Technical Section: Variational implicit surface meshing
Computers and Graphics
Variational B-spline level-set: a linear filtering approach for fast deformable model evolution
IEEE Transactions on Image Processing
An efficient local Chan-Vese model for image segmentation
Pattern Recognition
Classification Using Geometric Level Sets
The Journal of Machine Learning Research
Radial basis function based level set interpolation and evolution for deformable modelling
Image and Vision Computing
Parametric Level Set Methods for Inverse Problems
SIAM Journal on Imaging Sciences
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
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The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.