Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
On active contour models and balloons
CVGIP: Image Understanding
Computing minimal surfaces via level set curvature flow
Journal of Computational Physics
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
An Adaptive Level Set Method for Medical Image Segmentation
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Ordered Upwind Methods for Static Hamilton--Jacobi Equations: Theory and Algorithms
SIAM Journal on Numerical Analysis
Cortical Surface Reconstruction Using a Topology Preserving Geometric Deformable Model
MMBIA '01 Proceedings of the IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA'01)
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
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
Moving meshes by the deformation method
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
A Moving Grid Framework for Geometric Deformable Models
International Journal of Computer Vision
Point-Based geometric deformable models for medical image segmentation
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Pattern Recognition and Image Analysis
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Geometric deformable models based on the level set method have become very popular in the last several years. 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 our previously presented topology-preserving geometric deformable model (TGDM). In this paper, we incorporate an alternative adaptive grid technique called the moving grid method into the geometric deformable model framework. We find that it is simpler to implement than grid refinement, requiring no large, complex, hierarchical data structures. It also limits the number of contour vertices in the final contour and supports the incorporation of the topology-preserving constraint of TGDM. After presenting the algorithm, we demonstrate its performance using both simulated and real images.