By Topic

On quantization with the Weaire-Phelan partition

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Kashyap, N. ; Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA ; Nuehoff, D.L.

Until recently, the solution to the Kelvin problem of finding a partition of R3 into equal-volume cells with the least surface area was believed to be tessellation by the truncated octahedron. In 1994, D. Weaire and R. Phelan described a partition that outperformed the truncated octahedron partition in this respect. This raises the question of whether the Weaire-Phelan (WP) partition can outperform the truncated octahedron partition in terms of normalized moment of inertia (NMI), thus providing a counterexample to Gersho's conjecture that the truncated octahedron partition has the least NMI among all partitions of R3. In this correspondence, we show that the effective NMI of the WP partition is larger than that of the truncated octahedron partition. We also show that if the WP partition is used as the partition of a three-dimensional (3-D) vector quantizer (VQ), with the corresponding codebook consisting of the centroids of the cells, then the resulting quantization error is white. We then show that the effective NMI of the WP partition cannot he reduced by passing it through an invertible linear transformation. Another contribution of this correspondence is a proof of the fact that the quantization error corresponding to an optimal periodic partition is white, which generalizes a result of Zamir and Feder (1996)

Published in:

Information Theory, IEEE Transactions on  (Volume:47 ,  Issue: 6 )