Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computing the differential characteristics of isointensity surface
Computer Vision and Image Understanding
International Journal of Computer Vision
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
More-Than-Topology-Preserving Flows for Active Contours and Polygons
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Octree-Based Topology-Preserving Isosurface Simplification
CVPRW '06 Proceedings of the 2006 Conference on Computer Vision and Pattern Recognition Workshop
A topology preserving level set method for geometric deformable models
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Topology-preserving geometric deformable models (TGDMs) are used to segment objects that have a known topology. Their accuracy is inherently limited, however, by the resolution of the underlying computational grid. Although this can be overcome by using fine-resolution grids, both the computational cost and the size of the resulting surface increase dramatically. In order to maintain computational efficiency and to keep the surface mesh size manageable, we have developed a new framework, termed OTGDMs, for topology-preserving geometric deformable models on balanced octree grids (BOGs). In order to do this, definitions and concepts from digital topology on regular grids were extended to BOGs so that characterization of simple points could be made. Other issues critical to the implementation of OTGDMs are also addressed. We demonstrate the performance of the proposed method using both mathematical phantoms and real medical images.