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Level-set Spline

Variational B-spline level-set


Author: Olivier Bernard

Olivier Bernard is currently an Associate Professor at INSA (Lyon - France) and a member of the CREATIS-LRMN Laboratory (CNRS 5220, INSERM U630, INSA, Claude Bernard Lyon 1 University).

Algorithm Outline

We present here a new formulation of level-set where the implicit function is modelled as a continuous parametric function expressed on a B-spline basis. Starting from the level-set energy functional, this formulation allows computing the solution as a restriction of the variational problem on the space spanned by the B-splines. As a consequence, the minimization of the functional is directly obtained in terms of the B-splines parameters. We also show that each step of this minimization may be expressed through a separable convolution operation, which yields a very efficient algorithm. As a further consequence, each step of the level-set evolution may be interpreted as a filtering operation with a B-spline kernel. Such filtering induces an intrinsic smoothing in the algorithm, which can explicitly be controlled via the degree and the scale of the chosen B-spline kernel.


O. Bernard, D. Friboulet, P. Thevenaz and M. Unser "Variational B-spline level-set: a linear filtering approach for fast deformable model evolution," Submitted to IEEE transactions on Image Processing, 2007


Start the Java Applet (Java 1.3)

How to use

  • Choose the parameters
  • Click on "Run" button

Notes of the demo

The behaviour of this approach is illustrated on simulated images as well as experimental images from various fields. The segmentation experiments are based on the Chan-Vese functional, which aims at partitioning the image into regions with piecewise constant intensity. The following settings are applied to all experiments:

The influence of two parameters of the method are illustrated in this demonstration: a parameter nu which weights the curvature term in the functional, and a parameter h which controls the smoothing of the solution via the scale of the B-splines. We indicate the number of iterations needed to reach the final solution. A segmentation obtained through a simple binary threshold is used for comparison purposes


We give in the proposed paper a description of the results obtained for the images named: Spirale, donuts-Noisy-25dB, donuts-Noisy-20dB, donuts-Noisy-15dB, Yeast and Europe-Night-Lights.

2007 EPFL • • 06.12.2007