Smooth surface reconstruction from noisy range data

This paper shows that scattered range data can be smoothed at low cost by fitting a Radial Basis Function (RBF) to the data and convolving with a smoothing kernel (low pass filtering). The RBF exactly describes the range data and interpolates across holes and gaps. The data is smoothed during evaluation of the RBF by simply changing the basic function. The amount of smoothing can be varied as required without having to fit a new RBF to the data. The key feature of our approach is that it avoids resampling the RBF on a fine grid or performing a numerical convolution. Furthermore, the computation required is independent of the extent of the smoothing kernel, i.e., the amount of smoothing. We show that particular smoothing kernels result in the applicability of fast numerical methods. We also discuss an alternative approach in which a discrete approximation to the smoothing kernel achieves similar results by adding new centres to the original RBF during evaluation. This approach allows arbitrary filter kernels, including anisotropic and spatially varying filters, to be applied while also using established fast evaluation methods. We illustrate both techniques with LIDAR laser scan data and noisy synthetic data.