RBF Dipole Surface Evolution

The level set method can implement a wide variety of shape modeling operations (e.g. offsetting, skeletonization, morphing, blending, smoothing, sharpening, embossing, denoising, sculpting, growing, texturing and fitting) simply by specifying a corresponding speed function that controls the growth of an evolving voxel isosurface. The problem is that the basic level set method is implemented on a fixed resolution grid, which limits the utility of these shape modeling operations. We instead represent surfaces with a collection of radial basis function dipole pairs, and derive the motion of these dipoles to implement a surface propagation similar to the level set method but on a smooth, arbitrary resolution model. We demonstrate the utility of this approach with new level set methods for surface fitting, blending and center redistribution for RBF dipole models.