To conceal themselves on the seafloor European cuttlefish Sepia officinalis express a large repertoire of body patterns. Scenes with 3-D relief are especially challenging because neither is it possible to directly recover visual depth from the 2-D retinal image, nor for the cuttlefish to alter its body shape to resemble nearby objects. Here we characterise cuttlefish's camouflage responses to 3-D relief, and to cast shadows, which are complementary depth cues. Animals were recorded in the presence of cylindrical objects of fixed (15mm) diameter, but varying in height, greyscale and strength of cast shadows, and to corresponding 2-D pictorial images. With the cylinders the cuttlefish expressed a ‘3-D’ body pattern, which is distinct from previously described Uniform, Mottle, and Disruptive camouflage patterns. This pattern was insensitive to variation in object height, contrast, and cast shadow, except when shadows were most pronounced, in which case the body patterns resembled those used on the 2-D backgrounds. This suggests that stationary cast shadows are not used as visual depth cues by cuttlefish, and that rather than directly matching the 2-D retinal image, the camouflage response is a two-stage process whereby the animal first classifies the physical environment and then selects an appropriate pattern. Each type of pattern is triggered by specific cues that may compete allowing the animal to select the most suitable camouflage, so the camouflage response is categorical rather than continuously variable. These findings give unique insight into how an invertebrate senses its visual environment to generate the body pattern response.