Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Representation and Self-Similarity of Shapes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Stochastic Computation of Medial Axis in Markov Random Fields
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Amodal volume completion: 3D visual completion
Computer Vision and Image Understanding
The multiresolution gradient vector field skeleton
Pattern Recognition
Hierarchical Shape Decomposition via Level Sets
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Amodal volume completion: 3D visual completion
Computer Vision and Image Understanding
Gray skeletons and segmentation of shapes
Computer Vision and Image Understanding
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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Motivated by a need to define an object-centered reference system determined by the most salient characteristics of the shape, many methods have been proposed, all of which directly or indirectly involve an axis about which the shape is locally symmetric. Recently, a function v, called "the edge strength function", has been successfully used to determine efficiently the axes of local symmetries of 2-d shapes. The level curves of v are interpreted as succesively smoother versions of the initial shape boundary. The local minima of the absolute gradient \left\| {\nabla v} \right\| along the level curves of v are shown to be a robust criterion for determining the shape skeleton. More generally, at an extremal point of \left\| {\nabla v} \right\| along a level curve, the level curve is locally symmetric with respect to the gradient vector \nabla v. That is, at such a point, the level curve is approximately a conic section whose one of the principal axes coincides with the gradient vector. Thus, the locus ofthe extremal points of \left\| {\nabla v} \right\| along the level curves determines the axes of local symmetries of the shape. In this paper, we extend this method to shapes of arbitrary dimension.