December 2003
Volume 3, Issue 12
OSA Fall Vision Meeting Abstract  |   December 2003
Naïve misconceptions about perspective projection: A new model for the anisotropy of 3-d visual space
Author Affiliations
  • Harvey S. Smallman
    Pacific Science and Engineering Group, USA
Journal of Vision December 2003, Vol.3, 24. doi:
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      Harvey S. Smallman; Naïve misconceptions about perspective projection: A new model for the anisotropy of 3-d visual space. Journal of Vision 2003;3(12):24.

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      © ARVO (1962-2015); The Authors (2016-present)

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It is well established that perceived 3-D visual space distorts in various ways. Notably, perceived depth extents (in the median sagittal plane, Y) are compressed compared to physically-equal width extents (in the frontoparallel plane, X), e.g., Loomis et al. (1992). Several models invoke a fixed, inflexible mathematical transformation of physical space onto perceived space to account for this anisotropy (see Hecht et al., 1999). Here we report observations and a new model that suggest a far simpler, perhaps more intriguing explanation that emphasizes a flawed, yet active, scene reconstruction process.


In a series of four experiments, participants performed size matching (Exp 1), made free-hand drawings (Exp 2), reconstructed grids (Exp3) and did forced-choice recognition (Exp 4) in and of 3-D scenes in which the viewing angle and depth cues on the ground-plane (foreshortening or linear perspective) were manipulated. All but the recognition results could be quantitatively modeled by assuming that there is a misconception, akin to those of Naïve Physics, or simplifying perceptual “hack”, that X and Y taper at the same rate in the perspective projection (“things gets smaller with distance” rather than “widths get smaller with distance slower than depths do”). Supporting the notion of a widespread misconception were comments made on debriefing by the Exp 2 drawing participants and the fact that the misconception is even evident in the textbook perspective diagrams of a sensation and perception author (Gillam, 1981).


The misconception leads to an inappropriate cross-scaling of Y by linear perspective in depth cue combination, which leads to the misperceptions we observed. We show that the new model accounts for egocentric distance compression data of others. It also neatly accommodates the nature of the growth in error with shallower viewing angles because of the geometric deviation between X and Y taper.


Gillam, B.(1981). False perspectives. Perception, 10, 313–318.


Hecht, H., Van  Doorn, A., Koenderink, J. J.(1999). Compression of visual space in natural scenes and in their photographic counterparts. Perception and Psychophysics, 61(7), 1269–1286.


Loomis, J. M., Fujita, N., Da Silva, J., Fukisima, S. S.(1992). Visual space perception and visually directed action. Journal of Experimental Psychology: Human Perception and Performance, 18(4), 906–921.

Smallman, H. S.(2003). Naïve misconceptions about perspective projection: A new model for the anisotropy of 3-d visual space [Abstract]. Journal of Vision, 3( 12): 24, 24a,, doi:10.1167/3.12.24. [CrossRef]

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