Visual space

Object space and visual space

Physical objects occupy a Euclidean, three-dimensional space measurable with rulers and describable by coordinate systems. Visual space, by contrast, is the ordered ensemble of percepts in conscious experience and cannot be measured with rulers. Historically, philosophers relied on introspection and reasoning to describe it, but with the development of psychophysics beginning with Gustav Fechner, experimental procedures emerged to objectively describe visual space, including geometric descriptions.

For example, an observer asked to set two lines so they appear parallel yields a configuration that is parallel in visual space, which can then be compared to the actual physical layout. The visual field—the extent of physical space imaged on the retina—should be distinguished from visual space, though the German term Sehraum has caused confusion for both. Rudolf Carnap distinguished three kinds of space: formal spaces (logico-deductive structures), physical space (empirically determined objects), and perceptual space (immediate sensory experiences or apperceptions).

Visual space and geometry

Geometry studies space and the rules relating its elements. In Euclidean space, the Pythagorean theorem computes distances from Cartesian coordinates; on surfaces of constant curvature, such as a sphere, the rule is more complex but uniform. On a football-shaped surface, the metric varies by location. Ernst Mach in 1901 described physiological space as a threefold manifoldness that is neither everywhere alike, infinite, nor unbounded. Rudolf Luneburg in 1947 attempted a rigorous formulation, asking whether if physical objects A, B, C have correlates A', B', C' in visual space and C lies between A and B, then C' lies between A' and B'. Based on fragmentary psychophysical data, Luneburg concluded visual space was hyperbolic with constant curvature, arguing that such a transformation renders infinity into a dome (the sky). Subsequent experiments did not generally favor this proposition.

Neural representation of space

Gustav Theodor Fechner defined psychophysics as the functional relationship between mental and material worlds, but he distinguished inner from outer psychophysics, recognizing that a physical stimulus generates a percept via the sensory and nervous systems. Johannes Müller emphasized that what matters in a neural path is the connection it makes, and Hermann Lotze enunciated the principle of local signs. Together, these mean a nerve fiber from a fixed retinal location instructs target neurons about a stimulus at that location, and the orderly retinal array is preserved in a retinotopic mapping in primary visual cortex.

However, visual signals are analyzed in parallel channels for position, brightness, color, orientation, and depth; no single neuron or circuit represents both a feature and its accurate location. The unitary mapping of object space into coherent visual space requires conjoint activity across several nervous system parts that is beyond current neurophysiological research. Neural units in the hippocampus show activity only when an animal is in a specific place.

Space and its content

On an astronomical scale, physical space and its contents are interdependent per general relativity, but this is irrelevant in vision; distances in object space are independent of object nature. In visual space, however, an observer judging relative locations of a few light points in darkness is a simplistic extension that enabled Luneburg's geometric claims. In a richer visual world, percepts carry prior associations that affect their spatial disposition; identical physical separations can appear different depending on demarcating features, especially in depth.

Monocular vision uses cues like size, perspective, and relative motion to assign depth, but expanding a 2-dimensional manifold into a 3-dimensional visual world is mathematically ill-posed yet effectively accomplished. Binocular vision allows stereoscopic depth determination, but its linkage to the other two dimensions is uncertain. Everyday three-dimensional visual space results from many perceptual and cognitive layers atop the physiological representation.