Digital Curvature Flow and Its Application for Skeletonization

In this paper, we define digital curvature flow for planar digital objects. We define the principal normal vectors for points on the digital boundary of a binary planar object. Digital curvature flow is defined as the motion of points on the boundary curve according to principal normal vectors. Therefore, digital curvature flow is a digital version of curvature flow. Furthermore, this transformation could also be considered as discrete curvature flow on isotetic polygons, all edges of which are parallel to the axes of an orthogonal coordinate system.

[1]  Bastien Chopard,et al.  Cellular Automata Modeling of Physical Systems: Index , 1998 .

[2]  Azriel Rosenfeld,et al.  Topology-Preserving Deformations of Two-Valued Digital Pictures , 1998, Graph. Model. Image Process..

[3]  Atsushi Imiya,et al.  Boundary Extraction of Discrete Objects , 1998, Comput. Vis. Image Underst..

[4]  J. Sethian.  Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[5]  H. Blum.  Biological shape and visual science. I. , 1973, Journal of theoretical biology.

[6]  Atsushi Imiya,et al.  The Euler Characteristics of Discrete Objects and Discrete Quasi-Objects , 1999, Comput. Vis. Image Underst..

[7]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid , 2012 .

[8]  V. Boltyanski,et al.  Excursions into Combinatorial Geometry , 1996 .

[9]  Benjamin B. Kimia,et al.  On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks , 2004, International Journal of Computer Vision.

[10]  H. Blum.  Biological shape and visual science (part I) , 1973 .

[11]  Atsushi Imiya,et al.  Discrete Mean Curvature Flow , 1999, Scale-Space.

[12]  Guillermo Sapiro,et al.  Evolutions of Planar Polygons , 1995, Int. J. Pattern Recognit. Artif. Intell..

[13]  C. J. Hilditch,et al.  Linear Skeletons From Square Cupboards , 1969 .

[14]  Azriel Rosenfeld,et al.  Axial representations of shape , 1986, Computer Vision Graphics and Image Processing.

[15]  F. Bookstein.  The line-skeleton , 1979 .