Representing orientation: A coordinate-system hypothesis and evidence from developmental deficits

Abstract

This article concerns how the orientations of objects are represented in the human brain. We propose a coordinate-system hypothesis of orientation representation (COR) and show that the hypothesis provides an explicit basis for interpreting orientation errors. Next, we report results from three studies of individuals with developmental deficits in the processing of orientation information, demonstrating that the COR hypothesis can interpret the error patterns in each study. We conclude by discussing several issues concerning the interpretation of our results, the COR hypothesis, and the use of developmental deficits as a basis for inferences about normal cognition.

Acknowledgments

We thank Daniel Dilks, Uyen Le, and Emma Gregory for helpful comments, Lucila Halperin and Sara Shavel-Jessop for help in preparation of figures, Cary Savage and Daniel Dilks for their assistance with the studies of T.M. and B.C., respectively, and B.C., T.M., and A.H. for their cooperation in the studies.

Notes

¹ For expository convenience we have stated the hypothesis in terms of two-dimensional spatial representations; however, it generalizes straightforwardly to three-dimensional representations. Also for convenience we have characterized the coordinate system in Cartesian terms. Coordinate systems involving angular displacements—for example, a spherical coordinate system specifying azimuth (horizontal angular displacement), elevation (vertical angular displacement), and radial distance—could also provide a basis for interpreting A.H.'s errors. For present purposes the important assumption is that direction and magnitude of displacement are specified separately.

² Note that an orientation-invariant representation is not necessarily viewpoint independent. A representation of a three-dimensional object that described only the aspects of an object visible from the observer's viewpoint would be viewpoint dependent, but could still be invariant with respect to orientation in the picture plane. Hence, in positing orientation-invariant representations we do not intend to take a stance on the issue of viewpoint-dependent versus viewpoint-independent representations of three-dimensional objects.

³ In a two-dimensional representation, once a mapping has been established between an object axis and an external axis, the other mapping is fixed; there are no other degrees of freedom. For this reason we posit a single axis correspondence component with two values, rather than assuming two separate representations, one for each object–external axis pair (e.g., P–V and S–H). For three-dimensional representations the situation is more complex: Establishing a mapping between one object axis and one external axis does not fully determine the other mappings. Therefore, positing a separate representation for each of the three object–external axis pairings may be most plausible. Given this point, one might want to assume individual object–external axis representations even in the two-dimensional case, to maintain consistency with the three-dimensional representations. However, as far as we can see the choice between a single representation (e.g., PVSH) and separate representations (PV, SH) in the two-dimensional case has no implications for any of the issues we discuss. Hence, for convenience we adopt the single-representation alternative.

⁴ Once again the situation is more complex for three-dimensional representations, and considerations of consistency with these representations might lead one to posit separate tilt representations for each object–external axis pair even in the two-dimensional case.

⁵ If developmental deficits are contrasted with acquired deficits, B.C.'s impairment clearly falls into the acquired category because it resulted from obvious neural insult. However, her deficit is developmental in the sense of arising before brain development was complete. It is this sense of developmental that we consider most relevant to questions concerning the validity of inferences about normal cognition drawn from developmental deficits. See the General Discussion.

⁶ The points in the upper left and lower right corners of the scatterplot might seem to represent responses that were far from the correct orientation and very close to the up–down reflection orientation. For such responses, an interpretation in terms of random imprecision might be implausible. In fact, however, the responses in these corners are not very distant from the correct orientations. For example, one of the points in the upper left corner represents a target orientation of 30° and a response orientation of 348°. This response is not in fact 318° away from the target orientation (as it may appear in the scatterplot), but only 42° from the target. The points in the upper left corner of the scatterplot may be thought of as lying just below those in the lower left corner, and the points in the lower right corner may be thought of as lying just above the upper right corner.

⁷ For convenience we have stated the interpretation in terms of representing the target line. However, errors could also have originated in B.C.'s representations of response lines.

⁸ Unlike A.H. (but like B.C.) T.M. was accurate in localizing visual stimuli relative to herself. She made no errors in reaching for a wooden block on a table in front of her, and she also reached accurately for a specified object within a complex array of objects.

⁹ Although T.M.'s errors for both tilted and nontilted stimuli are each subject to two potential interpretations, one of the interpretations is shared by the two types of error: Both error types could have resulted from misrepresentation of polarity correspondence in relating one external reference frame to another. However, we do not consider this point a sufficient basis for ruling out the other possible interpretation for each error type.

¹⁰ We might also consider the possibility that A.H.'s location and orientation errors both result not from misrepresentation of polarity correspondence but from misspecification of displacement direction along reference axes. For the orientation errors we might posit that A.H. frequently misspecifies the direction of displacement along object axes when representing the locations of object parts within an object-centred frame (e.g., specifying the location of an object part as 20 units in the negative rather than the positive direction on the secondary object axis). This interpretation could conceivably be applied to the errors involving reflection across object axes; however, for whole-object reflections involving objects with multiple features (as in Figure 23A), we would have to posit multiple errors in which the displacement direction for each feature was misspecified for the same object axis. In contrast the polarity-correspondence interpretation needs to posit only a single representational error to account for the whole-object reflections. Also, mislocation of object parts in object-centred representations cannot account for the orientation errors involving reflection across external axes (see Figure 24A, and the reflections observed with diagonal arrow stimuli, illustrated in Figure 22). The association between location and orientation errors in A.H. clearly deserves careful consideration, especially in the light of the fact that location errors do not always co-occur with orientation errors. (For example, T.M. and B.C. did not make visual localization errors in tasks for which A.H. showed gross impairment, such as visually guided reaching.) More generally, the relationship between location and orientation representations is in need of careful exploration. However, this is a topic for subsequent theoretical and empirical work.

¹¹ McCloskey and Rapp (2000b) have reported evidence that at least some of A.H.'s localization errors arise within an attention-centred frame of reference, in which the origin of the coordinate system is defined by the focus of attention. However, A.H.'s orientation errors were not addressed in their study. Further, the conclusion about attention-centred representations has to do only with how the origin of the coordinate system is defined, and not with the basis for defining reference axes.