Modified Level Transformation for Bit Inversion Inwatermarking

The transformation function proposed in a previous paper performs both inverting a bit chosen in a multi-level signal and minimizing the resultant change of level. The remaining level changes, however, get larger in the intervals including the ends of the source level range than in the middle intervals. The principal object of the present paper is to remove this difference in transformation performance among the intervals and thus to obtain the same properties over all the source range. To avoid the ends of the level range, a translated and extended coordinate system is proposed. The transformation is then modified and formulated so as to involve the translating of levels. Furthermore, a function of varying the output levels in a random manner is added to the modified transformation. Consequently, the output levels can spread over the whole dynamic range. The effects of the random variations are evaluated through a stochastic analysis.