472:
189:
120:, Baird (1970), Ono (1970), Roscoe (1985, 1989), Hershenson (1982, 1989), Reed (1984, 1989), Enright (1989), Plug & Ross (1989, 1994), Higashiyama & Shimono (1994), Gogel, & Eby (1997), Ross & Plug (2002), and Murray, Boyaci & Kersten (2006). Specifically, these researchers cited have advocated a relatively new idea: that many of the best-known size illusions demonstrate that for most observers the (subjective) perceived visual angle,
1281:(1962/1910) who distinguished between the perceived oculocentric directions and the perceived egocentric directions. They, and other theorists, have pointed out that a viewed point's egocentric direction (d'B and d'A here) is determined by a process that necessarily combines the position of the point's image on the retina with information about the position of the eye with respect to the head (and body).
1077:
624:′, but most cannot reliably say how large a direction difference looks. That skill is not practiced because it is easier to use pointing gestures (Ono, 1970): For example, one often tells another person about the change in the directions seen for two viewed points by pointing something, say a finger or the eyes from one point to the other.
1263:
of one's head (Ono, 1970, Ono, Mapp, & Howard, 2002). Some other theories define the place from which one feels one is viewing the world as the visual egocenter (Roelofs, 19xx, McCready, 1964, 1965, Sakuma & Pfaff, 1979) which, among observers, ranges, in effect, from about midway between the
1175:
Describing the few existing explanations for visual angle illusions is beyond the scope of this present entry. The most recent theories have been presented mostly in articles concerning the moon illusion (Baird et al., 1990, Enright, 1989a, 1989b, Hershenson, 1982, 1989b, Higashiyama, 1992, McCready
964:
Conventional "textbook" theories of "size" and distance perception do not refer to the perceived visual angle (e.g., Gregory, 1963, 1970, 1998, 2008) and some researchers even deny that it exists (Kaufman & Kaufman, 2002). This idea that one does not see the different directions in which objects
131:
Indeed, various experiments have revealed most of the factors responsible for these visual angle illusions, and a few different explanations for them have been published (Baird, Wagner, & Fuld, 1990, Enright, 1987, 1989, Hershenson, 1982, 1989, Komoda & Ono, 1974, McCready, 1965, 1985, 1986,
933:
for the other (say, 17% larger) due to differences in their background patterns. And, in cortical Area V1, the sizes of the activity patterns related to the disks were unequal, despite the fact that the retinal images were the same size. The difference between these "cortical sizes" in Area V1 for
705:
Notice that humans experience both the linear size and the angular size comparisons at the same time, along with the distance comparison (Joynson, 1949). Thus any report merely that one object "looks larger" than another object is ambiguous. It needs to specify whether "looks larger" refers to the
76:, in which the Moon appears larger when it is near the horizon. It is replaced by a perceptual SDIH, in which the visual angle is replaced by the perceived visual angle. This new formulation avoids some of the paradoxes of the SDIH, but it remains difficult to explain why a given illusion occurs.
135:
On the other hand, nearly all discussions (and explanations) of those classic size illusions found in textbooks, the popular media, and on the internet use, instead, an older hypothesis that the visual angle is not perceivable (Gregory, 2008, Kaufman & Kaufman, 2002). They can describe and
79:
This paradigm is not universally accepted; many textbook explanations of size and distance perception do not refer to the perceived visual angle, and some researchers deny that it exists. Some recent evidence supporting the idea, reported by Murray, Boyaci and
Kersten (2006), suggests a direct
1061:
However, at least since 1962, researchers have pointed out that many classic "size" and distance illusions can be neither described nor explained using the SDIH, so a new hypothesis is needed (Boring 1962, Gruber, 1956, McCready, 1965, Baird, 1970, Ono 1970). For instance, consider the simple
1176:
1986, 1999–2007, Plug & Ross, 1989, Reed, 1989, Roscoe, 1989, and especially in two "moon illusion" books (Hershenson, 1989; Ross & Plug, 2002) which make it quite clear that vision scientists have not yet agreed upon any particular theory of visual angle illusions.
683:
Suppose one is looking through a window at a 30-foot-wide (9.1 m) house 240 feet away, so it subtends a visual angle of about 7 degrees. The 30-inch-wide (760 mm) window opening is 10 feet away, so it subtends a visual angle of 14 degrees.
60:
were of different sizes. Angular size illusions are contrasted with linear size illusions, in which two objects that are the same physical size do not appear so. An angular size illusion may be accompanied by (or cause) a linear size illusion at the same time.
714:) or to both of those qualitatively different "size" experiences (Joynson, 1949, McCready, 1965, 1985, Ono, 1970). Notice that in everyday conversations "looks larger" often refers to an angular size comparison rather than a linear size comparison.
881:
Also rejected is a popular idea that an object's "perceived size" results from a "scaling of retinal size"; an illogical process that somehow "magnifies" the very small "retinal size" to yield the viewed object's much larger perceived linear size
1171:
describes the
Ebbinghaus illusion and many other classic "size" illusions more completely and more logically than does the popular SDIH. What still needs to be explained, however, is why the basic visual angle illusion occurs in each example.
761:
would be expected to relate to each other for a given object is illustrated by Figure 2 and stated by the following equation (McCready, 1965, 1985, Ono, 1970, Komoda and Ono, 1974, Reed, 1989, Kaneko & Uchikawa, 1997).
55:
Angular size illusions are most obvious as relative angular size illusions, in which two objects that subtend the same visual angle appear to have different angular sizes; it is as if their equal-sized images on the
564:
This concept of the (subjective) visual direction is very old. However, as Wade, Ono & Mapp (2006) noted, it unfortunately has been ignored in many current theories of size perception, and size illusions.
819:
901:
for a target forming a constant sized retinal image (and thereby create a visual angle illusion). Indeed, the major discovery by Murray et al. (2006) concerns this flexible relationship between
937:
The researchers pointed out that their findings dramatically disagree with the hypothetical models of neural events being proposed in nearly all current theories of visual spatial perception.
