A fast algorithm for particle simulations
Journal of Computational Physics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
International Journal of Computer Vision
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation
International Journal of Computer Vision
Bayesian Fusion of Color and Texture Segmentations
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Gradient Vector Flow Fast Geometric Active Contours
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical methods for high dimensional Hamilton-Jacobi equations using radial basis functions
Journal of Computational Physics
Active Contours Using a Constraint-Based Implicit Representation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
International Journal of Computer Vision
An extended level set method for shape and topology optimization
Journal of Computational Physics
A Mumford-Shah level-set approach for the inversion and segmentation of X-ray tomography data
Journal of Computational Physics
TEXEMS: Texture Exemplars for Defect Detection on Random Textured Surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
MAC: Magnetostatic Active Contour Model
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
Active contouring based on gradient vector interaction and constrained level set diffusion
IEEE Transactions on Image Processing
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Generalized Hermitian Radial Basis Functions Implicits from polygonal mesh constraints
The Visual Computer: International Journal of Computer Graphics
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We present a study in level set representation and evolution using radial basis functions (RBFs) for active contour and active surface models. It builds on recent works by others who introduced RBFs into level sets for structural topology optimisation. Here, we introduce the concept into deformable models and present a new level set formulation able to handle more complex topological changes, in particular perturbation away from the evolving front. In the conventional level set technique, the initial active contour/surface is implicitly represented by a signed distance function and periodically re-initialised to maintain numerical stability. We interpolate the initial distance function using RBFs on a much coarser grid, which provides great potential in modelling in high dimensional space. Its deformation is considered as an updating of the RBF interpolants, an ordinary differential equation (ODE) problem, instead of a partial differential equation (PDE) problem, and hence it becomes much easier to solve. Re-initialisation is found no longer necessary, in contrast to conventional finite difference method (FDM) based level set approaches. The proposed level set updating scheme is efficient and does not suffer from self-flattening while evolving, hence it avoids large numerical errors. Further, more complex topological changes are readily achievable and the initial contour or surface can be placed arbitrarily in the image. These properties are extensively demonstrated on both synthetic and real 2D and 3D data. We also present a novel active contour model, implemented with this level set scheme, based on multiscale learning and fusion of image primitives from vector-valued data, e.g. colour images, without channel separation or decomposition.