EPFL | Biomedical Imaging Group | Quincunx Subsampling

On the Multidimensional Extension of the Quincunx Subsampling Matrix

D. Van De Ville, T. Blu, M. Unser

IEEE Signal Processing Letters, vol. 12, no. 2, pp. 112–115, February 2005.

The dilation matrix associated with the three-dimensional (3-D) face-centered cubic (FCC) sublattice is often considered to be the natural 3-D extension of the two-dimensional (2-D) quincunx dilation matrix. However, we demonstrate that both dilation matrices are of different nature: while the 2-D quincunx matrix is a similarity transform, the 3-D FCC matrix is not. More generally, we show that is impossible to obtain a dilation matrix that is a similarity transform and performs downsampling of the Cartesian lattice by a factor of two in more than two dimensions. Furthermore, we observe that the popular 3-D FCC subsampling scheme alternates between three different lattices: Cartesian, FCC, and quincunx. The latter one provides a less isotropic sampling density, a property that should be taken into account to properly orient 3-D data before processing using such a subsampling matrix.

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TITLE="On the Multidimensional Extension of the Quincunx Subsampling
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JOURNAL="{IEEE} Signal Processing Letters",
YEAR="2005",
volume="12",
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