A mathematical model for spatial orientation from pictorial perspective displays

A previously formulated mathematical model, describing how observers reconstruct three-dimensional spatial layouts from perspective projections, has been extended to more complex situations. The model assumes that the observer has a priori knowledge of certain characteristics of the viewed objects, like size, shape, or parallelism or perpendicularity of lines or planes. These assumptions are used in a three-dimensional process to reconstruct a spatial layout that `best matches' the perceived lines of sight to the object coordinates. Sources of errors and biases in this process are specified and their effects on model outputs are discussed. An experiment, in which eight subjects judged the relative direction of one object with respect to another, has been conducted to validate the model. The model has been found to generally reproduce the systematic trends of the experimental results and also has provided an analytical explanation for them. The mathematical model is expected to be a useful tool in analyzing and developing pictorial perspective flight displays.