Convexity analysis of active contour problems

A general active contour formulation is considered and a convexity analysis of its energy function is presented. Conditions under which this formulation has a unique solution are derived; these conditions involve both the active contour energy potential and the regularization parameters. This analysis is then applied to four particular active contour formulations, revealing important characteristics of their convexity, and suggesting that external potentials involving center of mass computations may be better behaved than the usual potentials based on image gradients. Most importantly, our analysis provides an explanation for the poor convergence behavior at concave boundaries and suggests an alternate algorithm for approaching these types of boundaries.

[1]  C VemuriBaba,et al.  Shape Modeling with Front Propagation , 1995 .

[2]  Jerry L. Prince,et al.  An active contour model for mapping the cortex , 1995, IEEE Trans. Medical Imaging.

[3]  Marie-Odile Berger,et al.  Towards autonomy in active contour models , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[4]  K. Lai.  Deformable contours: modeling, extraction, detection and classification , 1995 .

[5]  Charles R. Meyer,et al.  Optimal contour approximation by deformable piecewise cubic splines , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[7]  Frederic Fol Leymarie,et al.  Tracking Deformable Objects in the Plane Using an Active Contour Model , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[8]  F. Leymarie.  Tracking and Describing Deformable Objects Using Active Contour Models , 1990 .

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

[10]  Jerry L. Prince,et al.  Adaptive active contour algorithms for extracting and mapping thick curves , 1993, Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

[11]  R. Samadani.  Changes in connectivity in active contour models , 1989, [1989] Proceedings. Workshop on Visual Motion.

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

[13]  Laurent D. Cohen,et al.  Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[15]  Terry E. Weymouth,et al.  Using Dynamic Programming For Minimizing The Energy Of Active Contours In The Presence Of Hard Constraints , 1988, [1988 Proceedings] Second International Conference on Computer Vision.

[16]  De Lillo,et al.  Advanced calculus with applications , 1982 .

[17]  Pierre Soille,et al.  Morphological gradients , 1993, J. Electronic Imaging.

[18]  Frederic Fol Leymarie,et al.  New Method For Shape Description Based On An Active Contour Model , 1990, Other Conferences.

[19]  Mubarak Shah,et al.  A Fast algorithm for active contours and curvature estimation , 1992, CVGIP Image Underst..

[20]  Ramin Samadani,et al.  Evaluation Of An Elastic Curve Technique For Finding The Auroral Oval From Satellite Images Automatically , 1990 .

[21]  Norberto F. Ezquerra,et al.  Spatiotemporal detection of arterial structure using active contours , 1992, Other Conferences.

[22]  Roger L.T. Cederberg.  Chain-link coding and segmentation for raster scan devices , 1978 .