Abstract
The objective content of the visual world of a monocular, immobile observer is entirely due to “monocular cues”. These cues only partially constrain the geometry, the remaining ambiguities define a freedom of the observer to commit “mental changes of viewpoint”. Though fully idiosyncratic, such changes cannot possibly violate the optical data. We use this group of “visual congruences” (for that they must be) to deduce the geometry of monocentric visual space. Visual space is a homogeneous, flat non–Euclidean space. Homogeneity implies that the space admits of a group of isometries (the aforementioned cue ambiguities) or “free mobility of rigid configurations”. Thus visual space is the same near any one of its points. The theory has many applications, among more in the rendering of scenes at inappropriate sizes as is typical in printing.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abbot, E., Flatland, A.: Flatland: A Romance of many Dimensions. orig. 1884. Dover, New York (1992)
Barre, A., Flocon, A.: La perspective curviligne, de l’espace visuel a l’image construite. Flammarion, Paris (1968)
Berkeley, B.: An Essay towards a New Theory of Vision. Orig. 1709. In: Theory of Vision and Other Writing by Bishop Berkeley, 1925. Dent and Sons, New York (1925)
Cayley, A.: Sixth memoir upon the quantics. Philosophical Transactions of the Royal Society London 149, 61–70 (1859)
Coxeter, H.S.M.: Introduction to Geometry. Wiley, New York (1989)
Forsyth, D., Ponce, J.: Computer Vision—A modern Approach. Prentice Hall, Upper Saddle River (2002)
Hauck, G.: Die subjektive Perspektive und die horizontalen Curvaturen des Dorischen Styls. Wittwer, Stuttgart (1875)
Helmholtz, H.: On the Facts underlying Geometry. Orig. 1868. In: Cohen and Elkana, pp. 39–71 (1977)
Hildebrand, A.: The Problem of Form in painting and sculpture. Translated by M. Meyer and R. M. Ogden. First, German edition, Das Problem der Form, 1893. Stechert, New York (1945)
Klein, F.: Vergleichende Betrachtungen über neuere geometrische Forschungen. Mathematische Annalen 43, 63–100 (1893)
Luneburg, R.K.: Mathematical analysis of binocular vision. Princeton University Press, Princeton (1947)
Pirenne, M.H.: Optics, Painting and Photography. Cambridge University Press, Cambridge (1970)
Poincaré, H.: Science et la méthode. Flammarion, Paris (1908)
Sachs, H.: Ebene isotrope Geometrie. Friedrich Vieweg & Sohn, Braunschweig (1987)
Strubecker, K.: Differentialgeometrie des isotropen Raumes I. Sitzungsberichte der Akademie der Wissenschaften Wien 150, 1–43 (1941)
Swift, J.: Gulliver’s Travels and Other Works. Routledge (orig. 1726) (1906)
Yaglom, I.M.: A simple non–Euclidean geometry and its physical basis. Springer, New York (1979)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Koenderink, J.J. (2003). Monocentric Optical Space. In: Petkov, N., Westenberg, M.A. (eds) Computer Analysis of Images and Patterns. CAIP 2003. Lecture Notes in Computer Science, vol 2756. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45179-2_84
Download citation
DOI: https://doi.org/10.1007/978-3-540-45179-2_84
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40730-0
Online ISBN: 978-3-540-45179-2
eBook Packages: Springer Book Archive