Kernel-based adaptive sampling for image reconstruction and meshing

This paper introduces a kernel-based sampling approach for image reconstruction and meshing. Given an input image and a user-specified number of points, the proposed method can automatically generate adaptive distribution of samples globally. We formulate the problem as an optimization to reconstruct the image by summing a small number of Gaussian kernels to approximate the given target image intensity or density. Each Gaussian kernel has the fixed size and the same energy. After the optimization, the samples are well distributed according to the image intensity or density variations as well as faithfully preserved the feature edges, which can be used to reconstruct high-quality images. Finally, we generate the adaptive triangular or tetrahedral meshes based on the well-spaced samples in 2D and 3D images. Our results are compared qualitatively and quantitatively with the state-of-the-art in image sampling and reconstruction on several examples by using the standard measurement criteria.