SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Simplifying surfaces with color and texture using quadric error metrics
Proceedings of the conference on Visualization '98
Journal of the ACM (JACM)
Generating well-shaped Delaunay meshed in 3D
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
TetFusion: an algorithm for rapid tetrahedral mesh simplification
Proceedings of the conference on Visualization '02
Simplification of Tetrahedral Meshes with Error Bounds
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
WBIA '98 Proceedings of the IEEE Workshop on Biomedical Image Analysis
Mesh Simplification with Hierarchical Shape Analysis and Iterative Edge Contraction
IEEE Transactions on Visualization and Computer Graphics
Isosurface stuffing: fast tetrahedral meshes with good dihedral angles
ACM SIGGRAPH 2007 papers
A Variational Shape Optimization Approach for Image Segmentation with a Mumford-Shah Functional
SIAM Journal on Scientific Computing
Mesh Generation from 3D Multi-material Images
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part II
High-quality consistent meshing of multi-label datasets
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Guaranteed quality tetrahedral Delaunay meshing for medical images
Computational Geometry: Theory and Applications
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The modeling of physical processes in biomedical image analysis requires a discretization of the image space into simple shapes like triangles in two dimensions and tetrahedra in three dimensions. These discretizations are known as meshes, and the construction of the meshes as image-to-mesh conversion. There are a number of requirements on image-to-mesh conversion, the most critical of them being the shape of mesh elements in terms of the absence of small angles, the faithful geometrical representation of the tissues by the mesh elements, small number of elements for real-time Finite Element and Finite Volume analysis, and rapid execution times. We present a novel algorithm for triangular and tetrahedral image-to-mesh conversion which allows for guaranteed bounds on the smallest dihedral angle and on the distance between the boundaries of the mesh and the boundaries of the tissues. The algorithm produces a small number of mesh elements that comply with these bounds. We also describe and evaluate our implementation of the proposed algorithm on two publicly available three-dimensional medical atlases. The implementation is faster than a state-of-the art Delaunay code, and in addition solves the small dihedral angle problem.