Quasi-Interpolating Spline Models for Hexagonally-Sampled Data

The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. I...

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Bibliographic Details
Published in:IEEE transactions on image processing 2007-05, Vol.16 (5), p.1195-1206
Main Authors: Condat, L., Van De Ville, D.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation theory
Biomedical imaging
box-splines
Cartesian
Computer Graphics
Computer Science
Computer Simulation
Detection, estimation, filtering, equalization, prediction
Engineering Sciences
Exact sciences and technology
Filtering theory
hex-splines
Hexagonal lattice
hexagonal lattices
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Image reconstruction
Image sampling
Information, signal and communications theory
Interpolation
Lattices
linear shift invariant signal spaces
Mathematical models
Models, Statistical
Numerical Analysis, Computer-Assisted
quasi-interpolation
Reconstruction
Reconstruction algorithms
Reproducibility of Results
Sample Size
Sampled data
Sensitivity and Specificity
Signal and communications theory
Signal and Image processing
Signal processing
Signal processing algorithms
Signal Processing, Computer-Assisted
Signal, noise
Spline
Telecommunications and information theory
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Description
Summary:The reconstruction of a continuous-domain representation from sampled data is an essential element of many image processing tasks, in particular, image resampling. Until today, most image data have been available on Cartesian lattices, despite the many theoretical advantages of hexagonal sampling. In this paper, we propose new reconstruction methods for hexagonally sampled data that use the intrinsically 2-D nature of the lattice, and that at the same time remain practical and efficient. To that aim, we deploy box-spline and hex-spline models, which are notably well adapted to hexagonal lattices. We also rely on the quasi-interpolation paradigm to design compelling prefilters; that is, the optimal filter for a prescribed design is found using recent results from approximation theory. The feasibility and efficiency of the proposed methods are illustrated and compared for a hexagonal to Cartesian grid conversion problem
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2007.891808