposed method for 3D surface reconstruction of the brain using

2 MRI images from the matlab dataset mri. This method was implemented in Matlab (Version R9a The Mathworks Inc.). Segmentation based on region-based level set method The active contour model along with level set technology has been widely applied to many research fields, such as computer vision and image processing. Chan and Vese [3] introduced a variationial model based on the level set function, ( ), for which the zero level set segments the image domain into several intensity homogenous regions by minimizing the below functional..3 Segmentation of outer contour of the brain The purpose of the paper is to obtain the outer contours of each brain slice, to further study the relationship between the specific tissues inside the brain and 3D surface of the brain, and to accurately locate and navigate for diagnosis and treatment. Since there exist some tissues inside the boundary of each slice, the obtained results enclose clutters after segmentation using region-based level set method. Thus, it is necessary to improve the conventional region-based level set method. In this paper, we propose a method of extracting the outer contours via finding the contour with maximum area so that other contours are filtered out..4 3D surface reconstruction of the brain F( c, c v, ) H ( ( u ( c u ( c ( ( ( H ( ( ( H ( ( () Utilizing the above proposed region-based level set method to complete the segmentation, the outer contours of the brain may be obtained for each layer. After obtaining a series of outer boundaries of the brain from different layers, a 3D transparent skull is reconstructed by putting all slices together following their layer orders. 3 Experimental Results A 3D surface of the brain shown in Figure (a) and (b) are obtained using the MC algorithm [4]. In Figure (b), the MRI image on the top is also displayed using isocap. Where Ω is an image defined on ; and are constants;,, and are fixed parameters; ( ) is the Heaviside function; and ( ) is the Kronecker delta function. This minimization problem is solved by taking the Euler-Lagrange equations and updating the level set function by the gradient descent. In figure (a) and (b), the structure within the brain is not easy to be observed although the entire outer surface is smooth and realistic. The visualization of the entire brain in 3D form is more useful because it is directly and frequently utilized to diagnose and treat ( )[ div( ) ( u t ( u c ) ] c ) () For a 3D reconstruction, each slice of an object must be considered. For each slice, the targeted tissue must be detected and located in the D image. As an effective model, the level set technology provided by Chan and Vese [3] can detect the location of boundaries very well, and is insensitive to placement of the initial curve in the image. This model can also be employed to separate the brain s organs from their background. (a)

3 (b) Figure. 3D surface reconstruction of the brain using MC algorithm [4]. Figure (a) shows the 3D surface reconstruction without isocap. Figure (b) shows the 3D surface reconstruction with isocap diseases of the brain. Based on the results shown in Figure (a), the effect of transparency may be achieved by changing the alpha coefficient. 3D surface reconstruction of the brain with transparency is shown in figure (a) and (b). There are still some drawbacks. The extent and effect of transparency is not ideal. There are several internal tissues and organs extracted (see Figure (b)). These internal tissues are easily taken as the objects on the 3D surface. (see Figure (a)). In order to obtain only 3D outer surface from MRI and to make a 3D visual model for treatment of the specific tissue, we propose a more direct and more practical method. Fig. 3(a) shows the segmentation results using conventional region-based level set method. We can find that the results include both various issues in the brain and boundary of the brain. To achieve the transparent surface (a) (b) Figure. 3D surface reconstruction of the brain with transparent effect. Figure (a) shows the 3D surface reconstruction with transparent effect. There are several tissues inside the brain which are mistakenly taken as stuffs on the surface. Figure (b) shows the D projective image from 3D surface reconstruction with transparent effect. of the brain, only the outer boundary is needed. By utilizing the proposed method, the outer boundary of the brain is found and kept. Fig. 3(b) shows the separated outer boundary of the brain using proposed method. The separated outer boundary of the brain has further extracted and shown as Fig. 3(c). Using the proposed approach, we have reconstructed the 3D surface of the brain from the same MRI images. The obtained 3D surface reconstruction of the brain is shown as figure 4 (a) and (b). First, the boundaries of the brain from multiple MRIs are segmented using our level set method. During the process of segmentation, the other contours corresponding to internal tissues have been filtered. Only the outer contours reflecting the boundaries of the brain have been remained. After the series of outer boundaries are obtained by using proposed segmentation on all MRI images (7 frames) from the Matlab dataset, 3D surface reconstruction of the brain is secured by putting these outer boundaries together. The 3D model has the transparent effect since no links are inserted between slices. Figure 4(a) shows the 3D surface reconstruction of the brain with the transparent effect. In which, there are no any tissues that are extracted. But, any specific tissue may be easily added based on medical needs. Figure 4(b) shows the D projective image from 3D surface reconstruction of the brain with transparent effect.

4 Z-axis 3 3(a) Y-axis 4 5 X-axis 5 4 (a) 5 3(b) Y-axis 4 5 X-axis 4 (b) 3(c) Figure 3. The segmentation results of the brain MRI. Fig. 3(a). The segmentation results include various issues in the brain and boundary of the brain using conventional region-based level set method. Fig. 3(b). The segmentation results only contain the outer boundary of the brain using proposed region-based level set method. Fig. 3(c). The outer boundary of the brain is extracted after filtering out other contours. After obtaining a 3D surface reconstruction of the brain using proposed method, we can rotate the 3D surface of the brain to observe the surface and interior of the brain with a 36 view. The entire structure of the brain, the location of specific organs and the relationship Figure 4. 3D surface reconstruction of the brain with transparent effect using proposed method. Fig. 4(a). 3D surface reconstruction with transparent effect is obtained. There are not any issues left inside the brain. Fig. 4 (b). The D projective image from 3D surface reconstruction of the brain with transparent effect using proposed method. between the surface of the brain and its components can be reflected simultaneously with rotation. The surface and shape of the brain obtained from proposed method are similar to those from MC method. A 3D surface reconstruction of the brain provides spatial information and effective visualization of the brain, which enables physicians to seek and locate the position of an organ in the brain more easily. The ratio between the scale in the figures and real size of the brain should be calculated and adjusted according to each real case.

5 4 Conclusions This new approach is based on image segmentation using a level set method, which enables us to observe the brain from any direction, and to easily find the specific organ inside the brain. More importantly, the transparent effect of 3D surface reconstruction of the brain is better than that of an MC algorithm. The proposed method for 3D surface reconstruction of the brain not only displays the 3D surface of the brain, but also applies to other human organs, such as 3D reconstruction of STN. It is very applicable to study the relationship between the specific organ inside the brain and the surface of the brain. Also, it is very helpful to guide surgery manipulation. In a word, the proposed approach has precisely segmented the boundaries of the brain from MRIs, reconstructed 3D surface of the brain efficiently, and enabled physician to observe interior of the brain more easily as well. 5 References [] W. E. Lorensen and H. E. Cline, Marching cubes: A high resolution 3D surface construction algorithm, Computer Graphics,, 4, pages 63-69, 987. []B. Csébfalvi, A. König, E. Gröller, Fast surface rendering of volume data, In N.M. Thalmann, V. Skala (eds.), Proceedings of WSCG, the 8-th International Conference in Central Europe on Computer Graphics, Visualization and Interactive Digital Media, February 7 -,, Plzen, Czech Republic, Short communication papers, pp [3] T. F. Chan, L. Vese, Active contours without edges, IEEE Trans. Img. Process. (), 66 77,. [4] Matlab, Help, sections: Visualizing MRI data: Volume Visualization Techniques (3-D Visualization); Image Processing Toolbox.

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