Segmentation and Modeling of the Spinal Cord for Reality-based Surgical Simulator
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1 Segmentation and Modeling of the Spinal Cord for Reality-based Surgical Simulator Li X.C.,, Chui C. K.,, and Ong S. H.,* Dept. of Electrical and Computer Engineering Dept. of Mechanical Engineering, National University of Singapore 21 Lower Kent Ridge Road, Singapore ABSTRACT A semi-automatic spinal cord segmentation scheme aims to achieve a balance between laborious manual segmentation and computationally intensive fully-automatic segmentation scheme. In the proposed semi-automatic scheme, only data size and initial region-growing seed need to be specified. Seed selection determines the starting point of region growing, while edge detection, combined with statistical analysis, determines the stopping criteria. Geometric approximation is the post-region growing step based on the elliptical shape of the spinal cord, and 3-D reconstruction combines all segmented slices to build a 3-D model of spinal core. The test data are 2 sets of MRI T1-weighted cross-section comprising 28 slices and 20 slices, respectively. The accuracy of segmentation is evaluated by comparing automatic segmentation results with manual segmentation results. The test results showed good accuracy in segmentation and modeling. INTRODUCTION Segmentation aims to determine and reconstruct structures of interest with similar characteristics inside an image. [1][2] The object of interest is isolated from its surroundings so as to enable tasks such as visualization, measurement and reconstruction. In medical imaging, the spinal cord has been identified as a pre-surgery module that can be segmented from magnetic resonance imaging (MRI) T1-weighted cross-sections. The clinically manual segmentation is tedious, time consuming and non-repeatable. [3] Thus, an automatic or semi-automatic technique is required to accelerate the segmentation process. The scheme proposed in this paper is a semi-automatic method that combines manual intervention and automated processing. During the procedure, the user is prompted to input initial seed points with four mouse clicks on the desired region of first MRI image. An automated processing engine has been developed for segmentation and volumetric reconstruction. This procedure involves region growing, edge detection and geometrical approximation. Compared to a fully automatic technique, the proposed semi-automated scheme is expected to be less computationally intensive in finding the initial seed on the starting slice. The algorithm is designed to process MRI T1-weighted scan of any number of slices. Student Assistant Prof. * Corresponding Author, eleongsh@nus.edu.sg, Associate Prof. 1
2 SCHEME DESCRIPTION The proposed scheme comprises five steps: 1) seed selection, 2) edge detection, 3) region growing, 4) geometric approximation, and 5) 3-D reconstruction. Seed Selection After deciding the number of slices, seed selection is the only step that requires user input. This process starts with the user choosing four pixels within the spinal cord area of the initialization slice (1 st slice) of the MRI scan set. A simple analysis is ensued to prevent possible human error in selecting the four points, and the calculated pixel position is returned as the single seed of region growing. Seed selections in the subsequent slices proceed in a fully automatic manner. The region growing seed of the current slice is analyzed based on the final segmented shape on the previous slice (Figure 1). In this way, seed positions are updated each time the algorithm finishes processing a slice. The initial slice s seed position is not chosen as the universal seed for all slices. This scheme helps in increasing accuracy as the spine is curved. Figure 1: Illustration of seed selection scheme Edge Detection Edge detection serves as one of the stopping criteria for region growing process. The Canny edge detector is chosen to provide single edge response. Region Growing Staring from the seed, a pixel is added to the region only if it is connected to the region (or seed) being grown and meets the criteria of homogeneity and proximity. Region growing based on 4-connectivity is implemented on each 2D slice. The order of growth affects the results obtained in the case when the boundary is not well-defined. A biased direction of growth is likely to generate over-segmented results. To ensure unbiased region growing, a first-in-first-out (FIFO) structure is used. Currently, homogeneity serves as the pixel selecting criterion: 2
3 gray value of candidate pixel grown region mean < grown region variance * 0.67 (1) The above criterion is based on the grown region statistics; thus it is dynamically updated as region growing process proceeds. The stopping criteria mainly comprise edge detection and size limiting. The resultant edge map obtained from the Canny edge detector excludes pixels on detected edges from being adopted into the spinal cord region. Additionally, if the grown region exceeds a reasonable size limit, region growing stops. This size limit is based on object proportions in the MRI slices. Geometrical Approximation For segmentation of soft tissue like the spinal cord, the boundary of the region of interest can often be obtained by geometrical approximation of simple ellipses or polygons. Since the spinal cord is elliptical in shape, it is reasonable to use this structure information for further enhancement of result. During the process of geometrical approximation, the best fit ellipse is sought through three steps: Step 1: Estimating the centroid. Centroid estimation is based on the boundary pixels only, rather than all pixels in the grown region. This estimation accelerates computing the center of maximal inscribed ellipse within the grown region. Step 2: Estimating the Radius. The elliptical approximation needs two radii to generate the best-fit ellipse, but a single radius estimation helps to speed up locating the centroid and then further estimating the two radii of the ellipse. In this step, a circle is estimated to provide a rough guide to the length of the minor and major axis of the final ellipse approximation. In radius estimation, a set of horizontal lines are drawn across the binary image and the length of each chord is stored in an array (Figure 2). The radius is then calculated as half of the length of the chord with the maximum length. Figure 2: Radius estimation Step 3: Finding the ellipse. Based on the estimated centroid and radius, centroid translation, horizontal expansion and vertical expansion are performed to finalize the best-fit ellipse approximation. The fitting of the ellipse is measured by the number of intersection pixels between approximated ellipse and boundary of the grown region. The ellipse that has the largest number of such intersection pixels is considered as the best-fit elliptical approximation. 3
