  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.
