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A new approach to vector quantizer (VQ) codebook design for video data compression is described. This is based on the notion that symmetries in the data, which are seldom captured exactly in any training dataset, are both important perceptually and can lead to a more robust and effective codebook. The idea is illustrated using a 3-d wavelet transformed video sequences. After discussing the relevant symmetries, a codebook design method is presented, based on a modification of the Linde-Buzo-Gray algorithm. This is applied to various video sequences. Comparisons drawn with other work in the area demonstrate that the scheme has potential and is worthy of further investigation.