1028:
72:(SDIH), which states that the ratio of perceived linear size to perceived distance is a simple function of the visual angle. The SDIH does not explain some illusions, such as the
1264:
eyes to at least as far back as the center of the head, about 4 inches behind the eyes, approximately midway between the two ears, on the axis for horizontal head rotations.
367:
308:
1115:
be greater for the lower one than for the upper one. However, for most observers, both circles appear unequal while also appearing at the same distance (on the same page).
1183:) for which a few different explanations are being considered (McCready, 1965, 2007, Ono, 1970, Komoda & Ono, 1974, Ono, et al. 1974, Enright, 1987b, 1989a, 1989b).
698:
One can also say that the house "looks smaller and farther away" than the window, and that does not contradict the other statement because now we mean that the amount (
1716:
Higashiyama, A. (1992), "Anisotropic perception of visual angle: Implications for the horizontal-vertical illusion, overconstancy of size, and the moon illusion",
1125:
is larger for the lower circle than for the upper circle: It is as if its retinal image were larger. So. according to the "new" perceptual invariance hypothesis, (
627:
Therefore, in some experiments the observers aimed a pointer from one viewed point to the other, so the angle through which the pointer rotated was the measure of
32:
by a viewed object sometimes looks larger or smaller than its actual value. One approach to this phenomenon posits a subjective correlate to the visual angle: the
1473:
Enright, J.T. (1989b), "4. The eye, the brain and the size of the moon: Toward a unified oculomotor hypothesis for the moon illusion", in
Hershenson, M. (ed.),
1121:
The "paradox" completely vanishes, however, when the illusion is described, instead, as basically a visual angle illusion: That is, the perceived visual angle
874:
such as the retinal image. As Gogel (1969, 1997) has repeatedly emphasized, there is no "sensation" which could be called the "perceived retinal image size",
717:
Additional confusion has resulted from widespread use of the ambiguous terms "apparent size" and "perceived size", because they sometimes have referred to
948:
which is a visual angle illusion for most observers, (McCready, 1965, 1986, Restle 1970, Plug & Ross, 1989, p. 21, Ross & Plug, 2002).
1155:
is larger. That is, the reason the lower one looks a larger linear size on the page is because it looks a larger angular size than the upper one.
934:
the illusion disks was essentially the same as the difference produced by two non-illusory disks whose retinal image sizes differed by, say, 17%.
646:, observers in other experiments shifted their gaze from one object endpoint to the other, and the angle the eye rotated through was measured as
1510:
Gogel, W.C.; Eby, D.W. (1997), "Measures of perceived linear size, sagittal motion, and visual angle from optical expansions and contractions",
1118:
This commonly found disagreement between published data and the SDIH is known as the "size–distance paradox" (Gruber, 1956, Ono, et al. 1974).
2405:
860:
2434:
Wade, N.J.; Ono, H.; Mapp, A.P. (2006), "The lost direction in binocular vision: The neglected signs posted by Walls, Towne, and
Leconte",
2045:
2105:
Ono, H.; Mapp, A.P.; Howard, I.P. (2002), "The cyclopean eye in vision: The new and old data continue to hit you right between the eyes",
1186:
This is a partial list of "size and distance" illusions that begin as visual angle illusions (angular size illusions) for most observers.
695:
for the window; for instance a person might say the house "looks about 40 feet wide" and the window "looks about 3 feet wide."
702:) by which directions of the house's edges appear to differ is, say, about half the apparent direction difference for the window edges.
677:
1333:
Barbeito, R.; Ono, H (1979), "Four methods of locating the egocenter: a comparison of their predictive validities and reliabilities",
136:
explain only a linear size illusion, which is why they do not properly describe or explain the illusions that most people experience.
940:
Murray, et al. (2006) also noted that the flat illusion pattern they used can represent other classic "size" illusions, such as the
968:
That old SDIH logic (geometry) is typically illustrated using a diagram that resembles Figure 2, but has the physical visual angle
1921:
Paper presented at meeting of the
Midwestern Section of the Association for Research in Ophthalmology, Rochester MN. (May, 1964).
1037:
is typically called the "perceived size" or "apparent size"; more precisely it is the perceived linear size, measured in meters.
1804:
Kaneko, H.; Uchikawa, K. (1997), "Perceived angular size and linear size: the role of binocular disparity and visual surround",
2032:
1259:
In some theories the cyclopean eye is, in effect, approximately midway between where one feels one's eye are located in one's
847:
image normally determines the extent of the neural activity pattern the retina's neural activity eventually generates in the
143:
is the difference between two directions from a common point (the vertex). Accordingly, as described below, the visual angle
69:
1746:
Higashiyama, A.; Shimono, K. (1994), "How accurate is size and distance perception for very far terrestrial objects?",
687:
It can be said that the house "looks larger and farther away" than the window, meaning that the perceived linear size
1239:
2491:
2486:
2095:
Ono, H. (1970), "Some thoughts on different perceptual tasks related to size and distance", in Baird, J. C. (ed.),
867:
483:′ represents the place from which the observer feels that he or she is viewing the world. For present purposes,
917:
The Murray, et al. (2006) observers viewed a flat picture with two disks that subtended the same visual angle
533:′. The observer could simply say how many inches or meters that vertical distance looks. For a viewed object,
436:, toward some specific elevation value (say, 18 degrees). The difference between those real directions (
1437:
Enright, J.T. (1989a), "Manipulating stereopsis and vergence in an outdoor setting: Moon, sky and horizon",
1218:
824:
Ross & Plug (2002, Page 31) dubbed this new rule the "perceptual size–distance invariance hypothesis".
768:
638:, specifies the amount by which one should rotate one's eye to quickly look from one seen point to another
1400:
1355:
Enright, J.T. (1987a), "Art and the oculomotor system: Perspective illustrations evoke vergence changes",
982:
951:
A detailed meta-analysis of the Murray et al. (2006) results is available in McCready (2007, Appendix B).
