Chopp, D.L., Computing Minimal Surfaces via Level Set Curvature Flow, Jour. of Comp. Phys., 106, pp. 77-91, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....initial hypersurface is placed outside a shape, then it is shrunk and split until the front adheres to the object boundaries. However, the Level Set Methods are computationally inefficient. To overcome this drawback, two well known schemes have been proposed: the Narrow Band Method (NB) [4] and the Fast Marching Method[3] The NB is still computationally expensive. The time complexity is 2202 14 is the number of grid points along a side and the width of narrow band. The Fast Marching Method is a fast propagation method but has limited applicability. In this paper, we ....

....expense. To determine the in the original method, we must search for the closest front point over the entire computational domain. The time complexity 5681 , since the number of front points is 22628 2.2. Narrow Band Method In order to overcome the drawback, the Narrow Band Method(NB)[4] has been proposed. The main idea is to update at a small set of points in the neighborhood of the zero level set instead of updating at all the points on the grid. The region of narrow band is defined by W X V J ZYN [B , and are updated only within this band. Fig.1 shows a ....

D.L. Chopp: "Computing minimal surfaces via level set curvature flow," J. Computational Physics,vol.106, pp77-91, 1993

....at which there is more than one possible way to continue, do not cause any difficulty since they correspond to multiple paths of equal lengths that are all globally shortest. Angular errors that are accumulated by the back propagation procedure can be corrected using geodesic curvature flow [4], 12] to shorten the generated curve into a geodesic (between the moving obstacles) We remark that the above backtracking approximation is only one simple example, and the one used in our examples. For constraints imposed by different considerations like terrain traversability see Appendix. B. ....

D. L. Chopp, "Computing minimal surfaces via level set curvature flow," J. Comput. Phys., vol. 106, no. 1, pp. 77--91, May 1993.

.... limitations we use the fast geodesic active contours approach [15] which is based on the Weickert Romeny Viergever [41] semi implicit additive operator splitting (AOS) scheme and uses the narrow band approach to limit the computation to a tight region of few grid points around the zero level set [9], 1] We rely on the fact that the embedding function is a distance map. Gomes and Faugeras [16] proposed an approach, where the Hamilton Jacobi equation used to evolve the distance function is replaced by a PDE that preserves the function as a distance map (see also [37] which was applied ....

D. L. Chopp. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):77--91, May 1993.

....include in particular the ENO and WENO schemes. Even with these high order accurate approaches to solving the Hamilton Jacobi equations, one can obtain surprisingly inaccurate results when the level set function solution becomes too steep or too fiat, i.e. discontinuous or poorly conditioned. In [34], Chopp considered an application where certain regions of the flow had level sets piling up on each other increasing the local gradient, and other regions of the flow had level sets that separated from each other flattening out q. In order to reduce the numerical errors caused by both the ....

....where certain regions of the flow had level sets piling up on each other increasing the local gradient, and other regions of the flow had level sets that separated from each other flattening out q. In order to reduce the numerical errors caused by both the steeping and flattening effects, [34] introduced the notion that one should reinitialize the level set function periodically throughout the calculation. In [156] Rouy and Tourin proposed a numerical method for the shape from shading problem that was later generalized into the modern day reinitialization equation of Sussman, Smereka ....

[Article contains additional citation context not shown here]

Chopp, D., Computing minimal surfaces via level set curvature flow, J. Cornput. Phys. 106, 77-91 (1993). 46

.... limitations we use the fast geodesic active contours approach [13] which is based on the Weickert Romeny Viergever [32] semi implicit additive operator splitting (AOS) scheme and uses the narrow band approach to limit the computation to a tight region of few grid points around the zero level set [7, 1]. We rely on the fact that the embedding function is a distance map. Gomes and Faugeras [14] proposed an approach, where the Hamilton Jacobi equation used to evolve the distance function is replaced by a PDE that preserves the function as a distance map (see also [28] which was applied for ....

