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An edge-detection approach to investigating pigeon navigation
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Journal of Theoretical Biology 239 (2006) 71–78 www.elsevier.com/locate/yjtbi
An edge-detection approach to investigating pigeon navigation Kam-Keung Laua,, Stephen Robertsa, Dora Birob, Robin Freemana, Jessica Meadeb, Tim Guilfordb a
Machine Learning Research Group, University of Oxford, UK Animal Behaviour Research Group, University of Oxford, UK
b
Received 10 May 2005; received in revised form 21 July 2005; accepted 25 July 2005 Available online 29 August 2005
Abstract This study brings together work in pattern recognition and animal behaviour. By applying algorithms in pattern recognition, we examined how visual landscape information influences pigeons’ homing behaviour. We used an automated procedure (Canny edge detector) to extract edges from an aerial image of the experimental terrain. Analysis of pigeons’ homing routes recorded using global positioning system (GPS) trackers showed that the chosen homing paths, as well as changes in the birds’ navigational states, tended to coincide with these edges. This study demonstrates that some edge-containing land features attract homing pigeons and trigger changes in their navigational states. r 2005 Elsevier Ltd. All rights reserved. Keywords: Navigation; Homing pigeon; Vision; Pattern recognition; Edge detection
1. Introduction The orientational abilities of homing pigeons (Columba livia) have long attracted the attention of researchers. Several decades of investigation have identified a number of mechanisms and information sources that pigeons utilize whilst orienting within unfamiliar as well as familiar areas (see Wallraff, 2001; Wiltschko and Wiltschko, 2003 for recent reviews). According to the ‘‘Map-and-Compass’’ model first proposed by Kramer (1953), a pigeon displaced to an unfamiliar site would first attempt to locate its position relative to the home loft based on locally available cues (the ‘‘map phase’’)—these cues are thought primarily to be olfactory (Papi, 1992; Wallraff, 2001, 2004), with the possible involvement of magnetic information still under debate (Walker, 1998; Wallraff, 1999; Haugh et al., 2001; Reilly, 2002). A bearing appropriate for the loft is Corresponding author. Department of Engineering Science, Parks Road, Oxford OX1 3PJ, UK. Tel.: +44 1865 273000; fax: +44 1865 273907. E-mail address: [email protected] (K.-K. Lau).
0022-5193/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2005.07.013
then calculated and assumed (the ‘‘compass phase’’) with the aid of a time-compensated sun-compass (Kramer, 1953, 1961) or a magnetic compass (Walcott and Green, 1974; Ioale, 1984; Wiltschko et al., 2001). Within familiar areas, visual cues are known to contribute to orientation (Braithwaite and Guilford, 1991; Burt et al., 1997; Biro et al., 2003). The finding that birds deprived of both olfactory and correct suncompass information are capable of assuming homeward oriented flight paths suggests that they are able to extract directional information from visual landscape cues alone (Gagliardo et al., 1999), and tracking of clock-shifted birds supports this view, because birds can show direct homeward routes at least under some conditions (Holland et al., 2000; Bonadonna et al., 2000). This represents an alternative to map-andcompass navigation in the sense that it operates independently of a compass, and is often referred to as ‘‘pilotage’’ (Baker, 1984). Until recently, experimental methods aimed at testing behavioural hypotheses have concentrated on manipulating pigeons’ normal perception of navigational information. Pigeons were either deprived of or misled
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about olfactory, magnetic, sun position, and/or even visual information according to the experimental designs (Wallraff, 2001; Wiltschko and Wiltschko, 2003). Studies have also focused on the influence of particular visual land features (e.g. Biro, 2002; Guilford et al., 2004; Kiepenheuer, 1993; Dornfeldt, 1982; Lipp et al., 2004, etc.). Nevertheless, conclusions in these studies were made based on observation of pigeons’ flight paths in relation to subjectively identified features, rather than based on objective measures. The success of these studies has been limited by the precision of available tracking methods. Vanishing bearings and homing speed provide only very limited information about the homing; radio-tracking and following by aircraft cannot provide accurate position data (Meade et al., 2005; Wiltschko and Wiltschko, 2003). On-board compass heading recorders, developed in the late eighties (e.g. Bramanti et al., 1988; Bonadonna et al., 1997; Holland et al., 2000), give more detailed track information, but are inherently error prone. More recently, the development of miniature global positioning system (GPS) tracking devices for pigeons (von Hunerbein et al., 2000; Steiner et al., 2000) has led to the provision of precise positional information (4 m accuracy) for the detailed investigation of the influence of visual terrain on pigeons’ choice of flight path (Guilford et al., 2004; Roberts et al., 2004; Biro et al., 2004; Meade et al., 2005; Lipp et al., 2004). In this paper, rather than focusing on individual landscape features, we apply pattern recognition methodologies to explore how pigeons make use of general visual landscape for navigation. We will look specifically at the influence of ‘‘edges’’ contained within an aerial view of the landscape on the birds’ behaviour. There are three reasons to consider edges as the examined variable in this study. First, image processing theories suggest that edges capture