Efficient Reconstruction of Hexagonally Sampled Data using Three-Directional Box-Splines

Three-directional box-splines are particularly well-suited to interpolate and approximate hexagonally sampled data. In this paper, we propose a computationally efficient end-toend reconstruction process. First, we introduce a prefiltering step that is based on a quasi-interpolation scheme using lowcomplexity finite-impulse-response (FIR) filters. Second, we derive a closed analytical expression for three-directional box-splines of any order that leads to a fast evaluation of the spline surface. All operations act locally on the data, and thus are well adapted to applications dealing with large images. To demonstrate the feasibility of our method, we implemented the complete procedure and we present experimental results.

• Type: Conference
• Year: 2006
• Where: ICIP
• Authors: Laurent Condat, Dimitri Van De Ville, Michael Unser
• Keywords: Closed Analytical Expression, Complete Procedure, Efficient End-toend Reconstruction, Fast Evaluation, ICIP 2006, Image Processing, Spline Surface