471:
1179:
There also is the lesser-known, but evidently the largest visual angle illusion of oculomotor micropsia (
1658:
1278:
1196:
1180:
848:
380:
that averages about 17 mm. That is, a viewed object's retinal image size is approximately given by
331:
272:
85:
1679:
Hershenson, M. (1982), "Moon illusion and spiral aftereffect: Illusions due to the loom-zoom system?",
859:). This neurological relationship recently was confirmed by Murray, Boyaci, & Kersten (2006) using
155:, is the difference by which the directions of two viewed points from oneself appear to differ in the
1925:
McCready, D. (1965), "Size-distance perception and accommodation-convergence micropsia: A critique",
1405:
377:
1202:
1071:
139:
In order to clarify the new paradigm which replaces the old one, it helps to keep in mind that an
2376:
2235:
2190:
2132:
2076:
1829:
1793:
1639:
1565:
1462:
1426:
1380:
631:, (Komodo, 1970, Komodo & Ono, 1974, Ono, Muter, & Mitson, 1974, Gogel & Eby, 1997).
2084:
725:
without clarification, so the reader must try to ascertain what they mean. Also, in astronomy, "
1305:
Baird, J.C.; Wagner, M.; Fuld, K. (1990), "A simple but powerful theory of the moon illusion",
2451:
2401:
2368:
2300:
2263:
2227:
2182:
2124:
2068:
2011:
1981:
1942:
1869:
1821:
1765:
1735:
1696:
1647:
1611:
1557:
1529:
1499:
1454:
1418:
1372:
1322:
188:
17:
2143:
Ono, H.; Muter, P.; Mitson, L. (1974), "Size-distance paradox with accommodative micropsia",
2443:
2423:
2360:
2340:
2320:
2292:
2255:
2219:
2174:
2152:
2114:
2060:
2001:
1971:
1934:
1889:
1859:
1849:
1813:
1785:
1755:
1725:
1688:
1631:
1603:
1549:
1519:
1491:
1446:
1410:
1364:
1342:
1314:
1228:
1223:
852:
96:
Visual angle illusions have been explicitly described by many vision researchers, including
41:
965:
lie from oneself is a basis of the so-called "size–distance invariance hypothesis" (SDIH).
855:. This cortical area harbors a distorted but spatially isomorphic "map" of the retina (see
1208:
1100:
and form equal-sized retinal images. But the lower one "looks larger" than the upper one.
248:
29:
2210:
Plug, C.; Ross, H.E. (1994), "The natural moon illusion: A multifactor angular account",
1055:
2481:
1540:
Gregory, R.L. (1963), "Distortion of visual space as inappropriate constancy scaling",
1233:
1213:
941:
581:;, about which the observer might say "it appears toward a higher elevation than point
217:
204:(also called its "metric size" or "tape-measure size"). The extent's lower endpoint at
2119:
1391:
Enright, J.T. (1987b), "Perspective vergence: Oculomotor responses to line drawings",
561:, and the observer might simply say "it looks straight ahead and toward the horizon."
2475:
2427:
2344:
2324:
2274:
Reed, C.F. (1989), "11. Terrestrial and celestial passage", in
Hershenson, M. (ed.),
1938:
1880:
Komoda, M.K.; Ono, H. (1974), "Oculomotor adjustments and size-distance perception",
1864:
1797:
1495:
1450:
1414:
1190:
945:
726:
148:
73:
2380:
2239:
2194:
2165:
Oyama, T. (1977), "Feature analysers, optical illusions, and figural aftereffects",
1833:
1466:
1384:
2136:
2080:
1569:
1430:
1274:
639:
183:
156:
132:
1994, Ono, 1970, Oyama, 1977, Reed, 1984, 1989, Restle, 1970, Roscoe, 1985, 1989).
21:
2296:
124:, can change for a viewed target that subtends a constant (physical) visual angle
80:
relationship between the perceived angular size of an object and the size of the
2259:
1692:
2364:
1707:
Hershenson, M. (1989), "5. Moon illusion as anomaly", in
Hershenson, M. (ed.),
1607:
1318:
1080:
The two orange circles are exactly the same size; however, the one on the left
2201:
Plug, C.; Ross, H.E. (1989), "2. Historical Review", in
Hershenson, M. (ed.),
2026:, Psychology Department Report, University of Wisconsin–Whitewater, p. 40
1957:, Psychology Department Report, University of Wisconsin–Whitewater, p. 86
1789:
1260:
871:
856:
2387:
Roscoe, S.N. (1989), "3. The zoom-lens hypothesis", in
Hershenson, M. (ed.),
2046:"The representation of perceived angular size in human primary visual cortex"
487:′ can represent the cyclopean eye (Ono, 1970, Ono, Mapp & Howard, 2002).
2283:
Restle, F. (1970), "Moon illusion explained on the basis of relative size",
1076:
676:
232:
2455:
2304:
2128:
2072:
1873:
1651:
1615:
1561:
2372:
2267:
2231:
2015:
1985:
1946:
1854:
1825:
1769:
1739:
1700:
1533:
1503:
1458:
1422:
1376:
1326:
897:. But, as already noted, "other factors" can intervene to slightly change
262:
The optical (physical) angle between those chief rays is the visual angle
2186:
1273:
The subjective experiences of visual directions were fully researched by
468:
Figure 2 diagrams the perceived (subjective) values for a viewed object.
65:
2414:
Sakuma, Y.; Pfaff, W. (1979), "Considerations on the visual egocentre",
537:
thus is its perceived linear size in meters, (or apparent linear size).
2447:
2157:
2006:
1976:
1894:
1760:
1730:
1643:
1622:
Gruber, H.E. (1956), "The size-distance paradox: A reply to
Gilinsky",
1524:
1347:
643:
416:
2246:
Reed, C.F. (1984), "Terrestrial passage theory of the moon illusion",
1962:
McCready, D. (1985), "On size, distance and visual angle perception",
1553:
844:
240:
81:
57:
2223:
2178:
1817:
1635:
1368:
1307:
Journal of Experimental Psychology: Human Perception and Performance
2064:
1840:
Kaufman, L.; Kaufman, J.H. (2000), "Explaining the moon illusion",
609:, also called the perceived angular size or apparent angular size.
