International Journal of Computer Vision
A continuous skeletonization method based on level sets
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
An augmented Fast Marching Method for computing skeletons and centerlines
VISSYM '02 Proceedings of the symposium on Data Visualisation 2002
International Journal of Computer Vision
Matching and Embedding through Edit-Union of Trees
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Divergence-Based Medial Surfaces
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
Multi-scale 3-D Deformable Model Segmentation Based on Medial Description
IPMI '01 Proceedings of the 17th 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
Efficiently Computing Weighted Tree Edit Distance Using Relaxation Labeling
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Hippocampal Shape Analysis Using Medial Surfaces
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Reversible Surface Skeletons of 3D Objects by Iterative Thinning of Distance Transforms
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Discovering Shape Categories by Clustering Shock Trees
CAIP '01 Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns
Reversible surface skeletons of 3D objects by iterative thinning of distance transforms
Digital and image geometry
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Deformable M-Reps for 3D Medical Image Segmentation
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Automatic and Robust Computation of 3D Medial Models Incorporating Object Variability
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
Interactive modeling of topologically complex geometric detail
ACM SIGGRAPH 2004 Papers
A skeletal measure of 2D shape similarity
Computer Vision and Image Understanding
Simplified engineering analysis via medial mesh reduction
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Modeling with multiresolution subdivision surfaces
ACM SIGGRAPH 2006 Courses
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
International Journal of Computer Vision
Efficient and robust computation of an approximated medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
3D discrete skeleton generation by wave propagation on PR-octree for finite element mesh sizing
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Topology Repair of Solid Models Using Skeletons
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete bisector function and Euclidean skeleton in 2D and 3D
Image and Vision Computing
Defining and computing curve-skeletons with medial geodesic function
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Deriving the Medial Axis with geometrical arguments for planar shapes
Pattern Recognition Letters
Topology, Accuracy, and Quality of Isosurface Meshes Using Dynamic Particles
IEEE Transactions on Visualization and Computer Graphics
Shape matching and modeling using skeletal context
Pattern Recognition
Shape matching and modeling using skeletal context
Pattern Recognition
Adaptation of Eikonal Equation over Weighted Graph
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Surface Thinning in 3D Cubical Complexes
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Segmenting simplified surface skeletons
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 4
Efficient algorithms for image and high dimensional data processing using eikonal equation on graphs
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part II
Modelling postures of human movements
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Curvature correction of the Hamilton-Jacobi skeleton
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Robust skeletonization using the discrete λ-medial axis
Pattern Recognition Letters
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Generalized distance transforms and skeletons in graphics hardware
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
On Using Anisotropic Diffusion for Skeleton Extraction
International Journal of Computer Vision
Topological maps and robust hierarchical Euclidean skeletons in cubical complexes
Computer Vision and Image Understanding
Scale filtered euclidean medial axis
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Coarse-to-fine skeleton extraction for high resolution 3D meshes
Computer Vision and Image Understanding
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The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front, and is typically based on level set methods. However, there are more classical approaches rooted in Hamiltonian physics, which have received little consideration in computer vision.In this paper we first introduce a new algorithm for simulating the eikonal equation, which offers a number of computational and conceptual advantages over the earlier methods when it comes to shock tracking. Next, we introduce a very efficient algorithm for shock detection, where the key idea is to measure the net outward flux of a vector field per unit volume, and to detect locations where a conservation of energy principle is violated. We illustrate the approach with several numerical examples including skeletons of complex 2D and 3D shapes.