Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
On active contour models and balloons
CVGIP: Image Understanding
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast level set method for propagating interfaces
Journal of Computational Physics
International Journal of Computer Vision
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
A PDE-based fast local level set method
Journal of Computational Physics
Level-set-based deformation methods for adaptive grids
Journal of Computational Physics
Conditions of Nondegeneracy of Three-Dimensional Cells. A Formula of a Volume of Cells
SIAM Journal on Scientific Computing
A Moving Mesh Method Based on the Geometric Conservation Law
SIAM Journal on Scientific Computing
Moving meshes by the deformation method
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
An extended level set method for shape and topology optimization
Journal of Computational Physics
Active Contours Under Topology Control--Genus Preserving Level Sets
International Journal of Computer Vision
A 2D moving grid geometric deformable model
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
Area and length minimizing flows for shape segmentation
IEEE Transactions on Image Processing
Global Regularizing Flows With Topology Preservation for Active Contours and Polygons
IEEE Transactions on Image Processing
Self-Repelling Snakes for Topology-Preserving Segmentation Models
IEEE Transactions on Image Processing
Information Sciences: an International Journal
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Geometric deformable models based on the level set method have become very popular in the last decade. To overcome an inherent limitation in accuracy while maintaining computational efficiency, adaptive grid techniques using local grid refinement have been developed for use with these models. This strategy, however, requires a very complex data structure, yields large numbers of contour points, and is inconsistent with the implementation of topology-preserving geometric deformable models (TGDMs). In this paper, we investigate the use of an alternative adaptive grid technique called the moving grid method with geometric deformable models. In addition to the development of a consistent moving grid geometric deformable model framework, our main contributions include the introduction of a new grid nondegeneracy constraint, the design of a new grid adaptation criterion, and the development of novel numerical methods and an efficient implementation scheme. The overall method is simpler to implement than using grid refinement, requiring no large, complex, hierarchical data structures. It also offers an extra benefit of automatically reducing the number of contour vertices in the final results. After presenting the algorithm, we demonstrate its performance using both simulated and real images.