Extrinsic Reference Frames Research Articles

Reference frames in language and cognition: cross-population mismatches

AbstractNumerous studies have found evidence of a speech community’s referential practices in discourse being predictive of its members’ behavior in nonverbal tasks. In this article, we discuss a series of exceptions to this alignment pattern, drawing on data from eleven populations of Asia, Europe, the Middle East, North and Central America, and Oceania. These exceptions have not been discussed in conjunction with one another and the striking commonalities across the findings of these studies have gone unnoticed: (a) in discourses referring to small-scale space, either intrinsic frame use is dominant or both relative and geocentric frames are used frequently in addition to intrinsic frames; and (b) in recall/recognition memory, geocentric coding is more common than egocentric coding (in tasks that involve stationary stimulus configurations) in nine of the populations, while in the remaining two, there is evidence of extensive intrinsic coding even in nonverbal cognition. We discuss these findings in light of Haun’s innate geocentrism hypothesis (Haun, D. B. M., C. Rapold, J. Call, G. Janzen & S. C. Levinson. 2006. Cognitive cladistics and cultural override in hominid spatial cognition.Proceedings of the National Academy of Sciences103(46). 17568–17573). Our data offers partial support for this hypothesis, but simultaneously calls into question whether any extrinsic reference frames are available innately.

Interlimb Generalization of Learned Bayesian Visuomotor Prior Occurs in Extrinsic Coordinates.

Recent work suggests that the brain represents probability distributions and performs Bayesian integration during sensorimotor learning. However, our understanding of the neural representation of this learning remains limited. To begin to address this, we performed two experiments. In the first experiment, we replicated the key behavioral findings of Körding and Wolpert (2004), demonstrating that humans can perform in a Bayes-optimal manner by combining information about their own sensory uncertainty and a statistical distribution of lateral shifts encountered in a visuomotor adaptation task. In the second experiment, we extended these findings by testing whether visuomotor learning occurring during the same task generalizes from one limb to the other, and relatedly, whether this learning is represented in an extrinsic or intrinsic reference frame. We found that the learned mean of the distribution of visuomotor shifts generalizes to the opposite limb only when the perturbation is congruent in extrinsic coordinates, indicating that the underlying representation of learning acquired during training is available to the untrained limb and is coded in an extrinsic reference frame.

The use of front–back arrays by young children to code locations

Research suggests that during the first 2years of life, children use an egocentric reference system and an extrinsic reference frame, the latter being one allocentric reference system, to encode locations. However, little is known about children’s use of an object’s intrinsic structure, another allocentric reference system. The current study focused on the role of the front–back relationship, one of the simplest intrinsic reference frames, in children’s location encoding. Children (3- to 5-year-olds) participated in a hide-and-find game with one of three different intrinsic front–back array conditions: a facet-induced front–back array, a motion-induced front–back array, or no array. The results showed that whereas the ability to use a facet-induced front–back array began by 3years of age, children used a motion-induced front–back array to encode locations at 4years of age. These results provide evidence that the developmental trajectories of using an intrinsic reference frame to encode locations vary and depend on the specific spatial array involved.

Generalization and transfer of contextual cues in motor learning.

We continuously adapt our movements in daily life, forming new internal models whenever necessary and updating existing ones. Recent work has suggested that this flexibility is enabled via sensorimotor cues, serving to access the correct internal model whenever necessary and keeping new models apart from previous ones. While research to date has mainly focused on identifying the nature of such cue representations, here we investigated whether and how these cue representations generalize, interfere, and transfer within and across effector systems. Subjects were trained to make two-stage reaching movements: a premovement that served as a cue, followed by a targeted movement that was perturbed by one of two opposite curl force fields. The direction of the premovement was uniquely coupled to the direction of the ensuing force field, enabling simultaneous learning of the two respective internal models. After training, generalization of the two premovement cues' representations was tested at untrained premovement directions, within both the trained and untrained hand. We show that the individual premovement representations generalize in a Gaussian-like pattern around the trained premovement direction. When the force fields are of unequal strengths, the cue-dependent generalization skews toward the strongest field. Furthermore, generalization patterns transfer to the nontrained hand, in an extrinsic reference frame. We conclude that contextual cues do not serve as discrete switches between multiple internal models. Instead, their generalization suggests a weighted contribution of the associated internal models based on the angular separation from the trained cues to the net motor output.

