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# H2O: Reversible Hexagonal-Orthogonal Grid Conversion by 1-D Filtering

## L. Condat, B. Forster-Heinlein, D. Van De Ville

### Proceedings of the 2007 IEEE International Conference on Image Processing (ICIP'07), San Antonio TX, USA, September 16-19, 2007, pp. II-73-II-76.

In this work, we propose a new grid conversion algorithm between the hexagonal lattice and the orthogonal (a.k.a. Cartesian) lattice. The conversion process, named H2O, is easy to implement and is perfectly reversible using the same algorithm to return from one lattice to the other. The key observation of our approach is a decomposition of the lattice conversion as a sequence of shearing operations along three well-chosen directions. Hence, only 1-D fractional sample delay operators are required, which can be implemented by simple convolutions. The proposed algorithm combines reversibility and fast 1-D operations, together with high-quality resampled images.

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AUTHOR="Condat, L. and Forster-Heinlein, B. and Van De Ville, D.",
TITLE="${\mathrm{H}}_{2}{\mathrm{O}}$: {R}eversible Hexagonal-Orthogonal
Grid Conversion by {1-D} Filtering",
BOOKTITLE="Proceedings of the 2007 {IEEE} International Conference on
Image Processing ({ICIP'07})",
YEAR="2007",
editor="",
volume="",
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pages="{II}-73--{II}-76",