Shock Graphs and Shape Matching
International Journal of Computer Vision
Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
SIAM Journal on Optimization
International Journal of Computer Vision
IPMI '99 Proceedings of the 16th International Conference on Information Processing in Medical Imaging
A Skeletal Measure of 2D Shape Similarity
IWVF-4 Proceedings of the 4th International Workshop on Visual Form
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Alternative 2D Shape Representations using the Symmetry Set
Journal of Mathematical Imaging and Vision
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Deriving the Medial Axis with geometrical arguments for planar shapes
Pattern Recognition Letters
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
PDE-based robust robotic navigation
Image and Vision Computing
A skeleton family generator via physics-based deformable models
IEEE Transactions on Image Processing
Line-stepping for shell meshes
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Skeleton growing and pruning with bending potential ratio
Pattern Recognition
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
Shells and spheres: an n-dimensional framework for medial-based image segmentation
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
On the computation of the {3, 4, 5} curve skeleton of 3D objects
Pattern Recognition Letters
Extended grassfire transform on medial axes of 2D shapes
Computer-Aided Design
Skeleton pruning by contour partitioning
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On the generation and pruning of skeletons using generalized Voronoi diagrams
Pattern Recognition Letters
A skeleton pruning algorithm based on information fusion
Pattern Recognition Letters
Empirical mode decomposition on skeletonization pruning
Image and Vision Computing
Poisson Skeleton Revisited: a New Mathematical Perspective
Journal of Mathematical Imaging and Vision
Intensity-Based Skeletonization of CryoEM Gray-Scale Images Using a True Segmentation-Free Algorithm
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at non-medial ones, providing a theoretical justification for its use in the Hamilton-Jacobi skeletonization algorithm of [7]. We then specialize to the case of shrinking circular neighborhoods and show that the average outward flux measure also reveals the object angle at skeletal points. Hence, formulae for obtaining the boundary curves, their curvatures, and other geometric quantities of interest, can be written in terms of the average outward flux limit values at skeletal points. Thus this measure can be viewed as a Euclidean invariant for shape description: it can be used to both detect the skeleton from the Euclidean distance function, as well as to explicitly reconstruct the boundary from it. We illustrate our results with several numerical simulations.