Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
A 3D 6-subiteration thinning algorithm for extracting medial lines
Pattern Recognition Letters
Proceedings of the sixth ACM symposium on Solid modeling and applications
Volume conserving smoothing for piecewise linear curves, surfaces, and triple lines
Journal of Computational Physics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Affine-Invariant Skeleton of 3D Shapes
SMI '02 Proceedings of the Shape Modeling International 2002 (SMI'02)
Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition (Studies in Advanced Mathematics)
Plumber: a method for a multi-scale decomposition of 3D shapes into tubular primitives and bodies
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Robust on-line computation of Reeb graphs: simplicity and speed
ACM SIGGRAPH 2007 papers
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Enhancing 3D mesh topological skeletons with discrete contour constrictions
The Visual Computer: International Journal of Computer Graphics
Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Consistent computation of first- and second-order differential quantities for surface meshes
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Curve-Skeleton Extraction Using Iterative Least Squares Optimization
IEEE Transactions on Visualization and Computer Graphics
An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data
Journal of Computational Physics
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Medial curves have a wide range of applications in geometric modeling and analysis (such as shape matching) and biomedical engineering (such as morphometry and computer assisted surgery). The computation of medial curves poses significant challenges, in terms of both theoretical analysis and practical efficiency and reliability. In this paper, we propose a definition and analysis of medial curves and also describe an efficient and robust method called local orthogonal cutting for computing medial curves. Our approach is based on three key concepts: a local orthogonal decomposition of objects into substructures, a differential geometry concept called the interior center of curvature, and integrated stability and consistency tests. These concepts lend themselves to robust numerical techniques and result in an algorithm that is efficient and noise resistant. We illustrate the effectiveness and robustness of our approach with some highly complex, large-scale, noisy biomedical geometries derived from medical images, including lung airways and blood vessels. We also present comparisons of our method with some existing methods.