Avoiding instability in the diversity term
The overall loss and the relative contributions of the three components during optimization of a wind chimes texture using the diversity term from Sendik & Cohen-Or (2017) compared to the diversity term in our paper. Their diversity term can lead to negative losses, which in turn makes optimization difficult when the loss passes through zero. In part to avoid these instabilities we propose a new diversity term of the form Eq. 7 in our paper.
Loss during optimization
Left panel: loss during optimization of the wind chimes texture. Right panel: the fraction of the total loss each of the three terms contributes during optimization.
Matching the autocorrelation function
Autocorrelation functions of a rhythmic (top row) and non-rhythmic (bottom row) texture for the original (left column) and two weights on the autocorrelation loss. Whereas the non-rhythmic texture has a flat autocorrelation function, the autocorrelation function of the rhythmic texture displays structure that is reproduced only when the weight on the autocorrelation loss is large.