Allocentric and Egocentric Spatial Representations: Definitions, Distinctions, and Interconnections

Although the literatures on human spatial cognition and animal navigation often make distinctions between egocentric and allocentric (also called exocentric or geocentric) representations, the terms have not generally been well defined. This chapter begins by making formal distinctions between three kinds of representations: allocentric locational, egocentric locational, and allocentric heading representations. These distinctions are made in the context of wholebody navigation (as contrasted, e.g., with manipulation). They are made on the basis of primitive parameters specified by each representation, and the representational distinctions are further supported by work on brain mechanisms used for animal navigation. From the assumptions about primitives, further inferences are made as to the kind of information each representation potentially makes available. Empirical studies of how well people compute primitive and derived spatial parameters are briefly reviewed. Finally, the chapter addresses what representations humans may use for processing spatial information during physical and imagined movement, and work on imagined updating of spatial position is used to constrain the connectivity among representations. 1 Reference Frames and Spatial Representations Put simply, a reference frame is a means of representing the locations of entities in space. An entire chapter could be devoted to frames of reference, and several excellent ones have been (see, e.g., Berthoz, 1991; Brewer & Pears, 1993; Levinson, 1996; Soechting, Tong & Flanders, 1996). Nor is the literature deficient in discussions of allocentric and egocentric representations. In fact, the contrast between those two terms abounds in discussions of spatial perception, spatial cognition, and spatially directed action. Not everyone treats these terms equivalently, however. Allocentric is sometimes used synonymously with "exocentric" or "geocentric." To Paillard (1971) the geocentric reference frame was gravity-based and subsumed both allocentric Preprint of Klatzky, R. L. (1998). Allocentric and egocentric spatial representations: Definitions, distinctions, and interconnections. In C. Freksa, C. Habel, & K. F. Wender (Eds.), Spatial cognition An interdisciplinary approach to representation and processing of spatial knowledge (Lecture Notes in Artificial Intelligence 1404) (pp. 1-17). Berlin: Springer-Verlag. The author acknowledges support of Grant 9740 from the National Eye Institute for the study of Klatzky et al. (in press). This work has benefited from extensive discussions of spatial cognition with Jack Loomis. and egocentric representations. Pick (1988) has pointed out that although allocentric implies reference to another human, the term has assumed more general use. Exceptions notwithstanding, there is general understanding that in an egocentric reference frame, locations are represented with respect to the particular perspective of a perceiver, whereas an allocentric reference frame locates points within a framework external to the holder of the representation and independent of his or her position. While the general distinction between allocentric and egocentric representations is commonly made, it is far less common to see a specific proposal for what is represented in each. 2 Some Basic Definitions In this section, I define critical parameters that are conveyed by spatial representations. It is important to note that the parameters are being defined independently of the nature of the representation that conveys them. For example, the egocentric bearing of a point in space will be defined as an angle that is measured with respect to an object, ego, within the space. The egocentric bearing is a particular numerical value that could be derived from an egocentric or allocentric representation, given relevant input information. It is the parameter definitions, rather than processes that derive the parameters, that are specified in this section. 2.1 Spatial Parameters The parameters of a spatial representation are values that can be assigned to individual points (e.g., location of one point) or multiple points (e.g., distance between two points). Primitive parameters are those that the spatial representation conveys directly for all entities that are included in the representation. Derived parameters are those that can be computed from primitives, possibly in several computational steps. A locational representation is one that has primitives conveying the locations of points in space. A heading representation is one that has primitives conveying the heading of objects in space. 2.2 Points and Objects A "point" refers to a spatial location for which the values of the primitive parameters in a locational representation are known. An "object" comprises multiple points that are organized into a coherent entity. 2.3 Axis of Orientation of an Object The axis of orientation of an object is a line between points on the object that defines a canonical direction in space. Not all objects have an axis of orientation; for example, an object that is radially symmetrical has none. The axis of orientation of a person within a space is aligned with the sagittal plane. One can differentiate between the axis of orientation of the head vs. the body, but for most of the present paper, that distinction is irrelevant. 2.4 Heading of an Object An object's heading in space is the angle between the object's axis of orientation and some reference direction external to the object (see Figure 1). The heading of a moving object can be differentiated from its course, or direction of travel as defined over the past few locations that were occupied. Because the reference direction is external to the object (a heading that was defined relative to its own axis of orientation would always be zero), heading will sometimes be referred to as allocentric heading. 2.5 Bearing Between Two Points Like heading, bearing is defined with respect to a reference direction. The bearing from point A to point B is the angle between the reference direction and a line from A to B. If the reference direction is aligned with the axis of orientation of an "ego" (i.e., an oriented organism in the space), the bearing from A to B will be called egooriented. If any other reference direction is used, the bearing from A to B will be called allocentric. The egocentric bearing of a point, B, is equivalent to a bearing from ego to B, using ego's axis of orientation as the reference direction. Thus the egocentric bearing is a special case of the ego-oriented bearing, in which ego's location is the source point. The egocentric bearing of B is numerically (but not conceptually) equivalent to the difference between B's allocentric bearing from ego and ego's allocentric heading, when both are defined with respect to a common reference direction. (See Figure 1.) Allocentric Reference Direction Ego-oriented AB bearing Allocentric AB bearing