Image smoothing and enhancement via min/max curvature flow

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 gray-scale noise and full- image continuous noise present in black and white images, gray-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 an 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.

[1]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[2]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

[3]  M. Gage Curve shortening makes convex curves circular , 1984 .

[4]  J. Sethian Curvature and the evolution of fronts , 1985 .

[5]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[7]  Baba C. Vemuri,et al.  Shape Modeling with Front Propagation: A Level Set Approach , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  R Malladi,et al.  Image processing via level set curvature flow. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[9]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  J. Sethian Curvature Flow and Entropy Conditions Applied to Grid Generation , 1994 .

[11]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[12]  James A. Sethian,et al.  Image Processing: Flows under Min/Max Curvature and Mean Curvature , 1996, CVGIP Graph. Model. Image Process..

[13]  M. Grayson The heat equation shrinks embedded plane curves to round points , 1987 .

[14]  Baba C. Vemuri,et al.  Front Propagation: A Framework for Topology Independent Shape Modeling and Recovery , 1994 .

[15]  J. Sethian Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws , 1990 .