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.

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