title: The representation of visual depth perception based on the plenoptic function in the retina and its neural computation in visual cortex V1.
abstract: BACKGROUND
  How it is possible to "faithfully" represent a three-dimensional stereoscopic scene using Cartesian coordinates on a plane, and how three-dimensional perceptions differ between an actual scene and an image of the same scene are questions that have not yet been explored in depth. They seem like commonplace phenomena, but in fact, they are important and difficult issues for visual information processing, neural computation, physics, psychology, cognitive psychology, and neuroscience.
  
  
  RESULTS
  The results of this study show that the use of plenoptic (or all-optical) functions and their dual plane parameterizations can not only explain the nature of information processing from the retina to the primary visual cortex and, in particular, the characteristics of the visual pathway's optical system and its affine transformation, but they can also clarify the reason why the vanishing point and line exist in a visual image. In addition, they can better explain the reasons why a three-dimensional Cartesian coordinate system can be introduced into the two-dimensional plane to express a real three-dimensional scene.
  
  
  CONCLUSIONS
  1. We introduce two different mathematical expressions of the plenoptic functions, Pw and Pv that can describe the objective world. We also analyze the differences between these two functions when describing visual depth perception, that is, the difference between how these two functions obtain the depth information of an external scene.2. The main results include a basic method for introducing a three-dimensional Cartesian coordinate system into a two-dimensional plane to express the depth of a scene, its constraints, and algorithmic implementation. In particular, we include a method to separate the plenoptic function and proceed with the corresponding transformation in the retina and visual cortex.3. We propose that size constancy, the vanishing point, and vanishing line form the basis of visual perception of the outside world, and that the introduction of a three-dimensional Cartesian coordinate system into a two dimensional plane reveals a corresponding mapping between a retinal image and the vanishing point and line.
authors.forename: Zhao
authors.initials: Z
authors.lastname: Songnian
authors.forename: Zou
authors.initials: Z
authors.lastname: Qi
authors.forename: Liu
authors.initials: L
authors.lastname: Chang
authors.forename: Liu
authors.initials: L
authors.lastname: Xuemin
authors.forename: Sun
authors.initials: S
authors.lastname: Shousi
authors.affiliation: Beijing Information Science and Technology University, Beijing 100101, China. qiujun@bistu.edu.cn.
authors.forename: Qiu
authors.initials: Q
authors.lastname: Jun
mesh_terms: D003198:Computer Simulation; D003867:Depth Perception / Q000502:physiology*; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D012160:Retina / Q000502:physiology*; D014793:Visual Cortex / Q000502:physiology*; D014795:Visual Pathways / Q000502:physiology*
references.citation: J Neurosci. 1987 Nov;7(11):3416-68
references.pmid: 3316524
references.citation: BMC Neurosci. 2010 Mar 26;11:43
references.pmid: 20346118
references.citation: Neural Comput. 2003 Oct;15(10):2399-418
references.pmid: 14511527
references.citation: J Neurosci. 1999 Jul 1;19(13):5602-18
references.pmid: 10377367
references.citation: Atten Percept Psychophys. 2014 Feb;76(2):270-9
references.pmid: 24374558
references.citation: J Neurophysiol. 2004 Sep;92(3):1880-91
references.pmid: 15331652
references.citation: Biol Cybern. 1987;55(6):367-75
references.pmid: 3567240
references.citation: Proc R Soc Lond B Biol Sci. 1977 Jul 28;198(1130):1-59
references.pmid: 20635
references.citation: J Neurosci. 1984 Jan;4(1):309-56
references.pmid: 6198495
references.citation: Vision Res. 1986;26(9):1601-12
references.pmid: 3303677
references.citation: Vision Res. 1998 Aug;38(15-16):2387-400
references.pmid: 9798006
references.citation: Neuron. 2008 Jan 10;57(1):147-58
references.pmid: 18184571
references.citation: Nature. 1982 Oct 7;299(5883):515-24
references.pmid: 6750409
references.citation: Nat Neurosci. 2006 Mar;9(3):429-34
references.pmid: 16462737
references.citation: Science. 1990 Aug 31;249(4972):1037-41
references.pmid: 2396096
references.citation: Proc Natl Acad Sci U S A. 2005 Aug 30;102(35):12629-33
references.pmid: 16116075
references.citation: BMC Neurosci. 2012 Nov 29;13:145
references.pmid: 23190754