216:, which for present purposes can represent the center of the eye's
196:
Figure 1 illustrates an observer's eye looking at a frontal extent
2311:
Rock, I.; McDermott, W. (1964), "The perception of visual angle",
1075:
470:
187:
140:
44:
where the physical and subjective angles differ is then called a
2331:
Roelofs, C.O. (1959), "Considerations on the visual egocenter",
893:
normally determines the magnitude of the perceived visual angle
2097:
Human space perception: Proceedings of the Dartmouth conference
147:
is the difference between two real (optical) directions in the
2351:
Roscoe, S.N. (1985), "Bigness is in the eye of the beholder",
673:. Consider an example illustrated by the sketch at the right.
616:. For instance, a well-trained observer might say that point
525:
is the perceived linear extent by which the subjective point
1594:
Gregory, R.L. (2008), "Emmert's law and the moon illusion",
835:
As already noted, the magnitude of an object's visual angle
675:
2398:
The mystery of the moon illusion: Exploring size perception
235:
of the bundle of light rays that form the optical image of
1776:
Joynson, R.B. (1949), "The problem of size and distance",
415:, of the object's base from the eye, let's say toward the
1904:
Visual acuity under conditions that induce size illusions
1103:
According to the SDIH, "looks larger" can mean only that
585:′." The difference between the two perceived directions (
2024:
Toward the Distance-Cue Theory of Visual Angle Illusions
1151:
becomes larger for the lower one by the same ratio that
2044:
Murray, S.O.; Boyaci, H.; Kersten, D. (March 1, 2006),
866:
The retinal image is not perceived or sensed. That is,
985:
771:
334:
275:
514:′. The observer might simply say how far away point
1992:McCready, D. (1986), "Moon illusions redescribed",
1955:
Moon Illusions and Other Visual Illusions Redefined
1482:Gogel, W.C. (1969), "The sensing of retinal size",
1159:
Explaining visual angle illusions remains difficult
1022:
813:
745:The perceptual size–distance invariance hypothesis
506:is the perceived distance of the subjective point
361:
302:
2436:Journal of the History of the Behavioral Sciences
1088:The two central circles are the same linear size
960:The classical size–distance invariance hypothesis
870:long ago rejected any idea that people "sense" a
2099:, Psychonomic Monograph Supplement, vol. 3
1910:Dissertation Abstracts International, 1964, 24,
1906:, Doctoral dissertation, University of Michigan
1842:Proceedings of the National Academy of Sciences
1661:(1962) , translated by Southall, J.P.C. (ed.),
1589:(5th ed.), Oxford: Oxford University Press
427:specifies that endpoint's optical direction,
117:
8:
1778:Quarterly Journal of Experimental Psychology
921:and formed retinal images of the same size (
620:′ "looks about 25 degrees higher" than
2248:Journal of Experimental Psychology: General
1681:Journal of Experimental Psychology: General
972:substituted for the perceived visual angle
843:of its retinal image. And, the size of the
1147:correctly the same for both circles, then
1111:the same for both, the SDIH requires that
691:for the house's width is much larger than
2156:
2118:
2005:
1975:
1893:
1863:
1853:
1759:
1729:
1523:
1404:
1346:
1019:
994:
984:
810:
780:
770:
358:
338:
333:
299:
291:
274:
68:begins with a rejection of the classical
1107:is greater, and with the physical angle
1096:, so they subtend the same visual angle
113:
109:
105:
101:
1298:Psychophysical analysis of visual space
1252:
568:The object's other perceived endpoint,
518:′ looks, in inches or meters or miles.
97:
1674:, New York: Plenum Press (translation)
1143:larger for the lower circle, and with
889:Instead, the physical retinal extent
861:functional magnetic resonance imaging
814:{\displaystyle S'/D'=\tan \theta '\,}
7:
1023:{\displaystyle S'/D'=\tan \theta \,}
976:. The equation for the SDIH thus is
925:), but the perceived angular size,
710:) or to the perceived linear size (
151:, while the perceived visual angle
84:activity pattern it excites in the
70:size–distance invariance hypothesis
913:Visual angle illusions and area V1
828:Retinal size, "cortical size" and
665:It is important to understand how
362:{\displaystyle R/n=\tan \theta \,}
303:{\displaystyle \tan \theta =S/D\,}
14:
1163:The new hypothesis that includes
406:specifies the optical direction,
1918:Location of the Visual Egocenter
1663:Treatise on physiological optics
1300:, Oxford, London: Pergamon Press
1066:Example: the Ebbinghaus illusion
650:for that object (Yarbus (1967).