Motor adaptation and generalization of reaching movements using motor primitives based on spatial coordinates.

The brain processes sensory and motor information in a wide range of coordinate systems, ranging from retinal coordinates in vision to body-centered coordinates in areas that control musculature. Here we focus on the coordinate system used in the motor cortex to guide actions and examine physiological and psychophysical evidence for an allocentric reference frame based on spatial coordinates. When the equations of motion governing reaching dynamics are expressed as spatial vectors, each term is a vector cross product between a limb-segment position and a velocity or acceleration. We extend this computational framework to motor adaptation, in which the cross-product terms form adaptive bases for canceling imposed perturbations. Coefficients of the velocity- and acceleration-dependent cross products are assumed to undergo plastic changes to compensate the force-field or visuomotor perturbations. Consistent with experimental findings, each of the cross products had a distinct reference frame, which predicted how an acquired remapping generalized to untrained location in the workspace. In response to force field or visual rotation, mainly the coefficients of the velocity- or acceleration-dependent cross products adapted, leading to transfer in an intrinsic or extrinsic reference frame, respectively. The model further predicted that remapping of visuomotor rotation should under- or overgeneralize in a distal or proximal workspace. The cross-product bases can explain the distinct patterns of generalization in visuomotor and force-field adaptation in a unified way, showing that kinematic and dynamic motor adaptation need not arise through separate neural substrates.

Waves on a vortex filament: exact solutions of dynamical equations

In this paper, we take into account the dynamical equations of a vortex filament in superfluid helium at finite temperature (1 K < T < 2.17 K) and at very low temperature, which is called Biot–Savart law. The last equation is also valid for a vortex tube in a frictionless, unbounded, and incompressible fluid. Both the equations are approximated by the Local Induction Approximation (LIA) and Fukumoto’s approximation. The obtained equations are then considered in the extrinsic frame of reference, where exact solutions (Kelvin waves) are shown. These waves are then compared one to each other in terms of their dispersion relations in the frictionless case. The same equations are then investigated for a quantized vortex line in superfluid helium at higher temperature, where friction terms are needed for a full description of the motion.

Ipsilateral wrist–ankle movements in the sagittal plane encoded in extrinsic reference frame

When performing oscillatory movements of two joints in the sagittal plane, there is a directional constraint for performing such movements. Previous studies could not distinguish whether the directional constraint reflected movement direction encoded in the extrinsic (outside the body) reference frame or in the intrinsic (the participants’ torso/head) reference frame since participants performed coordinated movements in a sitting position where the torso/head was stationary relative to the external world. In order to discern the reference frame in the present study, participants performed paced oscillatory movements of the ipsilateral wrist and ankle in the sagittal plane in a standing position so that the torso/head moved relative to the external world. The coordinated movements were performed in one of two modes of coordination, moving the hand upward concomitant with either ankle plantarflexion or ankle dorsiflexion. The same directional mode relative to extrinsic space was more stable and accurate as compared with the opposite directional mode. When forearm position was changed from the pronated position to the supinated position, similar results were obtained, indicating that the results were independent of a particular coupling of muscles. These findings suggest that the directional constraint on ipsilateral joints movements in the sagittal plane reflects movement direction encoded in the extrinsic reference frame.

Extrinsic reference frames modify the neural substrates of object-location representations

