Local Geometric Cues Research Articles

Use of medial axis for reorientation by the Clark’s nutcracker (Nucifraga columbiana)

Many animals are challenged with the task of reorientation. Considerable research over the years has shown a diversity of species extract geometric information (e.g., distance and direction) from continuous surfaces or boundaries to reorient. How this information is extracted from the environment is less understood. Three encoding strategies that have received the most study are the use of principal axes, medial axis or local geometric cues. We used a modeling approach to investigate which of these three general strategies best fit the spatial search data of a highly-spatial corvid, the Clark’s nutcracker (Nucifraga columbiana). Individual nutcrackers were trained in a rectangular-shaped arena, and once accurately locating a hidden goal, received non-reinforced tests in an L-shaped arena. The specific shape of this arena allowed us to dissociate among the three general encoding strategies. Furthermore, we reanalyzed existing data from chicks, pigeons and humans using our modeling approach. Overall, we found the most support for the use of the medial axis, although we additionally found that pigeons and humans may have engaged in random guessing. As with our previous studies, we find no support for the use of principal axes.

Environmental scaling influences the use of local but not global geometric cues during spatial reorientation.

During spatial reorientation, the use of local geometric cues (e.g., corner angles) and global geometric cues (e.g., principal axis) is differentially influenced by enclosure size. Local geometric cues exert more influence in large enclosures compared to small enclosures, whereas the use of global geometric cues is not influenced by changes in enclosure size. Such effects are suggested to occur because of differences in training enclosures sizes or differences in testing enclosure sizes, but investigations of enclosure-size effects on spatial cue use have been confounded by environmental scaling between training and testing. We trained participants in a trapezoid-shaped enclosure to respond to a corner uniquely specified by both local and global geometric cues and tested participants in a rectangle (isolating the use of global geometric cues) and in a parallelogram (placing local and global geometric cues in conflict). Between groups, participants experienced different training environment sizes but identical testing environment sizes or identical training environment sizes but different testing environment sizes, and this allowed categorization with respect to the direction of environmental scaling. We found that environmental scaling between training and testing size (but not training size differences or testing size differences) influenced the relative use of local geometric cues. The use of global geometric cues was not influenced by enclosure size. Results challenge prior explanations of the influence of enclosure size on relative spatial cue use during spatial reorientation. (PsycINFO Database Record

Thinking outside of the box: Transfer of shape-based reorientation across the boundary of an arena

The way in which human and non-human animals represent the shape of their environments remains a contentious issue. According to local theories of shape learning, organisms encode the local geometric features of the environment that signal a goal location. In contrast, global theories of shape learning suggest that organisms encode the overall shape of the environment. There is, however, a surprising lack of evidence to support this latter claim, despite the fact that common behaviours seem to require encoding of the global-shape of an environment. We tested one such behaviour in 5 experiments, in which human participants were trained to navigate to a hidden goal on one side of a virtual arena (e.g. the inside) before being required to find the same point on the alternative side (e.g. the outside). Participants navigated to the appropriate goal location, both when inside and outside the virtual arena, but only when the shape of the arena remained the same between training and test (Experiments 1a and 1b). When the arena shape was transformed between these stages, participants were lost (Experiments 2a and 2b). When training and testing was conducted on the outside of two different-shaped arenas that shared local geometric cues participants once again explored the appropriate goal location (Experiment 3). These results provide core evidence that humans encode a global representation of the overall shape of the environments in, or around, which they navigate.

Blocking spatial navigation across environments that have a different shape.

According to the geometric module hypothesis, organisms encode a global representation of the space in which they navigate, and this representation is not prone to interference from other cues. A number of studies, however, have shown that both human and non-human animals can navigate on the basis of local geometric cues provided by the shape of an environment. According to the model of spatial learning proposed by Miller and Shettleworth (2007, 2008), geometric cues compete for associative strength in the same manner as non-geometric cues do. The experiments reported here were designed to test if humans learn about local geometric cues in a manner consistent with the Miller-Shettleworth model. Experiment 1 replicated previous findings that humans transfer navigational behavior, based on local geometric cues, from a rectangle-shaped environment to a kite-shaped environment, and vice versa. In Experiments 2 and 3, it was observed that learning about non-geometric cues blocked, and were blocked by, learning about local geometric cues. The reciprocal blocking observed is consistent with associative theories of spatial learning; however, it is difficult to explain the observed effects with theories of global-shape encoding in their current form.

Microhabitat use affects goby (Gobiidae) cue choice in spatial learning task.