605:) is the perceived visual angle
929:, for one disk was larger than
749:How the three perceived values
729:" refers to the physical angle
552:′ has the perceived direction,
529:′ appears directly above point
2145:Perception & Psychophysics
1994:Perception & Psychophysics
1964:Perception & Psychophysics
1882:Perception & Psychophysics
1748:Perception & Psychophysics
1718:Perception & Psychophysics
1672:The Theory of Binocular Vision
1665:, vol. 3, New York: Dover
1624:American Journal of Psychology
1512:Perception & Psychophysics
1240:apparent fronto-parallel plane
1092:and the same viewing distance
456:) is, again, the visual angle
321:are separated by the distance
1:
2396:Ross, H.E.; Plug, C. (2002),
2297:10.1126/science.167.3921.1092
2120:10.1016/S0042-6989(01)00281-4
572:′, has a perceived direction
402:outward through object point
2428:10.1016/0001-6918(59)90096-4
2391:, Hillsdale, NJ: L. Earlbaum
2345:10.1016/0001-6918(59)90096-4
2325:10.1016/0001-6918(64)90011-3
2278:, Hillsdale, NJ: L. Earlbaum
2205:, Hillsdale, NJ: L. Earlbaum
1939:10.1016/0042-6989(65)90065-9
1711:, Hillsdale, NJ: L. Earlbaum
1496:10.1016/0042-6989(69)90049-2
1477:, Hillsdale, NJ: L. Earlbaum
1451:10.1016/0042-6989(89)90162-4
1415:10.1016/0042-6989(87)90160-X
2400:, Oxford University Press,
2260:10.1037/0096-3445.113.4.489
2034:The moon illusion explained
1693:10.1037/0096-3445.111.4.423
612:It is not easy to quantify
475:Figure 2: Subjective values
192:Figure 1: Physical measures
118:Rock & McDermott (1964)
64:The perceived visual angle
2508:
2365:10.1177/001872088502700601
2031:McCready, D. (1999–2007),
1608:10.1163/156856808784532509
1319:10.1037/0096-1523.16.3.675
1069:
868:experimental psychologists
548:The perceived endpoint at
181:
1790:10.1080/17470214908416754
1335:Behav Res Methods Instrum
1054:, the equation expresses
955:The size–distance paradox
266:which can be calculated:
2464:Eye Movements and Vision
706:perceived angular size (
491:Perceived linear values
325:, given by the equation
1580:, New York: McGraw-Hill
541:Perceived visual angle
200:that has a linear size
1585:Gregory, R.L. (1998),
1576:Gregory, R.L. (1970),
1195:Oculomotor micropsia (
1085:
1024:
909:, as described below.
815:
737:apparent visual angle
680:
476:
419:. The line from point
363:
313:The retinal images at
304:
193:
38:perceived angular size
34:perceived visual angle
2462:Yarbus, A.L. (1967),
2022:McCready, D. (1994),
1953:McCready, D. (1983),
1916:McCready, D. (1964),
1902:McCready, D. (1963),
1855:10.1073/pnas.97.1.500
1279:Hermann von Helmholtz
1197:convergence micropsia
1181:convergence micropsia
1079:
1062:Ebbinghaus illusion.
1025:
849:primary visual cortex
816:
679:
474:
364:
305:
251:. Likewise, endpoint
191:
92:A relatively new idea
86:primary visual cortex
50:angular size illusion
46:visual angle illusion
1670:Hering, E. (1977) ,
1296:Baird, J.C. (1970),
1219:Müller-Lyer illusion
983:
839:determines the size
769:
398:The line from point
332:
273:
247:, let's say, on the
2291:(3921): 1092–1096,
2053:Nature Neuroscience
1578:The intelligent eye
1277:(1942/1879) and by
1203:Ebbinghaus illusion
1072:Ebbinghaus illusion
1040:When rearranged as
733:rather than to the
654:Difference between
255:is imaged at point
208:lies at a distance
2466:, New York: Plenum
2448:10.1002/jhbs.20135
2158:10.3758/BF03213948
2101:(13, Whole No. 45)
2007:10.3758/BF03207585
1977:10.3758/BF03211355
1895:10.3758/BF03213958
1761:10.3758/BF03205300
1731:10.3758/BF03212248
1659:Helmholtz, H. von.
1602:(3–5): 407–420 n,
1525:10.3758/BF03206024
1348:10.3758/bf03205428
1205:(Titchner circles)
1086:
1020:
944:and, as well, the
811:
681:
477:
464:Perceived measures
359:
300:
194:
163:Physical measures
2492:Visual perception
2487:Optical illusions
2416:Acta Psychologica
2407:978-0-19-850862-5
2389:The Moon Illusion
2333:Acta Psychologica
2313:Acta Psychologica
2276:The Moon Illusion
2203:The Moon Illusion
2113:(10): 1307–1324,
2090:on March 18, 2015
1709:The Moon Illusion
1548:(4894): 678–680,
1475:The Moon Illusion
1445:(12): 1815–1824,
1238:Curvature of the
872:proximal stimulus
721:and sometimes to
100:, (McCready
18:visual perception
2499:
2467:
2458:
2430:
2410:
2392:
2383:
2347:
2327:
2307:
2279:
2270:
2242:
2206:
2197:
2161:
2160:
2139:
2122:
2100:
2091:
2089:
2083:, archived from
2050:
2040:
2039:
2027:
2018:
2009:
1988:
1979:
1958:
1949:
1920:
