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The quantization of a linear projective transformation first proposed by Chen and Wornell is shown to allow for much better performance figures than those yielded by previous approaches. The procedure to achieve this improvement is explained through the proposal and analysis of an improved data hiding method called quantized projection (QP), based in the quantization of a statistic similar to those used at detection in spread-spectrum algorithms. Both the theoretical analysis and the empirical validation show that projection-based methods exhibit huge performance improvements over existing ones under the same conditions - i.e. same degree of diversity and level of random additive attacking distortion.