A geometric snake model for segmentation of medical imagery

We employ the new geometric active contour models, previously formulated, for edge detection and segmentation of magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound medical imagery. Our method is based on defining feature-based metrics on a given image which in turn leads to a novel snake paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus, the snake is attracted very quickly and efficiently to the desired feature.

[1]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[2]  G. Huisken Flow by mean curvature of convex surfaces into spheres , 1984 .

[3]  Brian White,et al.  Some recent developments in differential geometry , 1989 .

[4]  Demetri Terzopoulos,et al.  Topologically adaptable snakes , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[6]  Gang Xu,et al.  Robust active contours with insensitive parameters , 1994, Pattern Recognit..

[7]  S. Brendle,et al.  Calculus of Variations , 1927, Nature.

[8]  ISAAC COHEN,et al.  Using deformable surfaces to segment 3-D images and infer differential structures , 1992, CVGIP Image Underst..

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

[10]  S. Osher Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[11]  M. Gage,et al.  The heat equation shrinking convex plane curves , 1986 .

[12]  Luis Alvarez,et al.  Formalization and computational aspects of image analysis , 1994, Acta Numerica.

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

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

[15]  Yiannis Aloimonos,et al.  Active vision , 2004, International Journal of Computer Vision.

[16]  J. Sethian,et al.  Crystal growth and dendritic solidification , 1992 .

[17]  S. Zucker,et al.  Toward a computational theory of shape: an overview , 1990, eccv 1990.

[18]  Richard Szeliski,et al.  Tracking with Kalman snakes , 1993 .

[19]  M. Spivak A comprehensive introduction to differential geometry , 1979 .

[20]  V. Caselles,et al.  What is the best causal scale-space for 3D images , 1994 .

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

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

[23]  P. Lions Generalized Solutions of Hamilton-Jacobi Equations , 1982 .

[24]  P. Olver,et al.  Conformal curvature flows: From phase transitions to active vision , 1996, ICCV 1995.

[25]  Anthony J. Yezzi,et al.  Gradient flows and geometric active contour models , 1995, Proceedings of IEEE International Conference on Computer Vision.

[26]  Benjamin B. Kimia,et al.  On the evolution of curves via a function of curvature , 1992 .

[27]  Guillermo Sapiro,et al.  Experiments on geometric image enhancement , 1994, Proceedings of 1st International Conference on Image Processing.

[28]  Surendra Ranganath,et al.  Contour extraction from cardiac MRI studies using snakes , 1995, IEEE Trans. Medical Imaging.

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

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

[31]  OsherStanley,et al.  Feature-oriented image enhancement using shock filters , 1990 .

[32]  Bennett Chow,et al.  Deforming convex hypersurfaces by the $n$th root of the Gaussian curvature , 1985 .

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

[34]  I. Holopainen Riemannian Geometry , 1927, Nature.

[35]  M. Gage,et al.  The Curve Shortening Flow , 1987 .

[36]  A SethianJames,et al.  A Fast Level Set Method for Propagating Interfaces , 1995 .

[37]  R. LeVeque Numerical methods for conservation laws , 1990 .

[38]  Luis Alvarez,et al.  Axiomes et 'equations fondamentales du traitement d''images , 1992 .

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

[40]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[41]  F. Guichard,et al.  Axiomatisation et nouveaux opérateurs de la morphologie mathématique , 1992 .

[42]  J. Smoller Shock Waves and Reaction-Diffusion Equations , 1983 .

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

[44]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

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

[46]  Richard Szeliski,et al.  Modeling surfaces of arbitrary topology with dynamic particles , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[47]  Laurent D. Cohen,et al.  Using Deformable Surfaces to Segment 3-D Images and Infer Differential Structures , 1992, ECCV.

[48]  Guillermo Sapiro,et al.  Invariant Geometric Evolutions of Surfaces and Volumetric Smoothing , 1997, SIAM J. Appl. Math..

[49]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[50]  Ross T. Whitaker,et al.  Algorithms for implicit deformable models , 1995, Proceedings of IEEE International Conference on Computer Vision.

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

[52]  B KimiaBenjamin,et al.  Shapes, shocks, and deformations I , 1995 .