A variational method for the recovery of smooth boundaries

Variational methods for image segmentation try to recover a piecewise smooth function together with a discontinuity set which represents the boundaries of the segmentation. This paper deals with a variational method that constrains the formation of discontinuities along smooth contours. The functional to be minimized, which involves the computation of the geometrical properties of the boundaries, is approximated by a sequence of functionals which can be discretized in a straightforward way. Computer examples of real images are presented to illustrate the feasibility of the method.

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

[2]  L. Ambrosio,et al.  Approximation of functional depending on jumps by elliptic functional via t-convergence , 1990 .

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

[4]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[5]  L. Modica.  The gradient theory of phase transitions and the minimal interface criterion , 1987 .

[6]  Jayant Shah.  Uses of Elliptic Approximations in Computer Vision , 1996 .

[7]  Thomas J. Richardson,et al.  Scale independent piecewise smooth segmentation of images via variational methods , 1990 .

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

[9]  Maurizio Paolini,et al.  Semicontinuity and relaxation properties of a curvature depending functional in 2D , 1993 .

[10]  E. D. Giorgi,et al.  Some remarks on Γ-convergence and least squares method , 1991 .

[11]  Tom Ilmanen,et al.  Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature , 1993 .

[12]  Niklas Nordström,et al.  Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection , 1990, Image Vis. Comput..

[13]  Carlo Mantegazza,et al.  Curvature varifolds with boundary , 1996 .

[14]  David Mumford,et al.  Filtering, Segmentation and Depth , 1993, Lecture Notes in Computer Science.

[15]  J. Keller,et al.  Fast reaction, slow diffusion, and curve shortening , 1989 .

[16]  Benjamin B. Kimia,et al.  Image segmentation by reaction-diffusion bubbles , 1995, Proceedings of IEEE International Conference on Computer Vision.

[17]  Franco Tomarelli,et al.  Variational Methods for Discontinuous Structures , 1996 .

[18]  Riccardo March,et al.  Visual reconstruction with discontinuities using variational methods , 1992, Image Vis. Comput..

[19]  Demetri Terzopoulos,et al.  The Computation of Visible-Surface Representations , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Jean-Michel Morel,et al.  Variational methods in image segmentation , 1995 .

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

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

[23]  Jayant Shah.  Segmentation by nonlinear diffusion. II , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[25]  Jayant Shah,et al.  Recovery of surfaces with discontinuities by fusing shading and range data within a variational framework , 1996, IEEE Trans. Image Process..

[26]  Charles M. Elliott,et al.  The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature , 1996, European Journal of Applied Mathematics.

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

[28]  Jayant Shah.  A nonlinear diffusion model for discontinuous disparity and half-occlusions in stereo , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.