FIGURE 7 (a) Isosurface of a 3D object defined on a 643 grid; (b) positions of planes A and B on which the 3D GVF vectors are depicted in (c) and (d), respectively; (e) the initial configuration of a deformable surface using GVF and its positions after (f ) 10, (g) 40, and (h) 100 iterations. Reprinted from C. Xu and J. L. Prince, Snakes, shapes, and gradient vector flow. IEEE Trans, on Image Processing, 7(3):359-369, March, 1998. ©1998 IEEE.
FIGURE 8 A surface rendering of reconstructed cortical surface from one subject displayed from multiple views: (a) top, (b) left, and (c) medial. Cross-sectional views of the same reconstructed cortical surface superimposed on the extracranial-tissues-removed MR brain images: (d) axial, (e) coronal, and (f) sagittal. Reprinted from C. Xu, D. L. Pham, M. E. Rettman, D. N. Yu, and J. L. Prince. Reconstruction of the human cerebral cortex from magnetic resonance images. IEEE Trans, on Medical Imaging, 18(6):467-480, June 1999. © 1999 IEEE.
Figure 7 shows an experiment using a GVF deformable surface on a simulated 3D image created on a 643 grid. The object to be reconstructed, rendered using an isosurface algorithm, is shown in Fig. 7a. The 3D GVF field was computed using a numerical scheme similar to the one of 2D with ^ = 0. l5. This GVF result on the two planes shown in Fig. 7b is shown projected onto these planes in Figs 7c and 7d. The same characteristics observed in the 2D GVF field are apparent here as well. A deformable surface using 3D GVF was initialized as the sphere shown in Fig. 7e, which is neither entirely inside nor entirely outside the object. Intermediate results after l0 and 40 iterations of the deformable surface algorithm are shown in Figs 7f and g. The final result after l00 iterations is shown in Fig. 7h. The resulting surface is smoother than the isosurface rendering because of the internal forces in the deformable surface model.
Figure 8 shows an example of using the GVF deformable surface to reconstruct a surface representation of the central layer of the human cerebral cortex from a 3D MR brain image. Details of this work can be found in [20, 2l].
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