4 3D Reconstruction The image-guided spine procedure requires a 3D model of the segmented spinal cord based on the segmentation result from the full set of MRI slices. After processing each MRI slice, the segmented binary image is stored in a 3D matrix, with the number of slice as the z-axis of the 3D matrix, as to stack up all segmented images into a single 3D matrix. After the completion of processing all slices in the MRI set, the 3D matrix is re-scaled to display the final 3D structure of the spinal cord. RESULTS AND DISCUSSION The testing MRI T1-weighted set A and set B comprises 28 slices and 20 slices respectively. Each slice has 512x512 pixels in size and 16-bit (65536 levels) in gray scale. T2-weighted images are not adopted as the boundary of the spinal cord is not as well-defined as that of T1-weighted images. [4] To evaluate algorithm accuracy, an error measure is introduced. The automatically segmented area A is compared with manually segmented area M. The segmentation error is measured as the sum of non-overlapped areas versus the area of manual segmentation [5] : A A M M A M M (2) Details on segmenting the 1 st, 4 th and 25 th slices are illustrated in Figure 3: at the starting slice (1 st row in Figure 3), the grown region statistics helps to segment the spinal core with fairly good accuracy, due to the clear contrast between spinal core and its surroundings. The constraint on edge detection imposes a stricter limit, and the approximated segmentation is of the appropriate shape and accurately located. The spinal cord of the 4 th slice (2 nd row in Figure 3) displays a more vertically compressed shape compared to that of the 1 st slice. By continuously re-evaluating and updating seed location, the automatically decided seed falls in the correct region. Region growing based on local statistics provides a reliable segmented image, with edge detection as enhancement. The final segmentation after geometric approximation illustrates a more vertically compressed shape than the result of the 1st slice. Still, segmented ellipse lies at the accurate position. In the 25 th slice (3 rd row in Figure 3), the spinal core area exhibits a shape with a longer span in the vertical direction than in the horizontal direction. This accords with the geometric approximation, in which the vertical axis is slighter longer than the horizontal axis. This slice shows the importance of geometric approximation in acquiring satisfactory results. 4
5 Figure 3: Segmentation details of set A: (a) original image; (b) after region growing based on local statistics; (c) after region growing and edge detection; (d) after geo-approximation The rendered 3-D model is illustrated (Figure 4), perceiving with different display settings. By applying the proposed algorithm on MRI scan set A, the errors are acceptably small (Table 1). The 16 th slice investigated previously has the largest error value in this set, but its error still lies within the acceptable extent. Figure 4: 3-D model of set A Table 1: Error Evaluation of Set A Slice Error Slice Error Slice Error Slice Error
6 Similar to set A, region growing seed for the 1 st slice in set B starts from the user input (1 st column, Figure 5). Thus, its location correctness is guaranteed. Also, the segmented image has accurately described the elliptical shape of spinal core in the original image. In the 5 th MRI slice (2 nd column, Figure 5), automatic segmentation captures the correct location and shape of spinal cord. However, the segmentation fails to capture the slight rotation of the spinal core the segmented image is still symmetrical with respect to the x- and y-axes. In the 10 th slice (3 rd column, Figure 5), the spinal cord exhibits a horizontally-expanded ellipse compared to the previous shape. This horizontal expansion has been captured by the segmentation procedure. The spinal cord in the 15 th slice shows a round shape (4 th column, Figure 5), resulting in the round disk shape of the segmented image. In the last (20 th ) slice, the spinal cord shows a smaller shape than the 15 th slice (5 th column, Figure 5), which is reflected in the segmented image. Figure 5: Segmentation details of set B: (a) original image; (b) segmented binary image Applying the proposed algorithm on set B generates better results than on set A. The error rates are generally smaller than those of set A (Table 2). This result is due to the fact that spinal cord MRI cross-sections vary less significant throughout set B slices than set A slices, and thus the algorithm has less to adjust its parameters and seed locations. A relative steady data set presents higher accuracy in segmentation and building 3-D structure (Figure 6). Figure 6: 3D model of set B 6
7 Table 2: Error Evaluation of Set B Slice Error Slice Error Slice Error Slice Error CONCLUSIONS AND FUTURE WORK The proposed semi-automatic scheme of combining region growing, edge detection and geometrical approximation for the extraction of the spinal core from MRI T1-weighted data proves reliable. Integrating edge detection, region growing, and geometrical approximations of finding a best-fit ellipse would yield favorable results in reconstructing the spinal core model. More work could be done to reduce the error occurred in twisted/rotated images (5 th slice of set B), so that when the spinal core area on MRI scanned slice does not present an symmetric axis parallel to the x- or y-axes, the segmentation scheme could adapt to the rotation. REFERENCES 1. M. Sonka, V. Hlavac, R. Boyle, Image Processing Analysis and Machine Vision (2 nd Edition), Mar. 2007, PWS Publishing, 20 Park Plaza, Boston 2. Rafael C. Gonzalez and Richard E. Woods (2002), Digital Image Processing (2 nd Edition), Prentice Hall, Upper Saddle River, NJ 3. Booth, S. and Clausi, D. A., Image segmentation using MRI vertebral cross-sections, Electrical and Computer Engineering, Canadian Conference, May, R. Unnikrishnan, C. Pantofaru, and M. Hebert, Toward objective evaluation of image segmentation algorithms, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 6, June W. C. Schwartzkopf and A. C. Bovik, Maximum likelihood techniques for joint segmentation-classification of multi-spectral chromosome images, IEEE Trans. Medical Imaging, vol. 24, pp , Dec
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