Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
International Journal of Computer Vision
Geometric heat equation and nonlinear diffusion of shapes and images
Computer Vision and Image Understanding
Matching Hierarchical Structures Using Association Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
A tree-edit-distance algorithm for comparing simple, closed shapes
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Ligature instabilities in the perceptual organization of shape
Computer Vision and Image Understanding
Divergence-Based Medial Surfaces
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
A shock grammar for recognition
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
Matching and Embedding through Edit-Union of Trees
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Graph-Based Methods for Vision: A Yorkist Manifesto
Proceedings of the Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
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
Discovering Shape Categories by Clustering Shock Trees
CAIP '01 Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns
Down to the bone: simplifying skeletons
Proceedings of the 10th ACM symposium on Document engineering
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
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This paper presents a geometric measure that can be used to gauge the similarity of 2D shapes by comparing their skeletons. The measure is defined to be the rate of change of boundary length with distance along the skeleton. We demonstrate that this measure varies continuously when the shape undergoes deformations. Moreover, we show that ligatures are associated with low values of the shape-measure. The measure provides a natural way of overcoming a number of problems associated with the structural representation of skeletons. The first of these is that it allows us to distinguish between perceptually distinct shapes whose skeletons are ambiguous. Second, it allows us to distinguish between the main skeletal structure and its ligatures, which may be the result of local shape irregularities or noise.