In this work, we create artistic closed loop curves that trace out images and 3D shapes, which we then hide in musical audio as a form of steganography. We use traveling salesperson art to create artistic plane loops to trace out image contours, and we use Hamiltonian cycles on triangle meshes to create artistic space loops that fill out 3D surfaces. Our embedding scheme is designed to faithfully preserve the geometry of these loops after lossy compression, while keeping their presence undetectable to the audio listener. To accomplish this, we hide each dimension of the curve in a different frequency, and we perturb a sliding window sum of the magnitude of that frequency to best match the target curve at that dimension, while hiding scale information in that frequency's phase. In the process, we exploit geometric properties of the curves to help to more effectively hide and recover them. Our scheme is simple and encoding happens efficiently with a nonnegative least squares framework, while decoding is trivial. We validate our technique quantitatively on large datasets of images and audio, and we show results of a crowd sourced listening test that validate that the hidden information is indeed unobtrusive.

翻译：摘要：本文创建了可勾勒图像与三维形状的艺术闭合曲线，并以隐写形式将其隐藏于音乐音频中。我们利用旅行商问题艺术生成刻画图像轮廓的艺术平面环，并基于三角网格上的哈密顿回路构造填充三维曲面的艺术空间环。所设计的嵌入方案能在有损压缩后精准保留曲线的几何特征，同时确保音频听众无法察觉隐藏信息的存在。为实现这一目标，我们将曲线的每个维度隐藏于不同频率中，通过扰动该频率幅度的滑动窗口和，使其最佳匹配目标曲线在该维度的形态，同时将尺度信息隐藏于该频率的相位中。过程中我们利用曲线的几何特性提升隐藏与恢复效率。本方案结构简洁，编码通过非负最小二乘框架高效完成，解码过程亦仅需简单操作。我们在大规模图像与音频数据集上进行了定量验证，并通过众包听力测试证实隐藏信息确实具有不可察觉性。