Kernel-Based Sampling of Arbitrary Signals

Point sampling is widely used in several Computer Graphics' applications, such as point-based modelling and rendering, image and geometry processing. Starting from the kernel-based sampling, which approximates an input signal on a regular grid as the sum of Gaussian kernels, we introduce a set of additional variables that control the kernels' width and height. These additional variables allow us to improve the quality of the distribution of the samples, and to achieve a higher approximation accuracy and a more accurate feature preservation, with a slightly higher computational cost. To further improve the sampling with respect to the input data, we introduce a sampling initialisation for processing high resolution signals, without incurring in limits for memory allocation, and a sampling optimisation, which adaptively selects the number and location of the samples to achieve the target approximation accuracy, without oversampling the input signal. To show the generality of the proposed approach for unstructured data of arbitrary dimension, we apply our kernel-based sampling to different types of data, such as 2D images, solutions to PDEs on arbitrary domains, and vector fields.