Where does depth collide?

Depth perception is the recovery of three-dimensional distance and layout from the flat images formed on the two eyes. Wheatstone's 1838 Contributions to the physiology of vision showed with his stereoscope that the small differences between the left-eye and right-eye views are themselves a cue the visual system uses to reconstruct solid form, and Julesz's 1960 Binocular depth perception of computer-generated patterns demonstrated with random-dot patterns that this reconstruction works from those differences alone, with no shape visible in either image on its own. The referent here is a perceptual achievement of a viewer, the felt distance of things in a scene, and it is not the opacity of a medium along a line of sight or a point's centrality within a cloud of data.[1][2]

Unit

One viewer's perceived distance or three-dimensional layout of a scene

Recovery means

Not applicable

Measured by

Assessed by stereoacuity thresholds and depth-judgment tasks that vary binocular and monocular cues

Optical depth is a dimensionless measure of how strongly a medium attenuates radiation passing along a line of sight, set by the amount of absorbing and scattering material in the path. Schuster's 1905 Radiation through a foggy atmosphere introduced this bookkeeping of absorption and scattering through a layered atmosphere, and Chandrasekhar's 1950 Radiative transfer made it the standard variable of the field, with the transmitted intensity falling by a factor of e over one unit of optical depth. The referent is a property of the medium and the path, counted in units of attenuation, and it has nothing to do with a viewer's perceived distance or with a data point's standing in a distribution.[3][4]

Unit

A dimensionless attenuation along one line of sight, in e-foldings of intensity

Recovery means

Not applicable

Measured by

Computed as the path integral of the extinction coefficient, or inferred from the observed dimming of a background source

Data depth is a measure of how central, or how far from the outer edge, a point lies within a distribution or a batch of observations, giving a way to order multivariate data from the middle outward. Tukey proposed the idea in his 1975 address Mathematics and the picturing of data, where the deepest point serves as a multivariate median, and Liu's 1990 On a notion of data depth based on random simplices gave it a precise probabilistic definition and studied its properties. The referent is a number assigned to a point relative to a data set, largest at the center and small at the fringe, and it is unrelated to the perceived distance of objects to a viewer or to the attenuation of light through a medium.[5][6]

Unit

A depth value assigned to one point relative to a data set, largest at the center

Recovery means

Not applicable

Measured by

Computed by a depth function such as simplicial or halfspace depth over the sample