Abstract
In this paper, we define digital curvature flow for spatial digital objects. We define the principal normal vectors for points on the digital boundary of a binary spatial object. We apply the discrete curvature flow for the skeletonisation of binary objects in a space, and develop a transform which yields the curve-skeletons of binary objects in a space.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blum, H.: Biological shape and visual science, J. Theoretical Biology 38, 205–285 (1963)
Rosenfeld, A.: Axial representations of shapes. CVGIP 33, 156–173 (1986)
Bookstein, F.L.: The line-skeleton. CVGIP 11, 137–1233 (1979)
Amenta, N., Bern, M., Eppstein, D.: The crust and the β-skeleton: Combinatorial curve reconstruction. Graphical Models and Image Processing 60, 125–135 (1998)
Attali, D., Montanvert, A.: Computing and simplifying 2D and 3D continuous skeletons. CVIU 67, 261–273 (1997)
Giblin, P.J., Kimia, B.B.: On the local form and transitions of symmetry sets and medial axes, and shocks in 2D. In: Proceedings of ICCV, pp. 385–391 (1999)
Nystrom, I., Sanniti di Baja, G., Svensson, S.: Curve skeletonization by junction detection in surface skeletons. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 229–238. Springer, Heidelberg (2001)
Svensson, S., Nystrom, I., Sanniti di Baja, G.: Curve skeletonization of surface-like objects in 3D images guided by voxel classification. Pattern Recognition Letters 23, 1419–1426 (2002)
Sanniti di Baja, G., Svensson, S.: Surface skeletons detected on the D6 distance transform. In: Amin, A., Pudil, P., Ferri, F., Iñesta, J.M. (eds.) SPR 2000 and SSPR 2000. LNCS, vol. 1876, pp. 387–396. Springer, Heidelberg (2000)
Svensson, S., Borgefors, G., Nystrom, I.: On reversible skeletonization using anchor-points from distance transforms. Journal on Visual Communication and Image Representation 10, 379–397 (1999)
Svensson, S., Sanniti di Baja, G.: Using distance transforms to decompose 3D discrete objects. Image and Vision Computing 20, 529–540 (2002)
Hilditch, J.C.: Linear skeletons from square cupboards. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence 4, pp. 403–422. Edinburgh University Press, Edinburgh (1969)
Sethian, J.A.: Level Set Methods: Evolving Interfaces in Geometry Fluid Mechanics, Computer Vision, and Material Science. Cambridge University Press, Cambridge (1996)
Bruckstein, A.M., Shapiro, G., Shaked, D.: Evolution of planar polygons. Journal of Pattern Recognition and Artificial Intelligence 9, 991–1014 (1995)
Imiya, A., Eckhardt, U.: Discrete curvature flow. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 477–483. Springer, Heidelberg (1999)
Imiya, A., Eckhardt, U.: The Euler characteristics of discrete objects and discrete quasi-objects. CVIU 75, 307–318 (1999)
Imiya, A., Saito, M., Tatara, K., Nakamura, K.: Digital curvature flow and its application to skeletonization. Journal of Mathematical Imaging and Vision 18, 55–68 (2003)
Imiya, A., Eckhardt, U.: Discrete curvature flow. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 477–483. Springer, Heidelberg (1999)
Kovalevsky, V.A.: Finite topology as applied to image analysis. Computer Vision, Graphics and Image Processing 46, 141–161 (1989)
Françon, J.: Sur la topologie d’un plan arithmétique. Theoretical Computer Sciences 156, 159–176 (1996)
Toriwak, J.-I.: Digital Image Processing for Computer Vision, vol. 1, 2. Sokodo, Tokyo (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Imiya, A., Saito, M., Nakamura, K. (2004). Thinning by Curvature Flow. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_31
Download citation
DOI: https://doi.org/10.1007/978-3-540-30503-3_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23942-0
Online ISBN: 978-3-540-30503-3
eBook Packages: Computer ScienceComputer Science (R0)