1907:
1898:
1897:
1876:
1867:
1857:
1836:
1800:
1772:
1763:
1742:
1733:
1712:
1703:
1675:
1666:
1654:
1618:
1590:
1581:
1572:
1554:10.1038/199678a0
1536:
1527:
1506:
1478:
1469:
1433:
1408:
1399:(9): 1513–1526,
1387:
1351:
1350:
1329:
1301:
1282:
1271:
1265:
1257:
1229:Jastrow illusion
1224:Orbison illusion
1138:
1053:
1029:
1027:
1026:
1021:
1006:
998:
993:
853:Brodmann area 17
820:
818:
817:
812:
809:
792:
784:
779:
604:
455:
394:
368:
366:
365:
360:
342:
309:
307:
306:
301:
295:
42:optical illusion
2507:
2506:
2502:
2501:
2500:
2498:
2497:
2496:
2472:
2471:
2470:
2461:
2433:
2413:
2408:
2395:
2386:
2350:
2330:
2310:
2282:
2273:
2245:
2224:10.1068/p230321
2209:
2200:
2179:10.1068/p060401
2164:
2142:
2107:Vision Research
2104:
2094:
2087:
2048:
2043:
2037:
2030:
2021:
1991:
1961:
1952:
1927:Vision Research
1924:
1915:
1901:
1879:
1839:
1818:10.1068/p260017
1803:
1775:
1745:
1715:
1706:
1678:
1669:
1657:
1636:10.2307/1419056
1621:
1593:
1584:
1575:
1539:
1509:
1484:Vision Research
1481:
1472:
1439:Vision Research
1436:
1406:10.1.1.211.4341
1393:Vision Research
1390:
1369:10.1068/p160731
1354:
1332:
1304:
1295:
1291:
1286:
1285:
1272:
1268:
1258:
1254:
1249:
1209:Hering illusion
1161:
1126:
1074:
1068:
1041:
999:
986:
981:
980:
962:
957:
915:
833:
802:
785:
772:
767:
766:
747:
663:
603:
594:
586:
580:
560:
546:
500:
466:
454:
445:
437:
435:
414:
381:
330:
329:
271:
270:
186:
180:
94:
12:
11:
5:
2505:
2503:
2495:
2494:
2489:
2484:
2474:
2473:
2469:
2468:
2459:
2431:
2411:
2406:
2393:
2384:
2359:(6): 615–636,
2348:
2328:
2308:
2280:
2271:
2254:(4): 489–500,
2243:
2218:(3): 321–333,
2207:
2198:
2173:(4): 401–406,
2162:
2151:(2): 301–307,
2140:
2102:
2092:
2065:10.1038/nn1641
2059:(3): 429–434,
2041:
2028:
2019:
1989:
1970:(4): 323–334,
1959:
1950:
1933:(3): 189–206,
1922:
1913:
1899:
1888:(2): 353–360,
1877:
1848:(1): 500–505,
1837:
1801:
1784:(3): 119–135,
1773:
1754:(4): 429–442,
1743:
1724:(3): 218–230,
1713:
1704:
1687:(4): 423–440,
1676:
1667:
1655:
1630:(3): 469–476,
1619:
1596:Spatial Vision
1591:
1582:
1573:
1537:
1518:(5): 783–806,
1507:
1490:(9): 1079–94,
1479:
1470:
1434:
1388:
1363:(6): 731–746,
1352:
1330:
1313:(3): 675–677,
1302:
1292:
1290:
1287:
1284:
1283:
1266:
1251:
1250:
1248:
1245:
1244:
1243:
1236:
1234:Wundt illusion
1231:
1226:
1221:
1216:
1214:Ponzo illusion
1211:
1206:
1200:
1193:
1160:
1157:
1070:Main article:
1067:
1064:
1031:
1030:
1018:
1015:
1012:
1009:
1005:
1002:
997:
992:
989:
961:
958:
956:
953:
942:Ponzo illusion
914:
911:
832:
826:
822:
821:
808:
805:
801:
798:
795:
791:
788:
783:
778:
775:
746:
743:
662:
652:
634:Also, because
599:
590:
576:
556:
545:
539:
499:
489:
465:
462:
450:
441:
431:
423:through point
410:
378:nodal distance
370:
369:
357:
354:
351:
348:
345:
341:
337:
311:
310:
298:
294:
290:
287:
284:
281:
278:
231:indicates the
223:The line from
218:entrance pupil
182:Main article:
179:
161:
98:Joynson (1949)
93:
90:
13:
10:
9:
6:
4:
3:
2:
2504:
2493:
2490:
2488:
2485:
2483:
2480:
2479:
2477:
2465:
2460:
2457:
2453:
2449:
2445:
2441:
2437:
2432:
2429:
2425:
2421:
2417:
2412:
2409:
2403:
2399:
2394:
2390:
2385:
2382:
2378:
2374:
2370:
2366:
2362:
2358:
2354:
2353:Human Factors
2349:
2346:
2342:
2338:
2334:
2329:
2326:
2322:
2318:
2314:
2309:
2306:
2302:
2298:
2294:
2290:
2286:
2281:
2277:
2272:
2269:
2265:
2261:
2257:
2253:
2249:
2244:
2241:
2237:
2233:
2229:
2225:
2221:
2217:
2213:
2208:
2204:
2199:
2196:
2192:
2188:
2184:
2180:
2176:
2172:
2168:
2163:
2159:
2154:
2150:
2146:
2141:
2138:
2134:
2130:
2126:
2121:
2116:
2112:
2108:
2103:
2098:
2093:
2086:
2082:
2078:
2074:
2070:
2066:
2062:
2058:
2054:
2047:
2042:
2036:
2035:
2029:
2025:
2020:
2017:
2013:
2008:
2003:
1999:
1995:
1990:
1987:
1983:
1978:
1973:
1969:
1965:
1960:
1956:
1951:
1948:
1944:
1940:
1936:
1932:
1928:
1923:
1919:
1914:
1911:
1905:
1900:
1896:
1891:
1887:
1883:
1878:
1875:
1871:
1866:
1861:
1856:
1851:
1847:
1843:
1838:
1835:
1831:
1827:
1823:
1819:
1815:
1811:
1807:
1802:
1799:
1795:
1791:
1787:
1783:
1779:
1774:
1771:
1767:
1762:
1757:
1753:
1749:
1744:
1741:
1737:
1732:
1727:
1723:
1719:
1714:
1710:
1705:
1702:
1698:
1694:
1690:
1686:
1682:
1677:
1673:
1668:
1664:
1660:
1656:
1653:
1649:
1645:
1641:
1637:
1633:
1629:
1625:
1620:
1617:
1613:
1609:
1605:
1601:
1597:
1592:
1588:
1587:Eye and brain
1583:
1579:
1574:
1571:
1567:
1563:
1559:
1555:
1551:
1547:
1543:
1538:
1535:
1531:
