Department of Engineering Science, University of Oxford. 2. Department of Zoology, University of Oxford. Abstract. The development of familiar route learning is ...
Pigeon route learning is maximally facilitated at intermediate visual landscape edge densities Richard Mann1 , Chris Armstrong2 , Jessica Meade2 , Matthew Collett2 , Helen Wilkinson2 , Tim Guilford2 and Stephen Roberts1 1. Department of Engineering Science, University of Oxford 2. Department of Zoology, University of Oxford Abstract The development of familiar route learning is investigated on the micro-scale, revealing a rate of memorisation dependent on the visual information density of the landscape, represented by the density of edges in the region around the bird’s position. Thus, route memorisation (as indicated by increased fidelity from one flight to the next) appears to proceed most rapidly over landscapes of intermediate edge density. This suggests that whilst edges, or whatever it is that they represent, are important for route learning, they can also inhibit route learning at the higher densities characteristic of urban environments.
Pigeons released repeatedly from the same site have been observed to form idiosyncratic memorised paths to the home loft [10] which they faithfully recapitulate if released a short distance from the original site [3], strongly suggesting the use of familiar visual cues. Informal analysis has suggested strong road-following behaviour indicating a preference for prominent linear features in approximately the homeward direction [4, 3, 6, 8]. A naive hypothesis might argue that the bird’s ability to determine its position and required direction should increase monotonically with the amount of visual information available, leading to faster learning of the memorised route and greater fidelity in recapitulation. Certainly, we have found that birds are both attracted to edge containing locations in the landscape, and change their flight behaviour significantly when approaching them [7]. However, experiments by Wiltschko et al [12] have indicated that pigeons may be unable to form a memorised route in a highly urban environment (suburban Frankfurt, Germany). Such environments provide a wealth of visual information as defined by algorithmic analysis of aerial images, such as image entropy or edge density. This poses the question of whether there is an optimal density of information which a pigeon can memorise or process. Our previous research has multiply confirmed the route-following phenomenon [10, 3]. In the light of the results of [12] we decided to investigate whether urban environments systematically inhibited route-learning. To test this we released naive birds from 2 sites around the Oxford field station (Horspath and Weston Wood) that included a variety of 1
urban and rural enviroments under the plausible flight corridors. Birds were released 20 times from each site and were tracked from the first flight. Global analysis of the route learning in this data is discussed in our companion paper [1]. We also used data collected by [10], where birds were again released from unfamiliar sites (Bladon Heath and Church Hanborough) and tracked from the first flight.
Horspath Weston Wood Bladon Heath Church Hanborough
(a) Aerial landscape image
(b) Edge-filtered landscape image
Figure 1: Aerial image of the landscape around the Oxford field station (a) and the result of applying the edge detection filter (b). The aerial image (a) shows one example path from each release site to demonstrate the locations of the releases and the loft. While the birds were consistently able to increase the fidelity of their flight paths over time they appeared to have significantly greater faithfulness to these routes in some regions than in others. We decided to test how the ability of a bird to return to potentially memorised locations varied on the local scale, relating this characteristic to an algorithmic measure of visual information density. We began with an aerial image covering most of the area around the Oxford lofts over which the experimental flight paths taversed (Figure 1 (a)). At time of writing we have not yet succeeded in obtaining a suitbale image covering the entire relevant area, which is represented in [1], so our analysis is necessarily confined to a spatial subset of the data. Next we used a Canny edge-detection filter [5] to find strong discontinuities in intensity, edges, which have been shown to constitute the fundamental aspect of animal vision and the most statistically independent components of natural images [9, 2]. This produced the edge map shown in Figure 1 (b). We determined the density of edges in a region by using a Gaussian averaging filter on the edge map, selecting the width of the filter to eliminate areas of zero intensity and mimic the plausible area of observation for the bird (noting that details picked up in an edge map may only be visible from a sufficient angle). The eventual choice was a filter of width 667 m (100 pixels) in the first standard deviation. This choice produced the edge density map in Figure 2 (a). Note the striking clarity with 2
which urban regions are related to the original landscape map.