D. L. Chopp. Computing minimal surfaces via level set curvature ow. J. of Computational Physics, 106(1):77-91, May 1993. 9

....steady states computed this way involving complicated multiphase configurations are correct, as is the motion for unsteady viscous dominated flows. Inertial forces will be included through a level set based Hamilton s principle formulation in our future work; see also [9] We also note that Chopp [4], in related work, has constructed minimal surfaces in R 3 attached to given curves by evolving via level sets and mean curvature flow. He enforces the BEHAVIOR OF BUBBLES AND DROPS 497 boundary conditions by repeatedly reattaching the surface to the boundary. This method is different from ....

D. Chopp, Computing minimal surfaces via level set curvature flow, J. Comput. Phys. 106, 77 (1993).

.... limitations we use the fast geodesic active contours approach [13] which is based on the Weickert Romeny Viergever[32] semi implicit additive operator splitting (AOS) scheme and uses the narrow band approach to limit the computation to a tight region of few grid points around the zero level set [7, 1]. We rely on the fact that the embedding function is a distance map. Gomes and Faugeras [14] proposed an approach, where the Hamilton Jacobi equation used to evolve the distance function is replaced by a PDE that preserves the function as a distance map (see also [28] which was applied for ....

D. L. Chopp. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):77--91, May 1993.

....computed this way involving complicated multiphase configurations are correct, as is the motion for unsteady viscous dominated flows. Inertial forces will be included through a level set based Hamilton s principle formulation in our future work; see also [9] W e also note that Chopp [4], in related work, has constructed minimal surfaces in R 3 attached to given curves by evolving via level sets and mean curvature flow. He enforces the BEHAVIOR OF BUBBLES AND DROPS 497 boundary conditions by repeatedly reattaching the surface to the boundary. This method is dif ferent ....

D. Chopp, Computing minimal surfaces via level set curvature flow, J . Comput. Phys. 106, 77 (1993).

No context found.

Chopp, D.L., Computing Minimal Surfaces via Level Set Curvature Flow, Jour. of Comp. Phys., 106, pp. 77-91, 1993.

No context found.

Chopp, D.L., \Computing Minimal Surfaces via Level Set Curvature Flow", Jour. of Comp. Phys. , Vol. 106, pp. 77-91, 1993.

No context found.

D. Chopp. Computing Minimal Surfaces via Level Set Curvature Flow. Journal of Computational Physics, 106:77--91, 1993.

No context found.

D. L. Chopp, "Computing minimal surfaces via level set curvature flow," J. of Comp. Phys., vol. 106, pp. 77--91, 1993.

No context found.

D. Chopp. Computing minimal surfaces via level set curvature-flow. Journal of Computational Physics, 106:77--91, 1993.

No context found.

D. Chopp. Computing minimal surfaces via level set curvature-flow. Journal of Computational Physics, 106:77--91, 1993.

No context found.

D.L. Chopp, Computing Minimal Surfaces via Level Set Curvature Flow, Journal of Computational Physics 106:77-91, 1993

No context found.

D. L. Chopp, "Computing minimal surfaces via level set curvature flow," J. Comp. Phys., vol. 106, no. 1, pp. 77--91, May 1993.

No context found.

D. Chopp. Computing minimal surfaces via level set curvature-flow. Journal of Computational Physics, 106:77--91, 1993.

No context found.

D. L. Chopp. Computing minimal surfaces via level set curvature ow. J. of Computational Physics, 106(1):77-91, May 1993.

No context found.

D. L. Chopp. Computing minimal surfaces via level set curvature ow. Ph.D Thesis, Lawrence Berkeley Lab. and Dep. of Math. LBL-30685, Uni. of CA. Berkeley, May 1991.

No context found.

D. L. Chopp. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):7791, May 1993.

No context found.

D. L. Chopp. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):7791, May 1993.

No context found.

David L. Chopp. Computing minimal surfaces via level set curvature flow. J. Comput. Phys., 106(1):77--91, 1993.

No context found.

D. Chopp, "Computing minimal surfaces via level set curvature flows," LBL TR-University of Berkeley, 1991.

No context found.

D. Chopp, "Computing minimal surfaces via level set curvature flows," LBL TRUniversity of Berkeley, 1991.

No context found.

D. L. CHOPP, Computing Minimal Surfaces Via Level Set Curvature Flow, Ph.D. dissertation, Mathematics Department, Lawrence Berkeley Laboratory, Berkeley, CA, 1991.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC