Skeletonization
The skeletonization is a process to extract a region-based shape feature representing the general outline of an 2D or 3D object.
The notion skeleton was introduced by H. Blum as a result of the Medial Axis Transform (MAT) or Symmetry Axis Transform (SAT). The MAT determines the closest boundary point(s) for each point is in an object. An inner point belongs to the skeleton if it has at least two closest boundary points.
Useful resources:
1. A short introduction from Wikipedia: Topological skeleton
2. A brief summary about different skeletonization techniques from Kálmán Palágyi.
3. Computer Vision from the University of Wisconsin, The guide to implement the Hamilton-Jacobi Skeleton using matlab.
4. 3D thinning algorithm based on the ITK, Code.
5. EVG-Thin: A Thinning Approximation to the Extended Voronoi Graph, Code.
6. Efficient Binary Image Thinning using Neighborhood Maps, Graphics gems IV, Code.
7. Curve-skeleton by Cornea N. D., with source code.
8. Skeletonization project, VizLab, Rutgers University.
References:
Thinning:
1. Building skeleton models via 3-D medial surface/axis thinning algorithms. Computer Vision, Graphics, and Image Processing, 56(6):462–478, 1994.
Curve Skeleton:
1. Cornea N.D., Silver D., Min P., Curve-Skeleton Properties, Applications and Algorithms, IEEE Transactions on Visualization and Computer Graphics, Jun 2006. with source code
2. Cornea N.D., Silver D., Min P. (2005). Curve-Skeleton Applications. In Proceedings IEEE Visualization, pp. 95-102, 2005.
3. Cornea N.D., Silver D., Yuan X., Balasubramanian R., Computing Hierarchical Curve-Skeletons of 3D Objects, The Visual Computer 21(11):945-955, Springer-Verlag, October, 2005. with source code
Hamilton-Jacobi Skeleton:
1. K. Siddiqi et al., The Hamilton-Jacobi skeleton, Int. J. Computer Vision 48(3), 2002, 215-231.
2. K. Siddiqi et al., The Hamilton-Jacobi skeleton, Proc. Int. Conf. Computer Vision, 1999.
3. S. Bouix and K. Siddiqi, Divergence-based medial surfaces, Proc. European Conf. Computer Vision, 2000.
4. K. Siddiqi et al., Geometric shock-capturing ENO schemes for subpixel interpolation, computation, and curve evolution, Graphical Models and Image Processing 59(5), 1997, 278-301.
The notion skeleton was introduced by H. Blum as a result of the Medial Axis Transform (MAT) or Symmetry Axis Transform (SAT). The MAT determines the closest boundary point(s) for each point is in an object. An inner point belongs to the skeleton if it has at least two closest boundary points.
Useful resources:
1. A short introduction from Wikipedia: Topological skeleton
2. A brief summary about different skeletonization techniques from Kálmán Palágyi.
3. Computer Vision from the University of Wisconsin, The guide to implement the Hamilton-Jacobi Skeleton using matlab.
4. 3D thinning algorithm based on the ITK, Code.
5. EVG-Thin: A Thinning Approximation to the Extended Voronoi Graph, Code.
6. Efficient Binary Image Thinning using Neighborhood Maps, Graphics gems IV, Code.
7. Curve-skeleton by Cornea N. D., with source code.
8. Skeletonization project, VizLab, Rutgers University.
References:
Thinning:
1. Building skeleton models via 3-D medial surface/axis thinning algorithms. Computer Vision, Graphics, and Image Processing, 56(6):462–478, 1994.
Curve Skeleton:
1. Cornea N.D., Silver D., Min P., Curve-Skeleton Properties, Applications and Algorithms, IEEE Transactions on Visualization and Computer Graphics, Jun 2006. with source code
2. Cornea N.D., Silver D., Min P. (2005). Curve-Skeleton Applications. In Proceedings IEEE Visualization, pp. 95-102, 2005.
3. Cornea N.D., Silver D., Yuan X., Balasubramanian R., Computing Hierarchical Curve-Skeletons of 3D Objects, The Visual Computer 21(11):945-955, Springer-Verlag, October, 2005. with source code
Hamilton-Jacobi Skeleton:
1. K. Siddiqi et al., The Hamilton-Jacobi skeleton, Int. J. Computer Vision 48(3), 2002, 215-231.
2. K. Siddiqi et al., The Hamilton-Jacobi skeleton, Proc. Int. Conf. Computer Vision, 1999.
3. S. Bouix and K. Siddiqi, Divergence-based medial surfaces, Proc. European Conf. Computer Vision, 2000.
4. K. Siddiqi et al., Geometric shock-capturing ENO schemes for subpixel interpolation, computation, and curve evolution, Graphical Models and Image Processing 59(5), 1997, 278-301.
Active Contour Model
Active contour model, also called snake, is a framework for delineating an object outline from a possibly noisy 2D image. Active contour model provides a unified solution to several image processing problems such as the detection of light and dark lines, edges, and terminations; they can also be used in stereo matching, and for segmenting spatial and temporal image sequences. Snakes have often been used in medical research applications. In addition, many motion tracking system use snakes to model moving objects.
The main limitations of the models are (i) that they usually only incorporate edge information (ignoring other image characteristic) possibly combined with some prior expectation of shape; and (ii) that they must be initialized close to the feature of interest if they are to avoid being trapped by other local minima.
The main limitations of the models are (i) that they usually only incorporate edge information (ignoring other image characteristic) possibly combined with some prior expectation of shape; and (ii) that they must be initialized close to the feature of interest if they are to avoid being trapped by other local minima.
Level Set
Useful resources:
1. Wikipedia, Level set method, Data structure for level set method.
2. Multivac is a C++ library for front tracking in 2D with level set methods.
3. J.A. Sethian, Berkeley, with introduction and online books.
4. Stanley Osher, University of California, Los Angeles
1. Wikipedia, Level set method, Data structure for level set method.
2. Multivac is a C++ library for front tracking in 2D with level set methods.
3. J.A. Sethian, Berkeley, with introduction and online books.
4. Stanley Osher, University of California, Los Angeles