The ability to form spatial representations of object locations is an important component of successful spatial navigation. Evidence from behavioral studies suggests that environmental features that have a salient coordinate axis (e.g., a rectangular building or a geometrical room) may provide a reference frame for the encoding of object-location information. Here we used functional magnetic resonance imaging (fMRI) to determine the brain networks engaged when object-location representations are stored with respect to an extrinsic reference frame. Participants learned the layout of an object array in an active, virtual-navigation paradigm. A square mat positioned on the floor of the virtual arena acted as the extrinsic reference frame. Knowledge of the spatial arrangement of the object array was probed while participants underwent fMRI, using a spatial judgment task that required them to imagine orientations of the learned array that were either aligned or misaligned with the geometry of the mat. Consistent with previous findings, participants responded faster and were more accurate when the imagined orientation was aligned, as opposed to misaligned, with the extrinsic reference frame. Analysis of the fMRI data revealed important differences in brain activity between the two conditions. Significantly greater activity was observed in the aligned condition compared with the misaligned condition across a bilateral network of brain areas that included the inferior occipital gyri, inferior and middle temporal gyri, and fusiform gyri. By contrast, activity in the misaligned condition was significantly greater than in the aligned condition in bilateral dorsolateral prefrontal and anterior cingulate cortex, and in the right anterior prefrontal and anterior insular cortex. These results suggest that retrieval of spatial locations that are aligned with an extrinsic reference frame involve direct access to detailed and accurate representations within the ventral visual pathway, whereas spatial locations that are misaligned with this reference frame are only weakly represented and require active inferential processes through the recruitment of prefrontal cortical networks. Our findings are consistent with a “reference direction” account of spatial memory, which posits that inter-object spatial relationships are primarily encoded with respect to specified reference directions.

Motor memory is encoded as a gain-field combination of intrinsic and extrinsic action representations.

Actions can be planned in either an intrinsic (body-based) reference frame or an extrinsic (world-based) frame, and understanding how the internal representations associated with these frames contribute to the learning of motor actions is a key issue in motor control. We studied the internal representation of this learning in human subjects by analyzing generalization patterns across an array of different movement directions and workspaces after training a visuomotor rotation in a single movement direction in one workspace. This provided a dense sampling of the generalization function across intrinsic and extrinsic reference frames, which allowed us to dissociate intrinsic and extrinsic representations and determine the manner in which they contributed to the motor memory for a trained action. A first experiment showed that the generalization pattern reflected a memory that was intermediate between intrinsic and extrinsic representations. A second experiment showed that this intermediate representation could not arise from separate intrinsic and extrinsic learning. Instead, we find that the representation of learning is based on a gain-field combination of local representations in intrinsic and extrinsic coordinates. This gain-field representation generalizes between actions by effectively computing similarity based on the (Mahalanobis) distance across intrinsic and extrinsic coordinates and is in line with neural recordings showing mixed intrinsic-extrinsic representations in motor and parietal cortices.

What is the hierarchical representation of tasks involving objects with complex internal dynamics?

Event Abstract Back to Event What is the hierarchical representation of tasks involving objects with complex internal dynamics? Anastasia Sylaidi1* and Aldo A. Faisal1, 2 1 Imperial College London, Dep. of Bioengineering, United Kingdom 2 Imperial College London, Dep. of Computing, United Kingdom Motor circuits, limb kinematics and many real-world tasks are organised hierarchically [1-2]. This prompts the question how the brain represents hierarchical task dependencies and how these are mapped onto the nervous system and control of movement. It was previously suggested that the CNS represents object manipulation tasks with regard to an intrinsic frame of reference centered on the body’s actuators and sensors and/or an extrinsic frame of reference related to task context, environmental settings or properties of point-like objects [3-5]. Ultimately, these two reference frames have to be linked to support the completion of high-level tasks [1], such as pouring wine into a glass. Here, we examine how joint- and body-based reference frames are organised as parts of a hierarchical structure of task representation that underlies motor learning. Towards this end we focus on the manipulation of objects with naturalistic internal dynamic. We test 3 possible hierarchical schemes of motor learning in object manipulation tasks: (a) In the first one task dynamics are principally learned and represented in intrinsic joint-based reference frames, on which the extrinsic reference frame of the object depends. This predicts, that humans generalise learned motor tasks over all joint space, but with regard to only one object orientation. (b) Conversely, in the second scheme, task dynamics are principally learned in an object-centered reference frame. This predicts generalisation across object orientations, but not across joint configurations. (c) In the third scheme both reference frames are learned independently. In order to test which of the three candidate mechanisms underlies motor control we conducted a behavioural study. Human subjects were asked to perform a rotational task within a given accuracy inside a 3D virtual reality setup, using a bottle of complex or static internal dynamics. In 2 different experiments subjects learned a single training task and were subsequently instructed to complete multiple testing tasks, in which object or joint positioning varied (experiment 1 and 2 respectively). Their performance was estimated in terms of pivot point displacement and used to examine how learning is transferred from training to testing conditions. Our results revealed a significant increase of pivot point displacement from training to testing phases in both experiments and for both object types. (Wilcoxon test, p<0.0125). This increase demonstrates a poor generalization capability of learned task dynamics to novel task contexts. This observation provides supporting evidence that task representations are independently learned for both the body-centered and object-centered coordinate frames and ad-hoc combined during motor actions. Our results lead to further investigations of the frames’ respective timescales, their potentially weighted contribution to motor learning, as well as the dependence of this weight on the nature of object dynamics.

