Editing Müller-Lyer illusion (section)

==Centroid explanation==
[[File:BrentanoStimuli.tif|thumb|right|The classic Müller-Lyer figures (A) and three modifications (having no shaft line) of the Brentano versions of illusory figures comprising different contextual flanks: separate dots (B), the Müller-Lyer wings (C), and arcs of a circle (D, distances between the points seem to be different)]]

[[File:Sarcone’s Pulsating Star (Dynamic Müller-Lyer illusion).gif|thumb|A dynamic visual demonstration by Italian researcher [[Gianni A. Sarcone]]: the blue and black segments of the star are equal in length and always the same length, though they appear to alternately stretch and shrink.]]

[[File:Müller-Lyer illusion.gif|thumb| This variant of dynamic Müller-Lyer illusion by Italian researcher [[Gianni A. Sarcone]] shows that though the collinear blue and red segments seem to oscillate up and down, they are always the same length. Nothing moves except the arrows at the endpoints of each color segments. This visual illusion also involves a dynamic "[[neon color spreading]]" effect.]]

According to the so-called centroid hypothesis, judgments of distance between visual objects are strongly affected by the neural computation of the [[centroid]]s of the luminance profiles of the objects, in that the position of the centroid of an image determines its perceived location.<ref>{{cite journal | vauthors = Whitaker D, McGraw PV, Pacey I, Barrett BT | title = Centroid analysis predicts visual localization of first- and second-order stimuli | journal = Vision Research | volume = 36 | issue = 18 | pages = 2957–2970 | date = September 1996 | pmid = 8917796 | doi = 10.1016/0042-6989(96)00031-4 }}</ref> Morgan ''et al.'', suggest that the visual procedure of centroid extraction is causally related to a spatial pooling of the positional signals evoked by the neighboring object parts.<ref>{{cite journal | vauthors = Morgan MJ, Hole GJ, Glennerster A | title = Biases and sensitivities in geometrical illusions | journal = Vision Research | volume = 30 | issue = 11 | pages = 1793–1810 | date = 1990 | pmid = 2288091 | doi = 10.1016/0042-6989(90)90160-m }}</ref> Though the integration coarsens the positional acuity, such pooling seems to be quite biologically substantiated since it allows fast and reliable assessment of the location of the visual object as whole, irrespective of its size, the shape complexity, and illumination conditions. Concerning the Müller-Lyer and similar illusions, the pattern of neural excitation evoked by contextual flank (e.g., the Müller-Lyer wings themselves) overlaps with that caused by the stimulus terminator (e.g., the wings apex), thereby leading (due to the shift of the centroid of summed excitation) to its perceptual displacement. The crucial point in the centroid explanation regarding the positional shifts of the stimulus terminators in the direction of the centroids of contextual flanks was confirmed in psychophysical examination of illusory figures with rotating distractors.<ref>{{cite journal | vauthors = Bulatov A, Bertulis A, Mickienė L, Surkys T, Bielevičius A | title = Contextual flanks' tilting and magnitude of illusion of extent | journal = Vision Research | volume = 51 | issue = 1 | pages = 58–64 | date = January 2011 | pmid = 20932991 | doi = 10.1016/j.visres.2010.09.033 }}</ref> The relative displacement of all stimulus terminators leads to misjudgment of distances between them; that is, the illusion occurs as a side effect due to necessarily low spatial resolution of the neural mechanism of assessment of the relative location of the visual objects. Besides, it was shown<ref>{{cite journal | vauthors = Bulatov A, Bulatova N, Marma V, Kučinskas L | title = Quantitative study of asymmetry in the manifestation of the wings-in and wings-out versions of the Müller-Lyer illusion | journal = Attention, Perception, & Psychophysics | volume = 84 | issue = 2 | pages = 560–575 | date = February 2022 | pmid = 34921335 | doi = 10.3758/s13414-021-02412-z }}</ref> that well-known asymmetry in manifestation of the wings-in and wings-out modifications of the Müller-Lyer illusion can be successfully explained by supplemental effects of the [[Oppel-Kundt illusion|filled-space]] illusion.
[[File:RotatingBrentanoL.gif|thumb|right|Brentano figure with the rotating Müller-Lyer wings (distractors); actually, apices of the wings (stimulus terminators) are aligned and spaced equidistantly]]