| Operators |
mean_curvature_flow — Apply the mean curvature flow to an image.
mean_curvature_flow(Image : ImageMCF : Sigma, Theta, Iterations : )
The operator mean_curvature_flow applies the mean curvature flow or intrinsic heat equatio
u_t = div(grad u/|grad u|) |grad u| = curv(u) |grad u|
to the gray value function u defined by the input image Image at a time t_0 = 0. The discretized equation is solved in Iterations time steps of length Theta, so that the output image contains the gray value function at the time Iterations * Theta .
The mean curvature flow causes a smoothing of Image in the direction of the edges in the image, i.e. along the contour lines of u, while perpendicular to the edge direction no smoothing is performed and hence the boundaries of image objects are not smoothed. To detect the image direction more robustly, in particular on noisy input data, an additional isotropic smoothing step can precede the computation of the gray value gradients. The parameter Sigma determines the magnitude of the smoothing by means of the standard deviation of a corresponding Gaussian convolution kernel, as used in the operator isotropic_diffusion for isotropic image smoothing.
Input image.
Output image.
Smoothing parameter for derivative operator.
Default value: 0.5
Suggested values: 0.0, 0.1, 0.5, 1.0
Restriction: Sigma >= 0
Time step.
Default value: 0.5
Suggested values: 0.1, 0.2, 0.3, 0.4, 0.5
Restriction: 0 < Theta <= 0.5
Number of iterations.
Default value: 10
Suggested values: 1, 5, 10, 20, 50, 100, 500
Restriction: Iterations >= 1
M. G. Crandall, P. Lions; “Convergent Difference Schemes for
Nonlinear Parabolic Equations and Mean Curvature Motion”;
Numer. Math. 75 pp. 17-41; 1996.
G. Aubert, P. Kornprobst; “Mathematical Problems in Image
Processing”; Applied Mathematical Sciences 147; Springer, New
York; 2002.
Foundation
| Operators |