| 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
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.
The following images show the effect of the parameters Sigma, Theta, and Iterations. First, the input image is shown together with the result that is achieved if all parameters are set to their default values.
| (1) | (2) |
In the following images, the results are shown that are achieved if one parameter is varied while setting the other two parameters to their default values.
Sigma controls the amount of smoothing, prior to the computation of the gray value gradient. Be careful with very large values for Sigma, because they may lead to undesired effects.
| (1) | (2) | (3) |
Theta controls the step size during the iterative smoothing process. Larger values lead to a stronger smoothing.
| (1) | (2) | (3) |
Iterations controls the number of iterations that are performed. With an increasing number of iterations, the runtime increases, as well. Furthermore, a large number of iterations may lead to a loss of structure in the smoothed image.
| (1) | (2) | (3) |
Note that filter operators may return unexpected results if an image with a reduced domain is used as input. Please refer to the chapter Filters.
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 |