Kernel-Based Sampling of Arbitrary Data

Abstract

Point sampling is widely used in several Computer Graphics' applications, such as point-based modelling and rendering, image and geometric processing. Starting from the kernel-based sampling of signals defined on a regular grid, which generates adaptive distributions of samples with blue-noise property, we specialise this sampling to arbitrary data in terms of dimension and structure, such as signals, vector fields, curves, and surfaces. To demonstrate the novelties and benefits of the proposed approach, we discuss its applications to the resampling of 2D/3D domains according to the distribution of physical quantities computed as solutions to PDEs, and to the sampling of vector fields, 2D curves and 3D point sets. According to our experiments, the proposed sampling achieves a high approximation accuracy, preserves the features of the input data, and is computationally efficient.