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
Shape from shading
The Eikonal equation: some results applicable to computer vision
Shape from shading
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Simulating the Grassfire Transform Using an Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Ridge points in Euclidean distance maps
Pattern Recognition Letters
Topological segmentation of discrete surfaces
International Journal of Computer Vision
A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
International Journal of Computer Vision
A parallel thinning algorithm for medial surfaces
Pattern Recognition Letters
Shape from shading: level set propagation and viscosity solutions
International Journal of Computer Vision
Skeletonization via distance maps and level sets
Computer Vision and Image Understanding
FORMS: a flexible object recognition and modeling system
International Journal of Computer Vision
Extraction of shape skeletons from grayscale images
Computer Vision and Image Understanding
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution
Graphical Models and Image Processing
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Distance-ordered homotopic thinning: a skeletonization algorithm for 3D digital images
Computer Vision and Image Understanding
Shock Graphs and Shape Matching
International Journal of Computer Vision
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Complete Dense Stereovision Using Level Set Methods
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Skeletonizing Volume Objects Part 2: From Surface to Curve Skeleton
SSPR '98/SPR '98 Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
Proceedings of the Workshop on Geometry and Robotics
Segmentation of Carpal Bones from 3d CT Images Using Skeletally Coupled Deformable Models
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
3D/2D Registration via Skeletal Near Projective Invariance in Tubular Objects
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Marching Optimal-Parameter Ridges: An Algorithm to Extract Shape Loci in 3D Images
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Segmentation of Single-Figure Objects by Deformable M-reps
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Symmetry-Based Indexing of Image Databases
CBAIVL '98 Proceedings of the IEEE Workshop on Content - Based Access of Image and Video Libraries
Scale-Space Vector Fields for Feature Analysis
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Characterization and Recognition of 3D Organ Shape in Medical Image Analysis Using Skeletonization
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Local Symmetries of Shapes in Arbitrary Dimension
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Inexact Multisubgraph Matching Using Graph Eigenspace and Clustering Models
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
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)
An Eigenspace Projection Clustering Method for Inexact Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Indexing Hierarchical Structures Using Graph Spectra
IEEE Transactions on Pattern Analysis and Machine Intelligence
Force field feature extraction for ear biometrics
Computer Vision and Image Understanding
Alternative 2D Shape Representations using the Symmetry Set
Journal of Mathematical Imaging and Vision
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
The multiresolution gradient vector field skeleton
Pattern Recognition
Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tree Structure for Contractible Regions in R3
International Journal of Computer Vision
Statistical Multi-Object Shape Models
International Journal of Computer Vision
Deriving the Medial Axis with geometrical arguments for planar shapes
Pattern Recognition Letters
A geometric approach to monitoring threshold functions over distributed data streams
ACM Transactions on Database Systems (TODS)
Indexing through laplacian spectra
Computer Vision and Image Understanding
Strategies for shape matching using skeletons
Computer Vision and Image Understanding
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Tree Covering within a Graph Kernel Framework for Shape Classification
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Force field feature extraction for ear biometrics
Computer Vision and Image Understanding
Efficient implementation for spherical flux computation and its application to vascular segmentation
IEEE Transactions on Image Processing
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Medial axis of a planar region by offset self-intersections
Computer-Aided Design
Curvature dependent skeletonization
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
A Markov random field approach to multi-scale shape analysis
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Shape description using gradient vector field histograms
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Accurate spatial neighborhood relationships for arbitrarily-shaped objects using Hamilton-Jacobi GVD
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Joint sulci detection using graphical models and boosted priors
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
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
A similarity-based approach for shape classification using Aslan skeletons
Pattern Recognition Letters
Skeleton growing and pruning with bending potential ratio
Pattern Recognition
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
Sampled medial loci for 3D shape representation
Computer Vision and Image Understanding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Computation of the shock scaffold for unorganized point clouds in 3D
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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
On the computation of the {3, 4, 5} curve skeleton of 3D objects
Pattern Recognition Letters
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Structural and textural skeletons for noisy shapes
ISVC'05 Proceedings of the First international conference on Advances in Visual Computing
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Skeleton pruning by contour partitioning
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Skeletonization and distance transforms of 3D volumes using graphics hardware
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Retrieving articulated 3-d models using medial surfaces and their graph spectra
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
A stable skeletonization for tabletop gesture recognition
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part I
Computation and evaluation of medial surfaces for shape representation of abdominal organs
MICCAI'11 Proceedings of the Third international conference on Abdominal Imaging: computational and Clinical Applications
Pen stroke extraction and refinement using learned models
SBM'04 Proceedings of the First Eurographics conference on Sketch-Based Interfaces and Modeling
On the generation and pruning of skeletons using generalized Voronoi diagrams
Pattern Recognition Letters
Learning-Based symmetry detection in natural images
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Watershed delineation from the medial axis of river networks
Computers & Geosciences
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)
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 yet to be widely used by the computer vision community. In this paper we review the Hamiltonian formulation, which offers specific advantages when it comes to the detection of singularities or shocks. We specialize to the case of Blum's grassfire flow and measure the average outward flux of the vector field that underlies the Hamiltonian system. This measure has very different limiting behaviors depending upon whether the region over which it is computed shrinks to a singular point or a non-singular one. Hence, it is an effective way to distinguish between these two cases. We combine the flux measurement with a homotopy preserving thinning process applied in a discrete lattice. This leads to a robust and accurate algorithm for computing skeletons in 2D as well as 3D, which has low computational complexity. We illustrate the approach with several computational examples.