Reference Frames and 3-D Shape Perception of Pictured Objects: On Verticality and Viewpoint-From-Above

Research on the influence of reference frames has generally focused on visual phenomena such as the oblique effect, the subjective visual vertical, the perceptual upright, and ambiguous figures. Another line of research concerns mental rotation studies in which participants had to discriminate between familiar or previously seen 2-D figures or pictures of 3-D objects and their rotated versions. In the present study, we disentangled the influence of the environmental and the viewer-centered reference frame, as classically done, by comparing the performances obtained in various picture and participant orientations. However, this time, the performance is the pictorial relief: the probed 3-D shape percept of the depicted object reconstructed from the local attitude settings of the participant. Comparisons between the pictorial reliefs based on different picture and participant orientations led to two major findings. First, in general, the pictorial reliefs were highly similar if the orientation of the depicted object was vertical with regard to the environmental or the viewer-centered reference frame. Second, a viewpoint-from-above interpretation could almost completely account for the shears occurring between the pictorial reliefs. More specifically, the shears could largely be considered as combinations of slants generated from the viewpoint-from-above, which was determined by the environmental as well as by the viewer-centered reference frame.

In the text, we only mention one of the two comparisons related to that same R 2 value, i.e. the first comparison with the lowest difference between the picture orientations followed by the lowest difference between the participant orientations. For instance, we mention the comparisons of the Rot90 category but not the inverse comparisons belonging to the Rot270 category. affine regression regression analysis (z comp = a + bx + cy + dz ref, with 'z' The multiple (affine) regression analysis (z comp = a + bx + cy + dz ref , with z representing the depth values; with the image coordinates x and y, measured in screen pixels, referring to the positions on the image plane on which the depth values were calculated) took into account not only the depth dimension, but also the x-and y-dimension of the image plane. This regression analysis was considered as an affine transformation because of its geometrical properties: invariance of parallelism, collinearities and ratios. In contrast with the straight regression, the affine regression is not entirely reversible; therefore, the inverse comparisons did not result in duplicate R 2 values. are noted by an abbreviated notation, with " /" referring to the comparison between reference and comparison and with " -" referring to the combination of picture orientation and participant orientation in either the reference or the comparison or both. specific comparisons indicates the comparison (of Subset 1) between the pictorial reliefs based on pictures differing by 90 degrees, with reference picture F0 and comparison picture F90, and participant orientation VF90.
for instance: F0/F90-VF0 indicates the comparison (of Subset 2) between the pictorial reliefs based on the same picture orientation that was looked at from two different participant orientations, VF0 and VF90. The reference picture is thus the same as the comparison picture, i.e.F0. The reference participant orientation is VF0 and the comparison participant orientation VF90.
indicates the comparison (of Subset 3) between the pictorial reliefs with reference picture orientation F0 and reference participant orientation VF0; the comparison picture orientation is VF90. The difference between picture orientations is the same as the difference between participant orientations.
indicates the comparison (of Subset 4) between the pictorial reliefs with reference picture orientation F0 and reference participant orientation VF90; the comparison picture orientation is F90 and the comparison participant orientation is VF270. The orientations between pictures thus differ 90 degrees; the orientations between participants differ 180 degrees.
indicate the R 2 values of the straight regression of the comparisons with a correspondence between the picture orientations and the viewer centred reference frame on the one hand and the environmental reference frame on the other hand, with one of the picture orientations upright (F0) or upside down (F180) according to the environmental reference frame (Figure 7 (a), (c), (d)).
In the text, this texture is denoted by 'a fine, horizontal texture'.
indicates the R 2 values of the straight regression of the comparisons with a correspondence between the picture orientation and the environmental reference frame, with the picture orientation F0 or F180 (Figure 7 (b)).
In the text, this texture is denoted by 'a clumped grain texture'.
indicates the R 2 values of the straight regression of the comparisons with a correspondence between the picture orientations and the viewer centred reference frame, with the picture orientation upright or upside down with regard to the participant orientation (Figure 7 (c)).
In the text, this texture is denoted by 'a rough random texture'.
shear was calculated from the weights b and c of the image coordinates x and y in the affine regression. The arctangent of the ratio of the weights c and b determined the direction of the shear; a measure for the magnitude of the shear was limited between 0 and 1 by calculating sin{arctan[√(b 2 + c 2 )]}.
attitude change is used in the context of the behaviour of the shear slant is used in the context of the viewpoint-from-above (different from the previously used concept of 'slant' (see above)) The comparisons between pictorial reliefs were divided in four subsets: comparisons with only the picture orientation varied comparisons with only the participant orientation varied comparisons with the picture orientation varied to the same extent as the participant orientation comparisons with both the picture orientation and the participant orientation varied independently of each other Subset 1 Subset 2 Subset 3 Subset 4