TY - JOUR
T1 - Reversible, fast, and high-quality grid conversions
AU - Condat, Laurent
AU - Van De Ville, Dimitri
AU - Forster-Heinlein, Brigitte
N1 - Funding Information:
Manuscript received September 7, 2007; revised July 27, 2008. This work was supported by the Marie Curie Excellence Team Grant MEXT-CT-2004-013477, Acronym MAMEBIA, funded by the European Commission. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Peyman Milanfar.
PY - 2008/5
Y1 - 2008/5
N2 - A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations.
AB - A new grid conversion method is proposed to resample between two 2-D periodic lattices with the same sampling density. The main feature of our approach is the symmetric reversibility, which means that when using the same algorithm for the converse operation, then the initial data is recovered exactly. To that purpose, we decompose the lattice conversion process into (at most) three successive shear operations. The translations along the shear directions are implemented by 1-D fractional delay operators, which revert to simple 1-D convolutions, with appropriate filters that yield the property of symmetric reversibility. We show that the method is fast and provides high-quality resampled images. Applications of our approach can be found in various settings, such as grid conversion between the hexagonal and the Cartesian lattice, or fast implementation of affine transformations such as rotations.
KW - 2-D lattices
KW - Fractional delay filters
KW - Hexagonal grid
KW - Resampling
KW - Rotation
KW - Shears
UR - http://www.scopus.com/inward/record.url?scp=42649124940&partnerID=8YFLogxK
U2 - 10.1109/TIP.2008.919361
DO - 10.1109/TIP.2008.919361
M3 - Article
C2 - 18390374
AN - SCOPUS:42649124940
SN - 1057-7149
VL - 17
SP - 679
EP - 693
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
IS - 5
ER -