The formation of all sign systems is based on structures. Structures support the functioning of codes and organization of denotations, connotations, and groups of signs of visual art works. Due to codes, structure interrelations are manifested in characteristics, relations, differences-identities, and groups of elements, forming the structure of an art work. This role of structures was examined in the frames of theoretical ideas of antiquity and Renaissance. Its most complete application to the visual art is manifested in the ideas by Leonardo da Vinci. Developed structures organizing sign systems are illustrated by the analysis of Lady with an Ermine.