6. A geometrical scheme for curve evolution

6.1 Preliminary definitions6.2 Erosion6.3 Properties of the erosion6.4 Erosion and level sets 6.4.1 Consistency6.4.2 Convergence6.5 Evolution by a power of the curvature 6.5.1 Consistency6.5.2 Convergence6.6 A numerical implementation of the erosion 6.6.1 Scale covariance6.6.2 General algorithm6.6.3 Eroded set and envelope6.6.4 Swallow tails6.7 Numerical experiments 6.7.1 Evolving circles6.7.2 Convex polygons6.7.3 Unclosed curve6.7.4 Evolving non convex curves6.7.5 Invariance6.7.6 Numerical maximum principle6.7.7 Image filtering6.8 Bibliographical notes