A unified approach to noise removal, image enhancement, and shape recovery

We present a unified approach to noise removal, image enhancement, and shape recovery in images. The underlying approach relies on the level set formulation of the curve and surface motion, which leads to a class of PDE-based algorithms. Beginning with an image, the first stage of this approach removes noise and enhances the image by evolving the image under flow controlled by min/max curvature and by the mean curvature. This stage is 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. The noise removal/enhancement schemes applied in this stage contain only one enhancement parameter, which in most cases is automatically chosen. The other key advantage of our approach is that a stopping criteria is automatically picked from the image; continued application of the scheme produces no further change. The second stage of our approach is the shape recovery of a desired object; we again exploit the level set approach to evolve an initial curve/surface toward the desired boundary, driven by an image-dependent speed function that automatically stops at the desired boundary.

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

[2]  D. Chopp.  Computing Minimal Surfaces via Level Set Curvature Flow , 1993 .

[3]  V. Caselles,et al.  A geometric model for active contours in image processing , 1993 .

[4]  L. Álvarez,et al.  Signal and image restoration using shock filters and anisotropic diffusion , 1994 .

[5]  J. Sethian,et al.  Projection methods coupled to level set interface techniques , 1992 .

[6]  Farzin Mokhtarian,et al.  A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Baba C. Vemuri,et al.  Evolutionary Fronts for Topology-Independent Shape Modeling and Recoveery , 1994, ECCV.

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

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

[10]  J. Sethian.  AN ANALYSIS OF FLAME PROPAGATION , 1982 .

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

[12]  R. Bajcsy,et al.  Three dimensional object representation revisited , 1987 .

[13]  James A. Sethian,et al.  Flow under Curvature: Singularity Formation, Minimal Surfaces, and Geodesics , 1993, Exp. Math..

[14]  L. Rudin,et al.  Feature-oriented image enhancement using shock filters , 1990 .

[15]  Baba C. Vemuri,et al.  Constructing Intrinsic Parameters with Active Models for Invariant Surface Reconstruction , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

[18]  Demetri Terzopoulos,et al.  Regularization of Inverse Visual Problems Involving Discontinuities , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  J. Sethian,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[20]  Laurent D. Cohen,et al.  On active contour models and balloons , 1991, CVGIP Image Underst..

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

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

[23]  J. Sethian,et al.  Dynamical behaviour of a premixed turbulent open V-flame , 1995 .

[24]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

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

[26]  Ellen C. Hildreth,et al.  Implementation Of A Theory Of Edge Detection , 1980 .

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

[28]  Andrew Blake,et al.  Visual Reconstruction , 1987, Deep Learning for EEG-Based Brain–Computer Interfaces.

[29]  Guillermo Sapiro,et al.  Area and Length Preserving Geometric Invariant Scale-Spaces , 1995, IEEE Trans. Pattern Anal. Mach. Intell..

[30]  Mary Beth Ruskai,et al.  Wavelets and their Applications , 1992 .

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

[32]  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.

[33]  Demetri Terzopoulos,et al.  Constraints on Deformable Models: Recovering 3D Shape and Nonrigid Motion , 1988, Artif. Intell..

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