Analyzing Double Image Illusion through Double Indiscernibility and Lattice Theory

The figure-ground division plays a fundamental role in all image perceptions. Although there are a lot of studies about extraction of a figure such as detection of edges or grouping of texture, a few discussions about a relationship between obtained figure and ground. We focused on double image illusions having two complementary relationships between figure and ground and analyzed them. We divided the double image illusions according to two different interpretations and using these divisions we extracted and analyzed its logical structures by lattices derived from rough sets that we had developed. As a result we discovered unusual logical structures in double image illusions.