The paper's authors reasoned that if mimicry-based camouflage works through disguise rather than invisibility, a predator's experience might determine their response to mimic camouflage. They trained three experimental groups of young domestic chicks by introducing them into trial arenas containing either natural hawthorn branches, empty arenas, or hawthorn branches wrapped in purple thread. The wrapped branches were used to test whether the chicks would be more or less likely to attack something twig-like but differently colored (though this is only clear from the supplementary online material).
Larva of the brimstone moth Opisthograptis luteolata, looking distinctly twig-like. Photo by Michael E. Talbot.
The authors then presented chicks from each "training" group with either one of two species of hawthorn-twig-mimicking moth larvae (the brimstone moth, or the early thorn moth), or a hawthorn twig about the size of a caterpillar. Chicks that had previously encountered natural twigs waited longer to attack the caterpillars than chicks that hadn't previously seen twigs, or that saw the colored hawthorn branches. So, apparently, the chicks were reasoning (inasmuch as chicks reason) that the twig-like object in front of them was the same as the inedible twigs they had tried before.
This is an elegant experimental test of the effect of mimicry as mimicry – what the authors propose to call camouflage by "masquerade." However, it doesn't actually show that what the authors term camouflage by crypsis – blending into the background – isn't also contributing to the benefits that these caterpillars receive from their unique shape and coloration. There's no reason to think that twig-shaped caterpillars can't benefit in both ways, by being less visible in the first place, and then easily mistaken for a twig if they are seen.
In conclusion, here's some video footage of another natural mimic, the leaf insect.
Skelhorn, J., Rowland, H., Speed, M., & Ruxton, G. (2010). Masquerade: Camouflage without crypsis Science, 327 (5961), 51 DOI: 10.1126/science.1181931