Equidistant intervals in perspective photographs and paintings

Human vision is extremely sensitive to equidistance of spatial intervals in the frontal plane. Thresholds for spatial equidistance have been extensively measured in bisecting tasks. Despite the vast number of studies, the informational basis for equidistance perception is unknown. There are three possible sources of information for spatial equidistance in pictures, namely, distances in the picture plane, in physical space, and visual space. For each source, equidistant intervals were computed for perspective photographs of walls and canals. Intervals appear equidistant if equidistance is defined in visual space. Equidistance was further investigated in paintings of perspective scenes. In appraisals of the perspective skill of painters, emphasis has been on accurate use of vanishing points. The current study investigated the skill of painters to depict equidistant intervals. Depicted rows of equidistant columns, tiles, tapestries, or trees were analyzed in 30 paintings and engravings. Computational analysis shows that from the middle ages until now, artists either represented equidistance in physical space or in a visual space of very limited depth. Among the painters and engravers who depict equidistance in a highly nonveridical visual space are renowned experts of linear perspective.