1526:
1521:
1517:
1513:
1508:
1505:
1501:
1497:
1493:
1489:
1485:
1480:
1476:
1471:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1435:
1432:
1428:
1424:
1420:
1416:
1412:
1407:
1402:
1398:
1394:
1389:
1386:
1382:
1378:
1374:
1370:
1366:
1362:
1358:
1353:
1349:
1344:
1340:
1336:
1331:
1328:
1324:
1320:
1316:
1312:
1308:
1303:
1299:
1294:
1293:
1288:
1280:
1276:
1270:
1267:
1262:
1256:
1253:
1246:
1241:
1237:
1235:
1232:
1230:
1227:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1204:
1201:
1198:
1194:
1192:
1191:Moon illusion
1189:
1188:
1187:
1184:
1182:
1177:
1173:
1170:
1166:
1158:
1156:
1154:
1150:
1146:
1142:
1137:
1133:
1129:
1124:
1119:
1116:
1114:
1110:
1106:
1101:
1099:
1095:
1091:
1083:
1078:
1073:
1065:
1063:
1059:
1057:
1052:
1048:
1044:
1038:
1036:
1016:
1013:
1010:
1007:
1003:
1000:
995:
990:
987:
979:
978:
977:
975:
971:
966:
959:
954:
952:
949:
947:
946:moon illusion
943:
938:
935:
932:
928:
924:
920:
912:
910:
908:
904:
900:
896:
892:
887:
885:
879:
877:
873:
869:
864:
862:
858:
854:
851:, area V1 or
850:
846:
842:
838:
831:
827:
825:
806:
803:
799:
796:
793:
789:
786:
781:
776:
773:
765:
764:
763:
760:
756:
752:
744:
742:
740:
736:
732:
728:
727:apparent size
724:
720:
715:
713:
709:
703:
701:
696:
694:
690:
685:
678:
674:
672:
669:differs from
668:
661:
657:
653:
651:
649:
645:
641:
637:
632:
630:
625:
623:
619:
615:
610:
608:
602:
598:
593:
589:
584:
579:
575:
571:
566:
562:
559:
555:
551:
544:
540:
538:
536:
532:
528:
524:
519:
517:
513:
509:
505:
502:In Figure 2,
498:
494:
490:
488:
486:
482:
473:
469:
463:
461:
459:
453:
449:
444:
440:
434:
430:
426:
422:
418:
413:
409:
405:
401:
396:
392:
388:
384:
379:
376:is the eye's
375:
355:
352:
349:
346:
343:
339:
335:
328:
327:
326:
324:
320:
316:
296:
292:
288:
285:
282:
279:
276:
269:
268:
267:
265:
260:
258:
254:
250:
246:
242:
238:
234:
230:
226:
221:
219:
215:
211:
207:
203:
199:
190:
185:
178:
174:
170:
166:
162:
160:
158:
154:
150:
149:field of view
146:
142:
137:
133:
129:
127:
123:
119:
115:
111:
107:
103:
99:
91:
89:
87:
83:
77:
75:
74:Moon illusion
71:
67:
62:
59:
53:
51:
47:
43:
39:
35:
31:
27:
23:
19:
2463:
2442:(1): 61–86,
2439:
2435:
2419:
2415:
2397:
2388:
2356:
2352:
2336:
2332:
2316:
2312:
2288:
2284:
2275:
2251:
2247:
2215:
2211:
2202:
2170:
2166:
2148:
2144:
2110:
2106:
2096:
2085:the original
2056:
2052:
2033:
2023:
2000:(1): 64–72,
1997:
1993:
1967:
1963:
1954:
1930:
1926:
1917:
1909:
1903:
1885:
1881:
1845:
1841:
1812:(1): 17–27,
1809:
1805:
1781:
1777:
1751:
1747:
1721:
1717:
1708:
1684:
1680:
1671:
1662:
1627:
1623:
1599:
1595:
1586:
1577:
1545:
1541:
1515:
1511:
1487:
1483:
1474:
1442:
1438:
1396:
1392:
1360:
1356:
1338:
1334:
1310:
1306:
1297:
1275:Ewald Hering
1269:
1255:
1185:
1178:
1174:
1168:
1164:
1162:
1152:
1148:
1144:
1140:
1135:
1131:
1127:
1122:
1120:
1117:
1112:
1108:
1104:
1102:
1097:
1093:
1089:
1087:
1081:
1060:
1056:Emmert's law
1050:
1046:
1042:
1039:
1034:
1032:
973:
969:
967:
963:
950:
939:
936:
930:
926:
922:
918:
916:
906:
902:
898:
894:
890:
888:
883:
880:
875:
865:
840:
836:
834:
829:
823:
758:
754:
750:
748:
738:
734:
730:
722:
718:
716:
711:
707:
704:
699:
697:
692:
688:
686:
682:
670:
666:
664:
659:
655:
647:
640:eye tracking
635:
633:
628:
626:
621:
617:
613:
611:
606:
600:
596:
591:
587:
582:
577:
573:
569:
567:
563:
557:
553:
549:
547:
542:
534:
530:
526:
522:
520:
515:
511:
507:
503:
501:
496:
492:
484:
480:
478:
467:
457:
451:
447:
442:
438:
432:
428:
424:
420:
411:
407:
403:
399:
397:
390:
386:
382:
373:
371:
322:
318:
314:
312:
263:
261:
256:
252:
244:
236:
228:
224:
222:
213:
209:
205:
201:
197:
195:
184:Visual angle
176:
172:
168:
164:
157:visual field
152:
144:
138:
134:
130:
125:
121:
95:
78:
63:
54:
49:
45:
37:
33:
25:
22:visual angle
15:
2422:: 226–234,
2339:: 226–234,
2319:: 119–134,
1167:along with
521:Similarly,
212:from point
2476:Categories
2212:Perception
2167:Perception
1806:Perception
1357:Perception
1289:References
1261:body image
857:Retinotopy
735:subjective
24:, denoted
1798:144334816
1401:CiteSeerX
1341:: 31–36,
1017:θ
1014:
804:θ
800:
372:in which
356:θ
353:
283:θ
280:
243:at point
233:chief ray
30:subtended
16:In human
2456:16345004
2381:34272970
2305:17829398
2240:41311235
2195:21941416
2129:12044760
2073:16462737
1874:10618447
1834:41489059
1652:13354816
1616:18534112
1562:14074555
1467:26009881
1385:34545108
1139:), with
1084:smaller.
