Disambiguation of mental rotation by spatial frames of reference

Abstract

Previous research has shown that our ability to imagine object rotations is limited and associated with spatial reference frames; performance is poor unless the axis of rotation is aligned with the object-intrinsic frame or with the environmental frame. Here, we report an active effect of these reference frames on the process of mental rotation: they can disambiguate object rotations when the axis of rotation is ambiguous. Using novel mental rotation stimuli, in which the rotational axes between pairs of objects can be defined with respect to multiple frames of reference, we demonstrate that the vertical axis is preferentially used for imagined object rotations over the object-intrinsic axis for an efficient minimum rotation. In contrast, the object-intrinsic axis can play a decisive role when the vertical axis is absent as a way of resolving the ambiguity of rotational motion. When interpreted in conjunction with recent advances in the Bayesian framework for motion perception, our results suggest that these spatial frames of reference are incorporated into an internal model of object rotations, thereby shaping our ability to imagine the transformation of an object's spatial structure.

Keywords: internal model; mental rotation; reference frame.

Figure 1.

Examples of ambiguous stimuli and the planes of possible rotational axes. Below each pair of disks, the plane on which all the possible axes reside is depicted as a yellow circle intersecting the test disk. Two examples of the possible axes are also depicted on the plane: the magenta cylinder represents the environmental axis, and the green cylinder represents the object-intrinsic axis that produces the minimum rotation between the disks.

Figure 2.

Examples of a trial sequence and the expected adjustments. (a) Depiction of the trial sequence. (b) The expected adjustments of the arrow direction on the target disk. On the target disk the arrows to be adjusted are depicted with respect to the imagined rotation of the test disk about the vertical axis, the object-intrinsic axis, and the axis in the transverse (horizontal) plane, from top to bottom, respectively. These axes are depicted with the test disk (note that these are for illustration purposes only; they are never presented in the experiment). The different directions of the arrows correspond to different rotational axes between the test and the target disks.

Figure 3.

Scatter plots of the estimated rotational axes. For each of the 16 stimulus pairs in the vertical and the horizontal conditions the estimated rotational axes are plotted as thin gray lines as a distribution on the plane of possible rotational axes. The magenta line is the environmental axis (vertical or horizontal), and the green line is the object-intrinsic axis. In the vertical condition the dashed line is the axis in the transverse plane; in the horizontal condition the dashed line is the axis in the sagittal plane. The thick colored lines represent the modal directions of dominant clusters (blue for primary, orange for secondary, and yellow for tertiary). The lengths of these lines are scaled according to the mixing proportions within the corresponding mixture model. Above each plot, the stimulus pair in which the object-intrinsic axes (green cylinder), the environmental (magenta cylinder) axes, and the plane of possible rotational axes (yellow circle) are depicted; the number below the target disk denotes the angle of rotation about the environmental axis.

Figure 4.

Modal directions of dominant clusters in the distributions of estimated rotational axes. The directions are measured with reference to a coordinate system on the plane of possible rotational axes. In the vertical condition the x-axis points along the axis in the transverse plan and the y-axis points along the vertical axis. In the horizontal condition the x-axis points along the horizontal axis and the y-axis points to the axis in the sagittal plane. Symbols are blue for primary, orange for secondary, and yellow for tertiary clusters and are plotted as a function of the angle of rotation about the environmental axis. The dashed lines show the predicted directions of rotational axes with respect to the relevant reference frames. Error bars represent 95% circular confidence intervals.