Academic journal article Perception and Psychophysics

The Structure of Frontoparallel Haptic Space Is Task Dependent

Academic journal article Perception and Psychophysics

The Structure of Frontoparallel Haptic Space Is Task Dependent

Article excerpt

In three experiments, we investigated the structure of frontoparallel haptic space. In the first experiment, we asked blindfolded participants to rotate a matching bar so that it felt parallel to the reference bar, the bars could be at various positions in the frontoparallel plane. Large systematic errors were observed, in which orientations that were perceived to be parallel were not physically parallel. In two subsequent experiments, we investigated the origin of these errors. In Experiment 2, we asked participants to verbally report the orientation of haptically presented bars. In this task, participants made errors that were considerably smaller than those made in Experiment 1. In Experiment 3, we asked participants to set bars in a verbally instructed orientation, and they also made errors significantly smaller than those observed in Experiment 1. The data suggest that the errors in the matching task originate from the transfer of the reference orientation to the matching-bar position.

Several studies have aimed at determining the relationship between the structure of perceived visual space and Euclidean physical space (for an overview, see Wagner, 1985). In a Euclidean space, two parallel lines remain parallel when one (or both) of them is translated. However, Helmholtz (1867/1962) showed that wires arranged by a participant m a perceived frontoparallel plane do not lie in a physically frontoparallel plane. Moreover, Hillebrand (1902) found that two lines that appear to be equidistant in depth are not physically equidistant. These results have led to the suggestion that visually perceived space is distorted and not Euclidean, and they led Luneburg (1947) to conclude that visually perceived space is represented better by a curved Riemannian space. Specifically, Luneburg suggested that perceived space has a Riemannian structure with a negative curvature.

In the past decades, this assumption has been tested via studies in which the structure of visual space was investigated using a number of experimental methods, including distance matching (Meng & Sedgwick, 2001), orientation matching (Cuijpers, Kappers, & Koenderink, 2002), triangulation (Fukusima, Loomis, & Da Silva, 1997), pointing (Koenderink, van Doom, Kappers, & Lappin, 2002), and direct testing of axioms (Koenderink, van Doom, Kappers, & Todd, 2002; Todd, Oomes, Koenderink, & Kappers, 2001). The perceived relative orientation of two physically parallel bars at various positions in the visual field depends on the nature of the visually perceived space. For visual and haptic orientation matching tasks, Cuijpers, Kappers, and Koenderink (2003) quantitatively compared experimental data and predictions based on a Euclidean geometry or a Riemannian geometry with a positive or negative curvature. They found that neither model incorporated the experimental observations correctly, but that zero curvature yielded the best fit of the data. In addition, they showed that for other tasks, such as the pointing task, a Riemannian space did not yield an appropriate fit.

These investigations of visual space have been extended to the haptic modality. Blumenfeld (1937) asked participants to hold two strings parallel to each other that at one end were attached to a table at points equidistant from the median plane. The results were far from veridical: The lines produced diverged toward the participant as long as the distance between the lines was less than the distance between the shoulder joints; beyond this distance, the lines gradually became parallel, and for some of the participants they even converged.

Much evidence in the literature supports the existence of haptic oblique effects; that is, performance in certain tasks is worse when the orientation of the stimuli is (or should be made) oblique than when the stimuli are either horizontal or vertical (see, e.g., Appelle & Countryman, 1986; Appelle & Gravetter, 1985; Gentaz & Hatwell, 1995,1999; Lechelt, Eliuk, & Tanne, 1976; Lechelt & Verenka, 1980). …

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