crucial information in an image, albeit in a relatively more abstract manner than the original image itself (Russell and Norvig, 2003). Second, edge detection is both practically possible and objective, making any experimental results produced here reliable. Edges defined by lines or curves on an image across which there are significant changes in brightness, have long been a topic of investigation in pattern recognition studies; here we attempt to investigate directly their influence on pigeon homing behaviour. Established algorithms have been developed to detect edges on images (Heath et al., 1998). Third, previous studies of route choice in pigeons navigating within their familiar area (and perhaps even beyond) have discussed circumstantial evidence that birds are attracted to linear features of the landscape (roads, rivers, railway lines, forest edges, field boundaries, hedgerows) and may utilize these as navigational aids (Biro, 2002; Guilford et al., 2004; Biro et al., 2004; Lipp et al., 2004). Such linear features are likely to have high edge content. If visual
cues do affect pigeons’ navigational strategies and edges capture sufficient information in the visual landscape, we would expect to see a significant relationship between the pigeons’ flight path and the edges on the image, although this relationship may vary among individuals’ tracks and across different navigational states within the tracks. In this study, we will first look at the edge intensity under the tracks compared to their adjacent regions. More importantly, we will examine the Bayesian latent state model applied to bird tracks as discussed in Roberts et al. (2004) and Guilford et al. (2004). The previous study described in these papers applied a measure of flight track complexity and broke down short-distance (1–4 km) homing of pigeons into three (or two in some cases) classes of discrete navigational states with a sophisticated time-series model (Hidden Markov Model). The degree of complexity at each track point was calculated based on the irregularity of the track segment containing this track point. With this modelling, a homing track in this study consisted of many time points (at a sample rate of one per second) and typically contained about 5–10 navigational state changes from one state class to another. It has been argued that these state changes represent changes in navigational strategy caused by pigeons’ observations of the terrain (refer to Roberts et al. (2004) for technical details and Guilford et al. (2004) for biological implications). Here, we will look at the quantitative difference in edge intensity between locations under those state-change points and locations under other parts of the pigeons’ tracks.
2. Methods 2.1. The data set The data consisted of homing tracks with positions in latitudes and longitudes recorded at 1 Hz using GPS trackers (24 g) between June and August 2003. A total of 96 tracks were recorded from 12 adult homing pigeons released singly from 8 different sites, located at distances ranging from 3.0 to 7.1 km around the loft. Prior to the recorded flights, each pigeon was accustomed to carrying a tracker attached to its back by Velcro (see Biro et al., 2002, 2004) and familiarized with each site through four unrecorded releases. The Universal Transverse Mercator formula was used to convert latitudes and longitudes to actual physical positions (Crossley, 1999). 2.2. Detecting edges on aerial images The edge image was produced by running a Canny edge detection on the aerial image covering the region of interest, provided by Getmappings plc. Canny edge
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detection was developed by John F. Canny in 1986 (Canny, 1986) and is currently considered as the best edge detection method for general purposes (Heath et al., 1998). The analysed image covering the area of interest was first scaled to a manageable size of 2000 2000 pixel2, with each pixel representing an area of 6.67 times 6.67 m2 on the land. To apply the edge detection, the original colour image of the landscape was first converted into a greyscale image; Canny edge detection with various thresholds was then applied to the image to produce the edge images. Canny edge detection involves successive smoothing of the greyscale image at a variety of scales, followed by application of a pair of twodimensional convolution masks (one vertical and one horizontal) over the image. This produces the vertical and horizontal gradients (change of intensity) of the grey level image. By combining the these two gradient maps an edge image is created. Full details of the Canny edge detection process may be found in standard texts on image processing, e.g. (Fisher et al., 1996). Figs. 1a and b show an example of Canny edge detection. 2.3. Analysis 1: edge attraction Edge content below the tracks was compared with that over areas adjacent to the tracks. The presence of edges below each track point over an area of 3 3 pixel2 was examined. For each track, a percentage of track points containing edges was computed. Fig. 2 shows an example, in which points on a track are classified as with or without associated edge content edges over areas of 3 3 pixel2. Tracks were then randomly shifted 30 times within a small range (a maximum distance of about 50 pixels). To prevent the result generated at the original position from being compared with itself, a minimum shifting of 6 pixels was also used. The percentage of a track at the original position was compared to the mean percentage of the same track at the 30 randomly shifted positions. We note that the conclusions inferred from these comparisons are not sensitive to the precise values of the above randomizing parameters.
