2.2 Experimental data on the TAE

Although much is known about the anatomy of the early visual areas such as V1, the mechanisms of visual perception are not yet fully understood. Studies of visual illusions and aftereffects can help provide a window into this processing, giving clues about how the underlying systems must be operating. The tilt aftereffect is a particularly important phenomenon to study in a model of vision, since it is generally thought to arise in V1, the earliest cortical processing stage. Accordingly, there have been many studies of the TAE since the first experiments published by Gibson and Radner in 1937.

2.2.1 Measuring the TAE in humans

  A variety of experimental paradigms have been used to measure tilt aftereffects in humans, but most are variations on the following procedure (figure 2.3).

 

Figure 2.3: Psychological paradigm for tilt aftereffect experiments.

Subjects are tested in a dark room without any clues to orientation except gravity. The subject's head is immobilized, and the subject is directed to look at some fixation point in the visual field. Oriented geometric figures are used in most cases, generally lines, bars, or gratings (i.e., multiple parallel bars, as in figure 1.1). The figures are presented in various locations relative to the fixation point. First, a baseline is determined by presenting a test figure at a given angle. The perceived orientation of that figure for the subject is determined by various methods, such as:

Directly estimating the numerical angle.

This is generally considered unreliable since most subjects are poor judges of angles other than vertical and horizontal relative to the retina (Mansfield, 1974; Mitchell and Muir, 1976).

Setting the figure to apparent vertical.

This can be done with accuracy within a degree by most unadapted subjects (Howard and Templeton, 1966, p.179).

Setting a comparison figure parallel to the test figure.

This can be done with fairly high consistency, although it is not necessarily an accurate measure of the actual orientation. It is particularly useful because it can measure the effect for oblique testing angles.

After the baseline is computed, the subject views an adaptation figure of a different orientation for a fixed amount of time; this period is called tilt adaptation. Finally, the test figure is presented again, and its orientation measured once more. The difference between the final and initial readings of the perceived orientation of the test figure is the value of the tilt aftereffect for that particular angle separation between test and adaptation figures (Campbell and Maffei, 1971; Gibson and Radner, 1937; Mitchell and Muir, 1976; Muir and Over, 1970).

2.2.2 Human psychophysical data

The TAE was first documented in detail by Gibson and Radner (1937), who measured the angular function (figure 2.4) and time course of the aftereffect.

 

Figure 2.4: Original study of tilt aftereffect versus angle separation on retina.

The precise shape of the TAE versus angle curve varies widely for different subjects and different measurement paradigms, but generally retains the S-shape seen in figure 2.4.

Gibson and Radner introduced terminology that describes the aftereffect as composed of a direct effect and an indirect effect (figure 2.5).

 

Figure 2.5: Angle expansion and contraction effects.

The direct effect consists of a perceived expansion of small angles, i.e. the positive half of the `S' in figure 2.5. A maximum overestimation of a few degrees is experienced at an angular separation between 5° and 20° (Howard and Templeton, 1966, p.216). Larger angles begin to show less of an aftereffect, eventually reaching zero somewhere between 25° and 50° (Campbell and Maffei, 1971; Mitchell and Muir, 1976; Muir and Over, 1970). Even larger angles (up to 90°) generally result in the indirect effect, which consists of a smaller perceived contraction of the angle, peaking between 60° and 85° (Campbell and Maffei, 1971; Mitchell and Muir, 1976; Muir and Over, 1970). Note that for overlapping lines, the largest possible separation is 90° due to symmetry (figure 2.5).

Early studies found tilt aftereffects only for horizontal or vertical test lines (Gibson and Radner, 1937), as did some later studies (Campbell and Maffei, 1971). However, it has since been demonstrated that although subjects do not spontaneously report any difference in the perceived orientation of an oblique line (i.e., neither horizontal nor vertical) after adaptation, when asked to set a comparison line parallel to the test line they make systematic errors identical to those made on vertical or horizontal test lines (Mitchell and Muir, 1976). The variance of the settings was significantly larger for the oblique case, which contributed to the difficulty of establishing the effect for oblique lines. The current consensus is that the angular separation between the test and adaptation figures is the important parameter, not the obliqueness of the line with respect to the horizontal or vertical axis.

The magnitude of the TAE increases logarithmically with increasing adaptation time and decreases logarithmically with time elapsed since the adaptation period (Gibson and Radner, 1937). However, the magnitude of the effect saturates at approximately 4° (Campbell and Maffei, 1971; Greenlee and Magnussen, 1987; Magnussen and Johnsen, 1986; Mitchell and Muir, 1976). The maximum indirect effect documented in central (foveal) vision is approximately 2.5°, and reaches up to about 60% of the magnitude of the direct effect for a given subject and paradigm (Campbell and Maffei, 1971; Mitchell and Muir, 1976; Muir and Over, 1970). A preliminary report indicated that only a direct effect is seen for all angles 0° to 90° when the test and adaptation figures are in peripheral vision (Muir and Over, 1970), but this data has not yet been replicated by other laboratories.

The TAE is localized to what appear to be a specific set of orientation detectors. It is spatially localized on the retina (Gibson and Radner, 1937); adaptation for a figure in one location has no measurable effect on test figures in other locations sufficiently distant. It is spatially selective for frequency (Ware and Mitchell, 1974); adapting on a figure with narrow bars has no measurable effect upon a figure with wide bars, and vice versa. Finally, it transfers completely from one eye to the other (Campbell and Maffei, 1971; Gibson and Radner, 1937); adapting one eye causes equal effects upon test lines in the same location in the visual field for either eye.