  We theoretically evaluated the performance of our proposed associative
watermarking method in which the watermark is not embedded directly into the
image. We previously proposed a watermarking method that extends the
zero-watermarking model by applying associative memory models. In this model,
the hetero-associative memory model is introduced to the mapping process
between image features and watermarks, and the auto-associative memory model is
applied to correct watermark errors. We herein show that the associative
watermarking model outperforms the zero-watermarking model through computer
simulations using actual images. In this paper, we describe how we derive the
macroscopic state equation for the associative watermarking model using the
Okada theory. The theoretical results obtained by the fourth-order theory were
in good agreement with those obtained by computer simulations. Furthermore, the
performance of the associative watermarking model was evaluated using the bit
error rate of the watermark, both theoretically and using computer simulations.