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Figure 2: (a) Edge-density of the landscape using a Gaussian averaging filter. (b) The optimum edge-density contour segregates urban and forested areas from rural farmland A naive bird released for the first time from a new release site will typically make its way home in a relatively inefficient manner, but can be expected to return with a high degree of certainty if the release site is less than 25 km from the loft. It is noticeable that during this first flight birds are often observed to lock on to roads, rivers and other prominent features despite presumably having no memory of them. We hypothesise that during this first flight the bird will begin building visual memories for use on successive flights. On average, birds will be more likely to return closely to these memorised locations during the next flight than other locations on the original path. Therefore we use a metric of closest approach of the second flight to a point on the first to identify the likelihood that a visual memory has been formed for this location. Excluding areas within 667m of the loft to eliminate bias due to the inevitable constriction of paths at the start and finish, we recorded the edge density at each remaining point and the distance to the point of closest approach on the second path. In order to visualise the relationship between the two variables we collected the data into ‘bins’ of equal numbers of points, ordered by the edge density values. We then calculated for each the average edge-density and the average logarithm of the distance of closest approach (the distance of closest approach is a zero-bound value and is roughly exponentially distributed). We could not use the standard error of these averages directly as correlations within the bins would cause errors to be under-estimated by standard methods. Instead we applied a Bayesian model of the proposed relationship as a Gaussian process (GP) (see [11] for more information about GPs), which allowed us to directly infer the quantity of ’noise’ or error in our data and also determine both a best fit curve and 95% confidence intervals on that curve (Figure 3). We tested the model with different numbers of bins and found that 3
the results converged to a stable optimum with increasing bin number until numerical issues prevented going any further. The same optimum was found using a quadratic fit to all the data points individually. Best Fit 95% C.I.
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Figure 3: Dependence of distance of closest approach on edge density on locations beneath the first path The results indicate a gradual increase in the birds’ ability to return to familiar locations with increasing edge density in the low density regime. An optimum point is reached at 0.137 edges per pixel. Beyond this point there is a decline in the control exerted with increasing edge-density. This supports the idea that pigeons are unable to either memorise or process visual information that is too dense. We overlayed the edge density map on the landscape image, establishing a contour marking the areas within which edge-density was greater than this optimum. As Figure 2 (b) shows this contour almost perfectly outlines the urban areas in the landscape image, as well as including a number of areas of forest (this is easiest to see by comparison with Figure 2 (a)). This is supported by and provides confirmation of the findings of [12] that pigeons may be less able to memorise route information in urban environments. It is not obvious at this point whether this is because urban areas are just beyond this optimal point in terms of information density or whether the optimum is fixed 4
at this point because it coincides with the boundary of urban environments. The second hypothesis seems more parsimonious, but further experiments in dominantly rural or urban areas are needed to establish this. This research was conducted in accordance with UK animal welfare legislation and in accordance with the most recent edition of the ASAB’s ‘Guidelines for the treatment of animals in behavioural research and teaching’.
References [1] C. Armstrong, R. Mann, M. Collett, R. Freeman, S. Roberts, H. Wilkinson, and T. Guilford. Why do pigeons form habitual routes? Proceedings of the Royal Institute of Navigation, 2008. [2] A.J. Bell and T.J. Sejnowski. The ”independent components” of natural scenes are edge filters. Vision Research, 37(23):3327–3338, 1997. [3] D. Biro, J. Meade, and T. Guilford. Familiar route loyalty implies visual pilotage in the homing pigeon. Proceedings of the National Academy of Sciences of the U.S.A., 101(50):17440–17443, 2004. [4] Dora Biro. The Role of Visual Landmarks in the Homing Pigeon’s Familiar Area. PhD thesis, University of Oxford, 2002. [5] John F. Canny. A computational approach to edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence, 8:679–714, 1986. [6] T. Guilford, S. Roberts, D. Biro, and I. Rezek. Positional entropy during pigeon homing II: navigational interpretation of Bayesian latent state models. Journal of Theoretical Biology, 227(1):25–38, 2004. [7] K.K. Lau, S. Roberts, D. Biro, R. Freeman, J. Meade, and T. Guilford. An edgedetection approach to investigating pigeon navigation. Journal of Theoretical Biology, 239(1):71–78, 2006. [8] Hans-Peter Lipp, Alexei L. Vyssotski, David P. Wolfer, Sophie Renaudineau, Maria Savini, Gerhard Tr¨oster, and Giacomo Dell’Omo. Pigeon homing along highways and exits. Current Biology, 14:1239–1249, 2004. [9] David Marr. Vision: A computational investigation into the human representation and processing of visual information. Henry Holt and Co., 1982. [10] Jessica Meade, Dora Biro, and Tim Guilford. Homing pigeons develop local route stereotypy. Proceedings of the Royal Society B, 272:17–23, 2005. [11] Carl Edward Rasmussen and Christopher K. I. Williams. Gaussian Processes for Machine Learning. The M.I.T Press, 2006. 5
[12] R. Wiltschko, I. Schiffner, and B. Siegmund. Homing flights of pigeons over familiar terrain. Animal Behaviour, 74(5):1229–1240, 2007.
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