The metric of visual space

The geometric properties of visual space in the horizontal plane were measured by four different procedures. Five observers were asked to judge distances, angles, and areas defined by pairs and triplets of stakes, using magnitude estimation, category estimation, mapping, and perceptual matching. All judgments took place outdoors in a broad, open field under full-cue conditions. Stimuli oriented in depth were judged to be half as large as the same stimuli oriented in the frontal plane. Angles facing either directly toward or directly away from the observer were seen as approximately twice as large as those seen on their sides. Four mathematical models for visual space are examined. Both the hyperbolic model of Luneburg (1947) and the spherical model of Reid (1764/1813) fail, each for different reasons. Two other models, however, produce a reasonably complete description of visual space. In the first model, visual space is an affine-transformed version of a Euclidean physical space. In the second model, distances are viewed as vectors that can be broken down into in-depth and frontal components relative to the observer. The in-depth component of this vector is contracted by a constant amount in visual space.