Hyperbolic representation of global structure of visual space

Abstract Most studies on visual perception assume a limited region in visual space to be Euclidean. In a series of alley experiments, in which extensive configurations of stimulus points in a frameless space were dealt with, it was found that a horizontal or slanted plane extending from the subject is best described by hyperbolic geometry, whereas a frontoparallel plane in front of the subject is best described by Euclidean geometry. Theoretical problems around these findings and two properties of visual space (VS) were discussed: (1) VS is closed in the sense that no percepts can appear at an infinite distance. (2) VS is dynamic in the sense that its global structure critically depends upon the configuration of objects in the physical space. Two questions were also discussed: (1) How far is VS extended beyond the farthest percept under various conditions? (2) How does the sky, as the boundary of VS, in daytime as well as at night, change its shape in accordance with what we see in VS?

[1]  A A BLANK,et al.  Axiomatics of binocular vision; the foundations of metric geometry in relation to space perception. , 1958, Journal of the Optical Society of America.

[2]  Tarow Indow,et al.  Multidimensional mapping of visual space with real and simulated stars , 1968 .

[3]  Koch Sigmund Ed,et al.  Psychology: A Study of A Science , 1962 .

[4]  Michael Cook,et al.  The judgment of distance on a plane surface , 1978, Perception & psychophysics.

[5]  Hsien-chung Wang.  Two theorems on metric spaces. , 1951 .

[6]  H. Freudenthal.  Lie groups in the foundations of geometry , 1964 .

[7]  José Aparecido da Silva,et al.  Scaling apparent distance in a large open field: some new data. , 1983 .

[8]  Hsien-Chtjng Wang,et al.  TWO-POINT HOMOGENEOUS SPACES , 1952 .

[9]  T Indow,et al.  A critical review of Luneburg's model with regard to global structure of visual space. , 1991, Psychological review.

[10]  Michael A. Kemp,et al.  The Science of Art , 1989 .

[11]  L. Kaufman,et al.  Handbook of perception and human performance , 1986 .

[12]  W. Metzger.  Optische Untersuchungen am Ganzfeld , 1930 .

[13]  J. Koenderink,et al.  Surface perception in pictures , 1992, Perception & psychophysics.

[14]  Thomas F. Malone,et al.  Compendium of meteorology , 1951 .

[15]  A. Battro,et al.  Riemannian Geometries of Variable Curvature in Visual Space: Visual Alleys, Horopters, and Triangles in Big Open Fields , 1976, Perception.

[16]  T. Indow.  Alleys in visual space , 1979 .

[17]  T. Indow.  Alleys on an apparent frontoparallel plane , 1988 .

[18]  Paul M. Laporte,et al.  Mathematical Analysis of Binocular Vision , 1950 .

[19]  Rudolf K. Luneburg,et al.  Metric of binocular visual space , 1950 .

[20]  Jaap Van Brakel,et al.  Foundations of measurement , 1983 .

[21]  Margaret A. Hagen,et al.  The Perception of Pictures , 1982 .

[22]  T Indow,et al.  Parallel—and distance—alleys with moving points in the horizontal plane , 1984, Perception & psychophysics.

[23]  Michael D'Zmura,et al.  Geometric Representations of Perceptual Phenomena : Papers in Honor of Tarow indow on His 70th Birthday , 1995 .

[24]  M. Teghtsoonian,et al.  Scaling apparent distance in natural indoor settings , 1969 .

[25]  Herbert Busemann,et al.  The geometry of geodesics , 1955 .

[26]  M. Teghtsoonian,et al.  Scaling apparent distance in a natural outdoor setting , 1970 .

[27]  T. Künnapas,et al.  SCALES FOR SUBJECTIVE DISTANCE , 1960 .

[28]  Tarow Indow,et al.  An approach to geometry of visual space with no a priori mapping functions: Multidimensional mapping according to Riemannian metrics , 1982 .

[29]  Hyperbolic Geometry as an Alternative to Perspective for Constructing Drawings of Visual Space , 1977, Perception.

[30]  T Indow,et al.  Parallel-Alleys and Distance-Alleys on Horopter Plane in the Dark , 1984, Perception.

[31]  T Indow,et al.  Alleys on an Extensive Apparent Frontoparallel Plane: A Second Experiment , 1988, Perception.

[32]  The moon illusion: I. How high is the sky? , 1982 .