Perceived visual angle
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 relationship between the perceived angular size of an object and the size of the neural activity pattern it excites in the primary visual cortex.
Visual angle illusions have been explicitly described by many vision researchers, including Joynson (1949), (McCready 1963, 1965, 1985, 1999), Rock & McDermott (1964), 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, θ′, can change for a viewed target that subtends a constant (physical) visual angle θ.
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, 1994, Ono, 1970, Oyama, 1977, Reed, 1984, 1989, Restle, 1970, Roscoe, 1985, 1989).
In order to clarify the new paradigm which replaces the old one, it helps to keep in mind that an angle is the difference between two directions from a common point (the vertex).
The extent's lower endpoint at B lies at a distance D from point O, which for present purposes can represent the center of the eye's entrance pupil.
For instance, a well-trained observer might say that point A′ "looks about 25 degrees higher" than B′, but most cannot reliably say how large a direction difference looks.
As already noted, the magnitude of an object's visual angle θ determines the size R of its retinal image.
This neurological relationship recently was confirmed by Murray, Boyaci, & Kersten (2006) using functional magnetic resonance imaging.
That is, experimental psychologists long ago rejected any idea that people "sense" a proximal stimulus such as the retinal image.
But, as already noted, "other factors" can intervene to slightly change θ′ for a target forming a constant sized retinal image (and thereby create a visual angle illusion).
The Murray, et al. (2006) observers viewed a flat picture with two disks that subtended the same visual angle θ and formed retinal images of the same size (R), but the perceived angular size, θ′, for one disk was larger than θ′ for the other (say, 17% larger) due to differences in their background patterns.
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.
This idea that one does not see the different directions in which objects lie from oneself is a basis of the so-called "size–distance invariance hypothesis" (SDIH).
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).
The two central circles are the same linear size S and the same viewing distance D, so they subtend the same visual angle θ and form equal-sized retinal images.
This commonly found disagreement between published data and the SDIH is known as the "size–distance paradox" (Gruber, 1956, Ono, et al. 1974).
Describing the few existing explanations for visual angle illusions is beyond the scope of this present entry.
