The effectiveness of Convolutional Neural Networks stems in large part from their ability to
exploit the translation invariance that is inherent in many learning problems. Recently, it was …

Box splines provide smooth spline spaces as shifts of a single generating function on a
lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical …

We introduce a family of box splines for efficient, accurate, and smooth reconstruction of
volumetric data sampled on the body-centered cubic (BCC) lattice, which is the favorable …

Spline functions have received widespread attention in the fields of image sampling and
reconstruction. To enhance the performance of splines in reconstruction and reduce the …

We demonstrate that non-separable box splines deployed on body centered cubic lattices
(BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop …

In this paper, we demonstrate that quasi-interpolation of orders two and four can be
efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B …

In this paper, Cosine-Weighted B-spline (CWB) filters are proposed for interpolation on the
optimal Body-Centered Cubic (BCC) lattice. We demonstrate that our CWB filters can well …

We introduce a framework for construction of non-separable multivariate splines that are
geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like …

Abstract The Body Centered Cubic (BCC) and Face Centered Cubic (FCC) lattices along
with a set of box splines for sampling and reconstruction of trivariate functions are proposed …

We investigate the use of a Fourier-domain derivative error kernel to quantify the error
incurred while estimating the gradient of a function from scalar point samples on a regular …