We have investigated the potential stages of visual processing at which adaptation may occur to a slanted surface produced by horizontal magnification. Predictions of three hypotheses were tested utilizing a property of depth from binocular disparity, namely that slant scales with distance. If adaptation occurs at the disparity level, then the after-effect expressed in units of horizontal magnification will be independent of the test distance. If adaptation occurs at either a perceived slant or mapping level, then the after-effect, expressed in units of slant, will be independent of the test distance. If adaptation is contingent on distance, then the after-effect will not transfer over distance. Subjects adapted to a stereo-defined slanted surface at a distance of 57 cm. The after-effect was measured with a test stimulus at a distance of 28, 57, 85, or 114 cm by means of a nulling method. When the after-effect was expressed in units of slant, we found that it was larger at the adapting distance than other test distances, and that the after-effect was constant at test distances different from the adaptation distance. These results suggest that two types of adaptation occurred, namely adaptation on a mapping/perception level and adaptation contingent on distance.

*Z*

_{screen}), whereas the simulated test distance (

*Z*

_{simulated}) varied between measure-ment sessions (28, 57, 85, or 114 cm). The simulated test distance was specified by vertical disparity and vergence cues, both of which were altered by translating both eyes’ images horizontally in the opposite direction. The total amount of translation (Δ) is defined by with

*I*symbolizing the interocular distance.

^{2}when viewed through the Ferro-shutters. Each slant stimulus presentation was a different random-dot display to avoid changes in perceived image compression as a cue. The stimuli were presented at the center of the screen (straight-ahead).

*d*′ = 1). We estimated the

*SE*s of PSE and JND by performing 500 Monte Carlo simulations (termed bootstrap replications) on the data sets. The after-effect is defined as the difference in PSE between before and after adaptation (PSE

_{post}− PSE

_{pre}), and the estimated error is defined as the sum of

*SE*s of both PSEs (

*se*PSE

_{pre}+

*se*PSE

_{post}).

*p*> .05) as expected, whereas the offset of JC does, which indicates a preferred adaptation direction. For all subjects we found an offset significantly different from zero for one or two of the test distances (

*p*< .05). For further data analysis, we subtracted the offsets from the data.

*A*

_{disp}) and adaptation at the perception/mapping level (

*A*

_{perc}) (both transfer in different ways over distance), and adaptation that is fully contingent on distance (

*A*

_{cont}).

*A*

_{57}. The following paragraphs show how the predictions were made for adaptation expressed in horizontal magnification and slant angle. The predictions for subject CS are shown in Figure 3.

*M*) (1% magnification corresponds to

*M*= 0.01) and the veridical slant angle (

*S*), which is defined by with

*d*representing the distance and

*I*representing the interocular distance (Van Ee & Erkelens, 1998).

*p*< .05) than both the after-effects at shorter and greater test distance. This indicates that part of the after-effect is contingent on distance. This context-specific adaptation is only manifest when the test is presented at the same distance as the adaptation stimulus. The slopes at 28, 85, and 114 cm do not differ significantly from each other (

*p*> .05). This pattern of results indicates that the after-effect is a combination of adaptation at the perception/mapping level that transfers over distance and adaptation that is contingent on distance, which may be either high-level or low-level adaptation.

*p*< .05) than the slopes at 28 and 114 cm, but the slope at 85 cm does not differ significantly (

*p*> .05) from the slope at 57 cm. From this we might conclude that for JC, there is some adaptation at the disparity level. However, the errors in slant nulling (see the error bars of the original data points in Figure 4) are larger for this subject than for the other two subjects. When the inaccuracy in slant discrimination is taken into account, the four curves representing the four test distances are superimposed for JC. Therefore, we only found adaptation at the perception/mapping level for subject JC.

*SD*s of JND before and after adaptation for each subject. There is no significant difference between the JNDs before and after adaptation (

*p*> .05) when the JNDs are averaged over all test distances and all magnifications or when the JNDs are averaged over all magnifications at 57 cm. This indicates that there is no desensitizing, which agrees with our finding that there is no low-level disparity adaptation after-effect.

Average JND ± Standard Deviation JND | ||||
---|---|---|---|---|

Averaged over all distances | Averaged over 57 cm | |||

Before adaptation | After adaptation | Before adaptation | After adaptation | |

CS | 0.24 ± 0.07 | 0.22 ± 0.06 | 0.18 ± 0.01 | 0.20 ± 0.02 |

JC | 0.68 ± 0.30 | 1.02 ± 0.49 | 0.63 ± 0.12 | 1.34 ± 0.75 |

JD | 0.36 ± 0.17 | 0.44 ± 0.21 | 0.50 ± 0.27 | 0.55 ± 0.28 |

*p*> .05) when the data are expressed as slant angles. Furthermore, we found that when the after-effects are expressed as slant angles, the after-effect at 57 cm is significantly larger than the after-effects at other test distances (

*p*< .05) for two out of three subjects, indicating that the after-effect is partly contingent on distance. From the general pattern of results, we conclude that adaptation at the slant/mapping level occurs and adaptation is also partly contingent on distance.

*A*is the magnitude of all the measured adaptation (slope in Figure 2).

*A*

_{disp},

*A*

_{perc}, and

*A*

_{cont}are the predictions for the three hypotheses: adaptation only at the disparity level, adaptation only at the mapping/perception level, and adaptation that is only contingent on distance, respectively (slopes in Figure 3).

*w*

_{disp},

*w*

_{perc}, and

*w*

_{cont}are the proportions of total adaptation that occur at each of the three levels (σ

_{w}=1). Using

*w*, the proportions of adaptation at the various levels of stereo-depth processing can be quantified by means of a least squares fit.

*A*in Equation 7) are the dependent variable of the multiple regression. The three independent variables are the three predictions. The regression coefficient

*w*

_{disp}is not significantly different from zero (

*p*>> .05) for all subjects, which indicates that in this experiment adaptation at the disparity level that transfers over distance does not occur. This agrees with the results that the slopes at 28, 85, and 114 cm are superimposed when the data are expressed in slant angles. Therefore, the variable

*A*

_{disp}was eliminated and the regression was carried out on the remaining two variables (see Table 2). The regression coefficients (

*w*

_{perc}and

*w*

_{cont}) are significant (

*p*< .05) for CS and JD.

*R*

_{adj}

^{2}is close to 1 for both of them, which implies that the model fits their data very well. The model fits the data of JC not as good as for the other two subjects (

*R*

_{adj}

^{2}= 0.92). The contribution of adaptation contingent on distance (

*w*

_{cont}) is not significant (

*p*> .05).

w_{perc} | se w_{perc} | w_{cont} | se w_{cont} | R_{adj}^{2} | |
---|---|---|---|---|---|

CS | 0.64 | 0.02 | 0.36 | 0.04 | 0.99 |

JC | 0.74 | 0.04 | 0.26* | 0.11 | 0.92 |

JD | 0.51 | 0.01 | 0.49 | 0.03 | 0.99 |

*p*> .05). It might be possible that there is some fall off, which we cannot measure with the sparse sampling of test distances in the present experiments. For JC, the fall off is gradual, but this may be an artifact due to the low accuracy in slant discrimination of this subject.