A Mathematical Expression for Stereoscopic Depth Perception

Abstract

The metric nature of stereoscopic depth perception has remained an enigma. Several mathematical formulations proposed for measuring the stereoscopic effect have not shown to be reliable. This may be due to the lack of a conceptual distinction between the 3D model geometrically obtained by intersection of visual rays (geometric model), and the 3D model perceived in the observer's mind (perceptual model). Based on the assumption that retinal parallax is the only source of information on depth available to the brain, we developed an equation that shows real and perceptual space to be connected by a logarithmic function. This relationship has allowed us to formulate the vertical exaggeration for all sorts of stereoscopic conditions, including natural stereo-vision. The obtained formulations might involve possibilities of technological applications, such as the artificial recreation of a natural stereo-vision effect, and the design of stereoscopic instruments with a desired degree of vertical exaggeration.