**4.4 Discussion**

38 Haptics Rendering and Applications

frequency of subject responses. We summarize below the effects on the frequency of

Figure 7 indicates the mean values and standard errors of the percentages for the occurrence of the SWI obtained from each pictorial depth cue, i.e., solid cube (Cube), wire-frame cube (Frame) and square (Square). The white bars (A) indicate the Smaller condition in which the second object was smaller in size than the first. The smaller object was reported as heavier than the larger one. The gray bars indicate the Identical Condition in which sizes were identical between the first and second object. Although the graphical sizes remained constant in the Identical condition, for some reason, subjects accidentally reported a difference in heaviness between the first and the second lifts (See Sec. 2-1). The black bars (B) are those obtained from the Larger condition in which the second object was larger in size than the first. For these conditions, the larger object was reported as lighter than the smaller one. Again, the grey bars are those obtained from the Identical condition in which they

Fig. 7. Mean percentages (%) of the size-weight illusion (SWI) for each pictorial depth cue for each condition through which subjects compared the heaviness of the small size with that of the large (white bars), the large with the small (black bars), and the median with the

There was a significant effect of change in size (F (1,15) =28.15, p< .001), indicating that the SWI occurred significantly for each pictorial depth cue when the size was changed compared to the conditions when the size was not changed. There were, however, no effects of pictorial depth cues (F(2, 30) =0.26) nor for the direction of size change (F(1, 15 = 0.46), suggesting pictorial depth cues do not affect the frequency or strength of the SWI. A significant interaction was observed only between pictorial depth cue and direction of size change (F(2, 30) = 31.53, p < .001). This is due to the fact that the SWI occurred more frequently in the Smaller condition (57.8% in Cube, 67.2% in Frame and 59.4 % in Square) than in the Larger condition (51.6% in Cube, 34.4 % in Frame and 45.3% in Square). There were no significant differences in probability in the Identical condition: the probability when

**4.3 Results: Effects of depth cues and size on perceived heaviness, and the size-**

occurrence of the SWI.

reported the second object to be perceived as lighter.

equivalent median (gray bars).

**weight illusion** 

All subjects experienced the SWI for all three visual stimuli in Fig. 6B without any significant differences, suggesting that, contrary to our hypothesis, the SWI occurs to the same degree with any pictorial depth cues! Volumetric information of an object has long been thought to be critical in bringing about the SWI (Jones, 1986). As a result, numerous studies have investigated the phenomenon of the SWI and discussed based on the volume of an object as the essential parameter for size (Scripture, 1897; H.E. Ross, 1969; Ellis & Lederman, 1993). Furthermore, in studies related to motor programming for the lifting of an object, information of volume has also been thought to be a critical factor in estimating weight of an object as part of the process for producing the required lift forces (H.E. Ross, 1969; Gordon et al., 1991). Thus, Westwood and his colleagues (2002) proposed the necessity of a volumetric object description in the process of specifying the grip force and the load force necessary for lifting and manipulation because such forces must be scaled to the anticipated mass of the object either by estimating its volume and density or by accessing stored knowledge related to the mass of the other object. It was, therefore, hypothesized at the beginning of this study that the SWI would decrease in frequency or even disappear when dimensional cues were reduced from 3D structure such as a cube to a 2D structure such as a square. The results, however, indicated that all the subjects equally experienced the SWI for all three visual stimuli with any cues of a 2D graphical object. This suggests that whatever the pictorial depth cues are, these factors are not critical for the occurrence of the SWI. The present results, therefore, conclude, contrary to commonly accepted theory, that pictorial depth cues responsible for 3D perception are not crucially necessary in the process of producing the SWI. In short, the perceptual system of heaviness may not be responsive to the dimension provided by pictorial depth cues, at least under the VIRTUAL VISION + VIRTUAL HAPTIC environment of this experiment.
