Abstract
We present a class of PDE-based algorithms suitable for a wide range of image processing applications. The techniques are applicable to both salt- and-pepper grey-scale noise and full-image continuous noise present in black and white images, grey-scale images, texture images and color images. At the core, the techniques rely on a level set formulation of evolving curves and surfaces and the viscosity in profile evolution. Essentially, the method consists of moving the isointensity contours in a image under curvature dependent speed laws to achieve enhancement. Compared to existing techniques, our approach has several distinct advantages. First, it contains only one enhancement parameter, which in most cases is automatically chosen. Second, the scheme automatically stops smoothing at some optimal point; continued application of the scheme produces no further change. Third, the method is one of the fastest possible schemes based on a curvature-controlled approach.
Supported in part by the Applied Mathematics Subprogram of the Office of Energy Research under DE-AC03-76SF00098, and the National Science Foundation DARPA under grant DMS-8919074.
Supported in part by the NSF Postdoctoral Fellowship in Computational Science and Engineering
Chapter PDF
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
L. Alvarez, P. L. Lions, and J. M. Morel, “Image selective smoothing and edge detection by nonlinear diffusion. II,” SIAM Journal on Numerical Analysis, Vol. 29(3), pp. 845–866, 1992.
J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. PAMI-8, pp. 679–698, 1986.
M. Gage, “Curve shortening makes convex curves circular,” Inventiones Mathematica, Vol. 76, pp. 357, 1984.
M. Grayson, “The heat equation shrinks embedded plane curves to round points,” J. Diff. Geom., Vol. 26, pp. 285–314, 1987.
R. Malladi and J. A. Sethian, “Image processing via level set curvature flow,” Proc. Natl. Acad. of Sci., USA, Vol. 92, pp. 7046–7050, July 1995.
R. Malladi and J. A. Sethian, “Image processing: Flows under min/max curvature and mean curvature,” to appear in Graphical Models and Image Processing, March 1996.
R. Malladi and J. A. Sethian, “A unified approach for shape segmentation, representation, and recognition,” Report LBL-36069, Lawrence Berkeley Laboratory, University of California, Berkeley, August 1994.
R. Malladi, D. Adalsteinsson, and J. A. Sethian, “Fast method for 3D shape recovery using level sets,” submitted.
R. Malladi, J. A. Sethian, and B. C. Vemuri, “Evolutionary fronts for topology-independent shape modeling and recovery,” in Proceedings of Third European Conference on Computer Vision, LNCS Vol. 800, pp. 3–13, Stockholm, Sweden, May 1994.
R. Malladi, J. A. Sethian, and B. C. Vemuri, “Shape modeling with front propagation: A level set approach,” IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 17(2), pp. 158–175, Feb. 1995.
D. Marr and E. Hildreth, “A theory of edge detection,” Proc. of Royal Soc. (London), Vol. B207, pp. 187–217, 1980.
S. Osher and J. A. Sethian, “Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulation,” Journal of Computational Physics, Vol. 79, pp. 12–49, 1988.
P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Analysis and Machine Intelligence, Vol. 12(7), pp. 629–639, July 1990.
L. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Modelisations Matematiques pour le traitement d'images, INRIA, pp. 149–179, 1992.
G. Sapiro and A. Tannenbaum, “Image smoothing based on affine invariant flow,” Proc. of the Conference on Information Sciences and Systems, Johns Hopkins University, March 1993.
J. A. Sethian, “Curvature and the evolution of fronts,” Commun. in Mathematical Physics, Vol. 101, pp. 487–499, 1985.
J. A. Sethian, “Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws,” Journal of Differential Geometry, Vol. 31, pp. 131–161, 1990.
J. A. Sethian, “Curvature flow and entropy conditions applied to grid generation,” Journal of Computational Physics, Vol. 115, No. 2, pp. 440–454, 1994.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Malladi, R., Sethian, J.A. (1996). Flows under min/max curvature flow and mean curvature: Applications in image processing. In: Buxton, B., Cipolla, R. (eds) Computer Vision — ECCV '96. ECCV 1996. Lecture Notes in Computer Science, vol 1064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0015541
Download citation
DOI: https://doi.org/10.1007/BFb0015541
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61122-6
Online ISBN: 978-3-540-49949-7
eBook Packages: Springer Book Archive