This study investigated whether spatial learning ability and cue use of gobies (Gobiidae) from two contrasting habitats differed in a spatial task. Gobies were collected from the spatially complex rock pools and dynamic, homogenous sandy shores. Fishes were trained to locate a shelter under the simulated threat of predation and it was determined whether they used local or extra-maze (global) and geometric cues to do so. It was hypothesized that fishes from rock pools would outperform fishes from sandy shores in their ability to relocate shelter and the two groups would differ in their cue use. It was found that rock-pool species learnt the location of the correct shelter much faster, made fewer errors and used a combination of all available cues to locate the shelter, while sand species relied significantly more on extra-maze and geometric cues for orientation. The results reported here support the hypothesis that fishes living in complex habitats have enhanced capacity for spatial learning and are more likely to rely on local landmarks as directional cues than fishes living in mundane habitats where local cues such as visual landmarks are unreliable.

Does constraining field of view prevent extraction of geometric cues for humans during virtual-environment reorientation?

Environment size has been shown to influence the reliance on local and global geometric cues during reorientation. Unless changes in environment size are produced by manipulating length and width proportionally, changes in environment size are confounded by the amount of the environment that is visible from a single vantage point. Yet, the influence of the amount of the environment that is visible from any single vantage point on the use of local and global geometric cues remains unknown. We manipulated the amount of an environment that was visually available to participants by manipulating field of view (FOV) in a virtual environment orientation task. Two groups of participants were trained in a trapezoid-shaped enclosure to find a location that was uniquely specified by both local and global geometric cues. One group (FOV 50°) had visually less of the environment available to them from any one perspective compared to another group (FOV 100°). Following training, we presented both groups with a control test along with three novel-shaped environments. Testing assessed the use of global geometry in isolation, in alignment with local geometry, or in conflict with local geometry. Results (confirmed by a follow-up experiment) indicated that constraining FOV prevented extraction of geometric properties and relationships of space and resulted in an inability to use either global or local geometric cues for reorientation.

Geometric cues, reference frames, and the equivalence of experienced-aligned and novel-aligned views in human spatial memory

Spatial memories are often organized around reference frames, and environmental shape provides a salient cue to reference frame selection. To date, however, the environmental cues responsible for influencing reference frame selection remain relatively unknown. To connect research on reference frame selection with that on orientation via environmental shape, we explored the extent to which geometric cues were incidentally encoded and represented in memory by evaluating their influence on reference frame selection. Using a virtual environment equipped with a head-mounted-display, we presented participants with to-be-remembered object arrays. We manipulated whether the experienced viewpoint was aligned or misaligned with global (i.e., the principal axis of space) or local (i.e., wall orientations) geometric cues. During subsequent judgments of relative direction (i.e., participants imagined standing at one object, facing a second object, and pointed toward a third object), we show that performance was best when imagining perspectives aligned with these geometric cues; moreover, global geometric cues were sufficient for reference frame selection, global and local geometric cues were capable of exerting differential influence on reference frame selection, and performance from experienced-imagined perspectives was equivalent to novel-imagined perspectives aligned with geometric cues. These results explicitly connect theory regarding spatial reference frame selection and spatial orientation via environmental shape and indicate that spatial memories are organized around fundamental geometric properties of space.

Beacons and surface features differentially influence human reliance on global and local geometric cues when reorienting in a virtual environment

In the reorientation literature, non-geometric cues include discrete objects (e.g., beacons) and surface-based features (e.g., colors, textures, and odors). To date, these types of non-geometric cues have been considered functionally similar, and it remains unknown whether beacons and surface features differentially influence the extent to which organisms reorient via global and local geometric cues. In the present experiment, we trained human participants to approach a location in a trapezoid-shaped enclosure uniquely specified by global and local geometric cues. We explored the role of beacons on the use of geometric cues by training participants in the presence or absence of uniquely-colored beacons. We explored the role of surface features on the use of geometric cues by recoloring two adjacent walls at the correct location and/or adding a line on the floor which corresponded to the major principal axis of the enclosure. All groups were then tested in novel-shaped enclosures in the absence of unique beacons and surface features to assess the relative use of global and local geometric cues. Results suggested that beacons facilitated the use of global geometric cues, whereas surface features either facilitated or hindered the use of geometric cues, depending on the feature.

Influence of global shapes on children's coding of local geometric information in small-scale spaces

This research uses enclosed whole shapes, rather than visual form fragments, to demonstrate that children's use of local geometric information is influenced by global shapes in small-scale spaces. Three- to six-year-old children and adults participated in two experiments with a table-top task. In Experiment 1, participants were presented with a box of isosceles trapezoid shape and a box of rectangular shape to examine whether different shapes affect children's use of metric lengths plus sense. In Experiment 2, children and adults were presented with angular corners of the same size in a box of isosceles triangle shape and a box of irregular shape to examine whether global shapes influence children's use of local geometric cues. The results indicate that, although children are able to use one type of local geometric information on one shape, their use of the same information on another shape may still be limited. Therefore, global shapes influence children's use of local geometric information. The results support the view that there may be two different levels of geometric representations: whole shapes and local geometric information.