Extrinsic reference frames modify the neural encoding of object locations during active spatial navigation

Extrinsic reference frames modify the neural encoding of object locations during active spatial navigation

Spatial mental representations derived from survey and route descriptions: When individuals prefer extrinsic frame of reference

The present research investigates the role of individual differences in preference for adopting extrinsic frame of reference (EFR) in ability to represent mentally spatial information learned through survey and route descriptions. A sample of 191 participants (100 females and 91 males) was categorized as four groups with high (H-EFR), medium-high (MH-EFR), medium-low (ML-EFR) and low (L-EFR) preference. The groups listened to two spatial descriptions in survey and route perspectives, subsequently performing true/false verification and map drawing tasks. They also performed a number of visuo-spatial, verbal and geographical pointing tasks. Results showed a general better performance of the H-EFR group and of males – in comparison with lower-ability counterparts and females respectively – in spatial text recall tasks and in other spatial measures. Moreover, spatial ability interacts with text perspective: in verification test the H-EFR group outperformed the lower groups in survey and route inferential sentences and in map drawing the superiority of H-EFR group was shown with survey (but not with route) text. Overall, the results suggest that individuals with high preference for extrinsic frame of reference are able to manage environment information in both spatial perspectives even if they prefer to express it in survey format. That preference is specifically sustained by spatial abilities.

Flexible Representations of Dynamics Are Used in Object Manipulation

SummaryTo manipulate an object skillfully, the brain must learn its dynamics, specifying the mapping between applied force and motion. A fundamental issue in sensorimotor control is whether such dynamics are represented in an extrinsic frame of reference tied to the object or an intrinsic frame of reference linked to the arm. Although previous studies have suggested that objects are represented in arm-centered coordinates [1–6], all of these studies have used objects with unusual and complex dynamics. Thus, it is not known how objects with natural dynamics are represented. Here we show that objects with simple (or familiar) dynamics and those with complex (or unfamiliar) dynamics are represented in object- and arm-centered coordinates, respectively. We also show that objects with simple dynamics are represented with an intermediate coordinate frame when vision of the object is removed. These results indicate that object dynamics can be flexibly represented in different coordinate frames by the brain. We suggest that with experience, the representation of the dynamics of a manipulated object may shift from a coordinate frame tied to the arm toward one that is linked to the object. The additional complexity required to represent dynamics in object-centered coordinates would be economical for familiar objects because such a representation allows object use regardless of the orientation of the object in hand.

Transfer of Motor Learning across Arm Configurations

It has been suggested that the learning of new dynamics occurs in intrinsic coordinates. However, it has also been suggested that elements that encode hand velocity, and hence act in an extrinsic frame of reference, play a role in the acquisition of dynamics. To reconcile claims regarding the coordinate system involved in the representation of dynamics, we have used a procedure involving the transfer of force-field learning between two workspace locations. Subjects made point-to-point movements while holding a two-link manipulandum. Subjects were first trained to make movements in a single direction at the left of the workspace. They were then tested for transfer of learning at the right of the workspace. Two groups of subjects were defined. For the subjects in group j, movements at the left and right workspace locations were matched in terms of joint displacements. For the subjects in group h, movements in the two locations had the same hand displacements. Workspace locations were chosen such that for group j, the paths (for training and testing) that were identical in joint space were orthogonal in hand space. The subjects in group j showed good transfer between workspace locations, whereas the subjects in group h showed poor transfer. These results are in agreement with the idea that new dynamics are encoded in intrinsic coordinates and that this learning has a limited range of generalization across joint velocities.

