Cephalopod mollusks including octopus and cuttlefish are adept at adaptive camouflage, varying their appearance to suit the surroundings. This behavior allows unique access into the vision of a non-human species because one can ask how these animals use spatial information to control their coloration pattern. There is particular interest in factors that affect the relative levels of expression of the Mottle and the Disruptive body patterns. Broadly speaking, the Mottle is displayed on continuous patterned surfaces whereas the Disruptive is used on discrete objects such as pebbles. Recent evidence from common cuttlefish, Sepia officinalis, suggests that multiple cues are relevant, including spatial scale, contrast, and depth. We analyze the body pattern responses of juvenile cuttlefish to a range of checkerboard stimuli. Our results suggest that the choice of camouflage pattern is consistent with a simple model of how cuttlefish classify visual textures, according to whether they are Uniform or patterned, and whether the pattern includes visual edges. In particular, cuttlefish appear to detect edges by sensing the relative spatial phases of two spatial frequency components (e.g., fundamental and the third harmonic Fourier component in a square wave). We discuss the relevance of these findings to vision and camouflage in aquatic environments.