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.

翻译：我们通过理论分析评估了所提出的关联水印方法的性能，该方法不直接将水印嵌入图像中。我们先前提出了一种水印方法，通过应用关联记忆模型扩展了零水印模型。在该模型中，异联想记忆模型被引入图像特征与水印之间的映射过程，而自联想记忆模型则用于校正水印错误。本文通过实际图像的计算机仿真表明，关联水印模型的性能优于零水印模型。本文阐述了如何利用冈田理论推导关联水印模型的宏观状态方程。通过四阶理论获得的理论结果与计算机仿真结果高度吻合。此外，我们通过理论分析和计算机仿真，利用水印的误码率评估了关联水印模型的性能。