Pointing to Kinesthetic Targets in Space

An experiment investigated in human adults the sensorimotor transformation involved in pointing to a spatial target identified previously by kinesthetic cues. In the "locating phase," a computer-controlled mechanical arm guided the left [condition LR (left-right)] or right [condition RR (right-right)] finger of the blindfolded participant to one of 27 target positions. In the subsequent "pointing phase," the participant tried to reach the same position with the right finger. The final finger position and the posture of the arm were measured in both conditions. Constant errors were large but consistent and remarkably similar across conditions, suggesting that, whatever the locating hand, target position is coded in an extrinsic frame of reference (target position hypothesis). The main difference between the same-hand (RR) and different-hand (LR) conditions was a symmetric shift of the pattern of endpoints with respect to the midsagittal plane. This effect was modeled accurately by assuming a systematic bias in the perception of the postural angles of the locating arm. The analysis of the variable errors indicated that target position is represented internally in a spherical coordinate system centered on the shoulder of the pointing arm and that the main source of variability is within the planning stage of the pointing movement. Locating and pointing postures depended systematically on target position. We tested qualitatively the hypothesis that the selection of both postures (inverse kinematic problem) is constrained by a minimum-distance principle. In condition RR, pointing posture depended also on the locating posture, implying the presence of a memory trace of the previous movement. A scheme is suggested to accommodate the results within an extended version of the target position hypothesis.

Frames of reference and control parameters in visuomanual pointing.

Three hypotheses concerning the control variables in visuomanual pointing were tested. Participants pointed to a visual target presented briefly in total darkness on the horizontal plane. The starting position of the hand alternated randomly among 4 points arranged as a diamond. Results show that during the experiment, movement drifted from hypometric to hypermetric. Final positions depended on the starting position. Their average pattern reproduced the diamond of the starting points, either in same orientation (hypometric trials), or with a double inversion (hypermetric trials). The distribution of variable errors was elliptical, with the major axis aligned with the direction of the movement. Statistical analysis and Monte Carlo simulations showed that the results are incompatible with the final point control hypothesis (A. Polit & E. Bizzi, 1979). Better, but not fully satisfactory, agreement was found with the view that pointing involves comparing initial and desired postures (J. F. Soechting & M. Flanders, 1989a). The hypothesis that accounted best for the results is that final hand position is coded as a vector represented in an extrinsic frame of reference centered on the hand.

The Sequential Structure of Movement Outcome in Learning a Discrete Timing Task

The sequential structure of discrete movement outcomes in an elbow-flexion movement task was examined with a crossed design of 2 movement-time (125 and 500 ms) and 2 range-of-motion (5° and 20°) conditions over sets of 200 trials of practice. Traditional analyses of error score techniques, time-series analyses of the quantitative raw and differenced data, and a symbolic dynamic analysis of qualitative events arising from the data were conducted. The differenced data revealed a consistent order over 3-trial strings that was more apparent with larger steps in the data scores, but quantitative time-series and symbolic dynamic analyses of the raw movement-time data showed weaker relations. There were a few patterns of structure evident in the raw data time-series that were a function of the movement condition and the skill level of the subject. The analyses of the movement-time scores revealed that, in learning the discrete timing task, there is more order apparent in the intrinsic frame of reference of the difference scores than in the extrinsic frame of reference.

Errors in pointing are due to approximations in sensorimotor transformations.

1. We define an extrinsic frame of reference to represent the location of a point in extrapersonal space relative to a human subject's shoulder, and we define an intrinsic frame of reference to represent the orientation of the arm and forearm. 2. We examined the relations between coordinates in the extrinsic and intrinsic frames of reference under two experimental conditions: when subjects made inaccurate movements by pointing to virtual targets in the dark and when they made accurate movements by pointing to actual targets in the light. 3. When subjects made inaccurate movements, there was a close-to-linear relationship between the orientation angles of the arm (intrinsic coordinates) at its final position and the extrinsic coordinates of the target. When they made accurate movements, these relationships were more nonlinear. 4. Specifically, arm and forearm elevations depended principally on target distance and elevation, whereas the two yaw angles depended mainly on the target's azimuth. 5. We propose that errors in pointing occur because subjects implement a linear approximation to the transformation from extrinsic to intrinsic coordinates and that this transformation is one step in the process of transforming a visually derived representation of target location into an appropriate pattern of muscle activity.