Combining Curvature Motion and Edge-Preserving Denoising
In this paper we investigate a family of partial differential equations (PDEs) for image processing which can be regarded as isotropic nonlinear diffusion with an additional factor on the right-hand side. The one-dimensional analogues to this filter class have been motivated as scaling limits of one-dimensional adaptive averaging schemes. In 2-D, mean curvature motion is one of the most prominent examples of this family of PDEs. Other representatives of the filter class combine properties of curvature motion with the enhanced edge preservation of Perona-Malik diffusion. It becomes appearent that these PDEs require a careful discretisation. Numerical experiments display the differences between Perona-Malik diffusion, classical mean curvature motion and the proposed extensions. We consider, for example, enhanced edge sharpness, the question of morphological invariance, and the behaviour with respect to noise.
KeywordsCurvature Motion Morphological Invariance Small Time Step Size Shrinkage Time Convex Plane Curf
Unable to display preview. Download preview PDF.
- 2.Kimmel, R.: Numerical Geometry of Images: Theory, Algorithms, and Applications. Springer, New York (2003)Google Scholar
- 4.Gabor, D.: Information theory in electron microscopy. Laboratory Investigation 14(6), 801–807 (1965)Google Scholar
- 12.Sapiro, G.: Vector (self) snakes: a geometric framework for color, texture and multiscale image segmentation. In: Proc. 1996 IEEE International Conference on Image Processing, vol. 1, Lausanne, Switzerland, Sep. 1996, pp. 817–820. IEEE Computer Society Press, Los Alamitos (1996)CrossRefGoogle Scholar
- 17.Tschumperlé, D., Deriche, R.: Vector-valued image regularization with PDE’s: A common framework for different applications. IEEE Transactions on Image Processing 27(4), 1–12 (2005)Google Scholar