Radial basis function based level set interpolation and evolution for deformable modelling

a r t i c l e i n f o Keywords: Deformable model Level set Radial basis function Re-initialisation free 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. Ever since Kass et al. [1] introduced the active contour or snake model, there has been a multitude of works on the development of active contour models, some theoretical and some tuned to certain applications. Traditional snakes suffer from several issues, such as limited capture range and difficulties in reaching concavities. The application of the level set method [2] to the active contour model has enabled the latter to adapt to complex topologies. It avoids the need to reparameterise the curve and the contours are able to split or merge in order to capture an unknown number of objects without resorting to dedicated contour tracking. However, the original level set based active contour [3] has proved to be of limited …