Multiple Pictures of a Perspective Scene Reveal the Principles of Picture Perception

A picture is a powerful and convenient medium for inducing the illusion that one perceives a real three-dimensional scene. The relative invariance of picture perception across viewing positions has aroused the interest of painters, photographers and visual scientists. Many studies have been devoted to perceptual invariance when pictures are viewed from oblique directions. Invariance across viewing distances has received less attention. This study presents a computational analysis of pictures of perspective scenes taken from different distances between camera and physical objects. Distances and directions of pictorial objects were computed as function of viewing distance to the picture and compared with distances and directions of the physical objects as function of camera position. The computations show that pictorial distance and direction are determined by angular size of the depicted objects. Pictorial distance and direction are independent of camera position, focal length of the lens, and picture size. Ratios of pictorial distances, directions and sizes are constant as function of viewing distance. The constant ratios are proposed as the reason for invariance of picture perception over a range of viewing distances. Reanalysis of distance judgments obtained from the literature shows that perspective space, previously proposed as the model for visual space, is also a good model for pictorial space. The geometry of pictorial space contradicts some conceptions about picture perception.