Enclosure size and the use of local and global geometric cues for reorientation

Multiple spatial cues are utilized to orient with respect to the environment, but it remains unclear why feature (i.e., objects in the environment) and geometric (i.e., shape of the environment) cues are differentially influenced by enclosure size, and the extent to which local (i.e., wall lengths and corner angles) and global (i.e., principal axis of space) geometric cues are influenced by enclosure size. In the present study, we investigated the extent to which environmental size influenced the use of corner angle (i.e., a local geometric cue) and the principal axis of space (i.e., a global geometric cue) for reorientation. We developed an orientation task that allowed the manipulation of enclosure size during training and the isolation of the use of the principal axis of space during testing. Participants were trained to respond to a location in either a small or a large trapezoid-shaped enclosure uniquely specified by both local (i.e., wall lengths and corner angles) and global (i.e., principal axis of space) geometric cues. During testing, we presented both groups with a small and large rectangle (to assess the use of principal axis of space) and a small and large parallelogram (to asses relative use of corner angles and the principal axis of space when in conflict). Enclosure size influenced the relative use of corner angles but not of the principal axis of space. Results suggest that corner angles function like features and that changes in the use of feature cues are the source of the relative reliance on feature and geometric cues during changes of enclosure size.

Neither by global nor local cues alone: evidence for a unified orientation process

A substantial amount of empirical and theoretical debate remains concerning the extent to which an ability to orient with respect to the environment is determined by global (i.e., principal axis of space), local (i.e., wall lengths, angles), and/or view-based (i.e., stored representation) accounts. We developed an orientation task that allowed the manipulation of the reliability of the principal axis of space (i.e., searching at the egocentric left- and/or right-hand side of the principal axis) between groups while maintaining goal distance from the principal axis, local cues specifying the goal location (i.e., short wall left, short wall right, and obtuse angle), and visual aspects of the goal location consistent across groups. Control and test trials revealed that participants trained with a reliable principal axis of space utilized both global and local geometric cues, whereas those trained with an unreliable principal axis of space utilized only local geometric cues. Results suggest that both global and local geometric cues are utilized for reorientation and that the reliability of the principal axis of an enclosure differentially influences the use of geometric cues. Such results have implications for purely global-based, purely local-based, and purely view-based matching theoretical accounts of geometry learning and provide evidence for a unified orientation process.

Use of local and global geometry from object arrays by adult humans

Disoriented men and women were trained to search for a goal hidden in front of one of four objects forming a rectangular-shaped array. The angular properties of these objects (either 50° or 75°) served as local geometric cues and the rectangular shape of the array served as global geometric cues. Upon successful completion of training, transformation tests were conducted during which either the local angle cues were removed and the global geometry was preserved (Global Cues test) or the local angles were preserved and the global geometry was removed (Local Cues test). A Cue Conflict test was also conducted which placed the local geometry in direct competition with the global geometry for control of search behavior. Results from testing showed that neither men nor women could successfully use only the global geometric cues provided by the shape of the array to reorient. Analyses of sex differences for the use of local cues revealed that men showed clear evidence that they had successfully encoded the local angular cues whereas women did not. Furthermore, the size of the training angle may have affected the encoding of local cues.

Subcellular curvature at the perimeter of micropatterned cells influences lamellipodial distribution and cell polarity

This paper employs substrates that are patterned with shapes having well-defined geometric cues to characterize the influence of curvature on the polarization of highly metastatic B16F10 rat melanoma cells. Substrates were patterned using microcontact printing to define adhesive islands of defined shape and size on a background that otherwise prevents cell adhesion. Cells adherent to these surfaces responded to local curvature at the perimeter of the adhesive islands; convex features promoted the assembly of lamellipodia and concave features promoted the assembly of stress filaments. Cells adherent to rectangular shapes displayed a polarized cytoskeleton that increased with the aspect ratio of the shapes. Shapes that combined local geometric cues, by way of concave or convex edges, with aspect ratio were used to understand the additive effects of shape on polarization. The dependence of cell polarity on shape was determined in the presence of small molecules that alter actomyosin contractility and revealed a stronger dependence on contractility for shapes having straight edges, in contrast to those having curved edges. This study demonstrates that the cytoskeleton modulates cell polarity in response to multiple geometric cues in the extracellular environment.