Abstract
We consider the shape of “visual space”. One immediate complication is that there are numerous “visual spaces”, often confused in the literature. Here we focus on visual awareness, rather than optically guided behavior, and “contemplative”, rather than “enactive” vision. Even so, the number of conceptually different “visual spaces” is appreciable. Important distinctions are between visual space as a rigid image of physical space, and visual space as an entity that depends critically upon an observer’s present state. For instance, in judging the relation between two locations, an observer may fixate one or the other. Conceivably, “visual space” will change the moment the observer swaps fixations. If that is indeed the case, then many of the conventional ways to address visual space, or to analyze raw psychophysical data, become effectively invalid. Here we re-analyze a number of available data-sets from such a perspective. We suggest that our notions of “the shape of visual space” need revision and re-investigation.
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
Similar content being viewed by others
Notes
- 1.
“Enaction” was introduced by Jerome Bruner [2, 3] who distinguished between iconic and symbolic knowledge. It is presently (also by us) used for knowledge that comes through action. It is acquired through motor skilled motor actions, such as handling objects and locomotion. Enactive vision is not necessarily accompanied by any acute visual awareness.
- 2.
“Contemplation” is commonly defined as “to admire something and think about it”. It typically involves no motor action, but acute awareness, and is akin to meditation. Contemplative vision is also akin to artistic vision, and is so described in Hildebrand [10] with the notion of “far image” (G. Fernbild), and “serenely viewing eye” (G. das ruhig schauende Auge).
- 3.
One distinguishes “interospecific” and “exterospecific” information. We don’t use the origin of the terms, but they were used by Gibson [7] to differentiate between information that relates to the observer and to the external world. For an ideal camera–eye eye–movements do not reveal any novel information about the scene, since no novel perspectives are gained. They lead to pure interospecific information. (E.g., the optic nerve activity may be used to monitor eye movements.)
References
Berkeley G An essay towards a new theory of vision. Printed by Aaron Rhames, at the Back of Dick’s Coffee-House, for Jeremy Pepyat, Bookseller Skinner-Rows Dublin, MDCCIX
Bruner J (1966) Toward a theory of instruction. Belknap Press of Harvard University Press, Cambridge
Bruner J (1968) Processes of cognitive growth: infancy. Clark University Press, Worcester
Coxeter HSM (1989) Introduction to geometry. Wiley classics library Series. Wiley, New York
Doumen MJA, Kappers AML, Koenderink JJ (2005) Visual space under free viewing conditions. Percept Psychophys 67:1177–1189
Gibson DJJ (1950) The perception of the visual world. Houghton Mifflin, Boston
Gibson JJ (1986) The ecological approach to visual perception. Houghton Mifflin, Boston
von Helmholtz H (1892) Handbuch der physiologischen Optik. Voss, Hamburg
Hilbert D, Cohn-Vossen S (1952) Geometry and the imagination, 2nd edn. Chelsea, New York
Hildebrand A (1893) In: Das Problem der Form in der bildenden Kunst. Heitz, Strassburg
Koenderink JJ (2011) Geometry of imaginary spaces. J Physiol (Paris). doi:10.1016/j.jphysparis.2011.11.002
Koenderink JJ, van Doorn AJ (2008) The structure of visual spaces. J Math Imaging Vis 31:171–187
Koenderink JJ, van Doorn AJ (2012) Gauge fields in pictorial space. SIAM J Imaging Sci 5(4):1213–1233
Koenderink JJ, van Doorn AJ, Lappin JS (2000) Direct measurement of the curvature of visual space. Perception 29:69–80
Koenderink JJ, van Doorn AJ, Kappers AML, Todd JT (2002) Pappus in optical space. Percept Psychophys 64:380–391
Koenderink JJ, van Doorn AJ, Kappers AML, Lappin JS (2002) Large-scale visual frontoparallels under full-cue conditions. Perception 31:1467–1476
Koenderink JJ, van Doorn AJ, Lappin JS (2003) Exocentric pointing to opposite targets. Acta Psychol 112:71–87
Koenderink JJ, van Doorn AJ, Kappers AML, Doumen MJA, Todd JT (2008) Exocentric pointing in depth. Vis Res 48:716–723
Koenderink JJ, van Doorn AJ, Todd JT (2009) Wide distribution of external local sign in the normal population. Psychol Res 73:14–22
Koenderink JJ, van Doorn AJ, de Ridder H, Oomes AHJ (2010) Visual rays are parallel. Perception 39:1163–1171
Koenderink JJ, Albertazzi L, van Doorn AJ, van Ee R, van de Grind WA, Kappers AML, Lappin JS, Norman JF, Oomes AHJ, te Pas SF, Phillips F, Pont SC, Richards WA, Todd JT, Verstraten FAJ, de Vries S (2010) Does monocular visual space contain planes? Acta Psychol 134:40–47
Koenderink JJ, van Doorn AJ, Wagemans J (2011) Depth. i-Perception 2:541–564
Luneburg RK (1950) The metric of binocular visual space. J Opt Soc Am 50:637–642
Mach E (1906) Space and geometry. Open Court Publishing, Chicago
Necker LA (1832) Observations on some remarkable optical phaenomena seen in Switzerland; and on an optical phænomenon which occurs on viewing a figure of a crystal or geometrical solids. Lond Edinburgh Philos Mag J Sci 1(5):329–337
Oomes AHJ, Koenderink JJ, van Doorn AJ, de Ridder H (2009) What are the uncurved lines in our visual field? A fresh look at Helmholtz’s checkerboard. Perception 38:1284–1294
Pont SC, Nefs HT, van Doorn AJ, Wijntjes MWA, te Pas SF, de Ridder H, Koenderink JJ (2012) Depth in box spaces. Seeing Perceiving 25:339–349
Riemann B (1854) Über die Hypothesen, welche der Geometrie zu Grunde liegen. Aus dem dreizehnten Bande der Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 10 June 1854
Wagemans J, van Doorn AJ, Koenderink JJ (2011) Measuring 3D point configurations in pictorial space. i-Perception 2:77–111
Acknowledgement
This work was supported by the Methusalem program by the Flemish Government (METH/08/02), awarded to Johan Wagemans.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
Koenderink, J., van Doorn, A. (2013). The Shape of Space. In: Dickinson, S., Pizlo, Z. (eds) Shape Perception in Human and Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-5195-1_10
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5195-1_10
Publisher Name: Springer, London
Print ISBN: 978-1-4471-5194-4
Online ISBN: 978-1-4471-5195-1
eBook Packages: Computer ScienceComputer Science (R0)