1004:′
991:′
807:′
790:′
777:′
227:through
66:paradigm
2373:3914446
2285:Science
2268:6240520
2232:7971109
2137:8467032
2081:8391410
2016:3703663
1986:4034350
1947:5862949
1826:9196687
1770:8036122
1740:1561047
1701:6219186
1644:1419056
1570:4153670
1534:9259645
1504:5350376
1459:2631401
1431:9183517
1423:3445485
1377:3454431
1327:2144580
845:retinal
644:saccade
510:′ from
417:horizon
239:on the
2454:
2404:
2379:
2371:
2303:
2266:
2238:
2230:
2193:
2187:917729
2185:
2135:
2127:
2079:
2071:
2014:
1984:
1945:
1912:5573.)
1872:
1862:
1832:
1824:
1796:
1768:
1738:
1699:
1650:
1642:
1614:
1568:
1560:
1542:Nature
1532:
1502:
1465:
1457:
1429:
1421:
1403:
1383:
1375:
1325:
1242:(AFPP)
1134:= tan
1033:Here,
757:, and
479:Point
241:retina
175:, and
82:neural
58:retina
20:, the
2482:Angle
2377:S2CID
2236:S2CID
2191:S2CID
2133:S2CID
2088:(PDF)
2077:S2CID
2049:(PDF)
2038:(PDF)
1908:(See
1865:26692
1830:S2CID
1794:S2CID
1640:JSTOR
1566:S2CID
1463:S2CID
1427:S2CID
1381:S2CID
1247:Notes
1082:seems
385:= 17
249:fovea
141:angle
40:. An
2452:PMID
2402:ISBN
2369:PMID
2301:PMID
2264:PMID
2228:PMID
2183:PMID
2125:PMID
2069:PMID
2012:PMID
1982:PMID
1943:PMID
1870:PMID
1822:PMID
1766:PMID
1736:PMID
1697:PMID
1648:PMID
1612:PMID
1558:PMID
1530:PMID
1500:PMID
1455:PMID
1419:PMID
1373:PMID
1323:PMID
1049:tan
905:and
658:and
495:and
317:and
114:1999
110:1985
106:1965
102:1963
2444:doi
2424:doi
2361:doi
2341:doi
2321:doi
2293:doi
2289:167
2256:doi
2252:113
2220:doi
2175:doi
2153:doi
2115:doi
2061:doi
2002:doi
1972:doi
1935:doi
1890:doi
1860:PMC
1850:doi
1814:doi
1786:doi
1756:doi
1726:doi
1689:doi
1685:111
1632:doi
1604:doi
1550:doi
1546:199
1520:doi
1492:doi
1447:doi
1411:doi
1365:doi
1343:doi
1315:doi
1011:tan
797:tan
350:tan
277:tan
116:),
48:or
36:or
2478::
2450:,
2440:42
2438:,
2420:16
2418:,
2375:,
2367:,
2357:27
2355:,
2337:16
2335:,
2317:22
2315:,
2299:,
2287:,
2262:,
2250:,
2234:,
2226:,
2216:23
2214:,
2189:,
2181:,
2169:,
2149:15
2147:,
2131:,
2123:,
2111:42
2109:,
2075:,
2067:,
2055:,
2051:,
2010:,
1998:39
1996:,
1980:,
1968:37
1966:,
1941:,
1929:,
1886:15
1884:,
1868:,
1858:,
1846:97
1844:,
1828:,
1820:,
1810:26
1808:,
1792:,
1780:,
1764:,
1752:55
1750:,
1734:,
1722:51
1720:,
1695:,
1683:,
1646:,
1638:,
1628:69
1626:,
1610:,
1600:21
1598:,
1564:,
1556:,
1544:,
1528:,
1516:59
1514:,
1498:,
1486:,
1461:,
1453:,
1443:29
1441:,
1425:,
1417:,
1409:,
1397:27
1395:,
1379:,
1371:,
1361:16
1359:,
1339:11
1337:,
1321:,
1311:16
1309:,
1169:S′
1165:θ′
1153:θ′
1149:S′
1145:D′
1141:θ′
1136:θ′
1132:D′
1130:/
1128:S′
1123:θ′
1113:D′
1105:S′
1058:.
1047:D′
1045:=
1043:S′
1035:S′
974:θ′
931:θ′
927:θ′
907:θ′
899:θ′
895:θ′
886:.
884:S′
878:.
876:R′
863:.
830:θ′
759:D′
755:S′
753:,
751:θ′
741:.
739:θ′
723:S′
719:θ′
712:S′
708:θ′
700:θ′
693:S′
689:S′
671:S′
667:θ′
660:S′
656:θ′
648:θ′
642:,
636:θ′
629:θ′
614:θ′
607:θ′
597:d′
595:−
588:d′
574:d′
554:d′
543:θ′
535:S′
523:S′
504:D′
497:S′
493:D′
460:.
446:−
395:.
393:mm
259:.
220:.
198:AB
171:,
167:,
159:.
153:θ′
128:.
122:θ′
112:,
108:,
104:,
88:.
52:.
28:,
2446::
2426::
2363::
2343::
2323::
2295::
2258::
2222::
2177::
2171:6
2155::
2117::
2063::
2057:9
2004::
1974::
1937::
1931:5
1892::
1852::
1816::
1788::
1782:1
1758::
1728::
1691::
1634::
1606::
1552::
1522::
1494::
1488:9
1449::
1413::
1367::
1345::
1317::
1199:)
1109:θ
1098:θ
1094:D
1090:S
1051:θ
1008:=
1001:D
996:/
988:S
970:θ
923:R
919:θ
903:R
891:R
841:R
837:θ
794:=
787:D
782:/
774:S
731:θ
622:B
618:A
601:B
592:A
583:B
578:A
570:A
558:B
550:B
531:B
527:A
516:B
512:O
508:B
485:O
481:O
458:θ
452:B
448:d
443:A
439:d
433:A
429:d
425:A
421:O
412:B
408:d
404:B
400:O
391:D
389:/
387:S
383:R
374:n
347:=
344:n
340:/
336:R
323:R
319:a
315:b
297:D
293:/
289:S
286:=
264:θ
257:a
253:A
245:b
237:B
229:O
225:B
214:O
210:D
206:B
202:S
177:θ
173:R
169:D
165:S
145:θ
126:θ
26:θ
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
