Surface approximation using GPU-based localized fourier transform

The process of surface reconstruction has received considerable interest from researchers in recent years. Surface reconstruction plays a major role in many applications, such as visualization, geometric modeling and multiresolution analysis. In this paper, we present an approach that approximates a surface from a set of oriented points. Our algorithm combines the implicit surface and frequency-based frameworks to convert the indicator function of the surface into an implicit function from which we can extract the required surface. In contrast to traditional frequency-based approaches, our approach avoids voxelization of the input points and calculates the Fourier coefficients directly from the surface, which reduces the amount of memory required to settle the voxel grid and eliminates the mathematical errors corresponding to this voxelization. In addition, we exploit the recent advances of GPUs embedded in graphics cards to accelerate the calculation of the Fourier coefficients. Finally, some examples are given to demonstrate the validity of the proposed technique.