Symmetric box-splines on root lattices

Root lattices are efficient sampling lattices for reconstructing isotropic signals in arbitrary dimensions, due to their highly symmetric structure. One root lattice, the Cartesian grid, is almost exclusively used since it matches the coordinate grid; but it is less efficient than other root lattices. Box-splines, on the other hand, generalize tensor-product B-splines by allowing non-Cartesian directions. They provide, in any number of dimensions, higher-order reconstructions of fields, often of higher efficiency than tensored B-splines. But on non-Cartesian lattices, such as the BCC (Body-Centered Cubic) or the FCC (Face-Centered Cubic) lattice, only some box-splines and then only up to dimension three have been investigated. This paper derives and completely characterizes efficient symmetric box-spline reconstruction filters on all irreducible root lattices that exist in any number of dimensions n ≥ 2 (n ≥ 3 for Dn and D∗ n lattices). In all cases, box-splines are constructe...

• Type: Journal
• Year: 2011
• Where: JCAM
• Authors: Minho Kim, Jörg Peters
• Keywords: Box Splines, Cubic Lattice, JCAM 2011, Polynomial Degree