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9 December 1992 Comparison of implementation strategies for deformable surfaces in computer vision
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Deformable surfaces are useful in a number of biomedical computer vision applications for defining well behaved object models. Given an initial estimate of a three-dimensional object boundary, we can fit an elastic surface to the image data which has prescribed smoothness and data integrity properties. In this paper, we evaluate four methods for implementing deformable surfaces. The first uses finite differences and a locally greedy gradient following algorithm to minimize a surface functional similar to the controlled continuity stabilizer described by Terzopoulos. The second solves the Euler-Lagrange equations associated with this functional with a direct iterative method which does not invert these linear equations. The third method uses Gauss-Seidel to iteratively solve these linear equations once per deformation step. The fourth method uses successive over relaxation (SOR) for this task. All four algorithms have O(n) space and time requirements (where n is the number of points on the parametric surface) and typically converge in time proportional to the distance form the initial estimate to the final surface. These methods are local and iterative in nature and lend themselves well to parallel solution on a fine grained architecture such as the connection machine. We present a comparison of the space, time, and convergence properties of these methods. Applications of deformable models to segmentation of CT, MRI, and nuclear medicine images are also discussed.
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John M. Gauch, Mohamad Seaidoun, and Michael Harm "Comparison of implementation strategies for deformable surfaces in computer vision", Proc. SPIE 1768, Mathematical Methods in Medical Imaging, (9 December 1992);

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