Fig. 1. (a, b) An example of applying the Canny edge detection: the edges of the aerial image in (a) were detected as shown in (b).
2.4. Analysis 2: state-change regions The second analysis involved first replicating the previous work on Bayesian latent state modelling, and second a statistical comparison of edge intensity. To apply the state modelling, each track was first computed with the ‘‘embedding space decomposition’’ method to produce a value of entropy (measuring stochastic complexity) for each position on the track. These values were then entered into a hidden Markov model (variational learning optimization algorithm) for classification into different entropy states which may relate to different underlying navigational states or strategies The
Fig. 2. An example showing points on a track being classified as with or without edges over areas of 3 3 pixel2.
details of this entropy-state-classification method, and its interpretation can be found in (Roberts et al., 2004; Guilford et al., 2004).
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Three putative classes of navigational states were identified in the computation: high, middle and low entropic states, and so there are four categories of state changes: from low to middle entropy, from middle to high entropy, from high to middle entropy and from middle to low entropy. We have hence separated our edge analysis allowing for different categories of state changes. With the state-change points generated for each track in the computation, the difference in edge intensity between these state-change points and their adjacent track points was analysed. Then similar calculations were done for points, which were one time-step, two time-step, three time-step, etc. before and after the statechange points. This built up a distribution of percentage before and after the state changes which was then examined statistically.
3. Results 3.1. Analysis 1: edge attraction
Percentage of positions containing edges
Clear results were shown in all of our analyses. The first analysis examined the difference in edge intensity under the flight paths compared to the adjacent areas. Fig. 3 shows the percentages of track points with edges underneath (an area of 3 3 pixel2). The edge intensity of the tracks at the original positions was larger than that in the randomized positions for all 8 release sites studied. A statistical comparison with two-way repeated-measures ANOVA was used (Howell, 2001). The first factor was a between-group factor with 2 levels: original position and randomized positions. The second factor, a repeated-measures factor, was site, with the site
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Fig. 3. The percentage of positions containing edges for the pigeon tracks at the original positions and at randomized positions The error bars show the ranges of 71 standard deviation from the means.
reference numbers as the factor levels. It was found that the edge content under pigeons’ flight tracks was significantly higher than that of the random adjacent areas (F ð1; 22Þ ¼ 3014, po:0005), showing that there was a general tendency for pigeons to fly over regions with higher-than-average edge density. 3.2. Analysis 2: state-change regions The dotted irregular curves in Figs. 4a–d show the edge intensity across regions along the relative positions of the state-change points. The x-axis represents the position on the track in relation to the state change and is in seconds. Negative numbers are prior to the state change. To reduce the effect of any random fluctuation at each individual time-step, temporal smoothing was applied to the dotted irregular curves in Fig. 4a–d. This was done by taking moving averages of each 21 consecutive positions sequentially along the dimension of the relative position to the state-change point. The choice of a 21-point filter is arbitrary; we note that the conclusions inferred from the data are not sensitive to its precise value. The smooth curves in Figs. 4a–d show the smoothed distribution of the dotted irregular curves. Fig. 4a shows the edge intensity over the range of positions containing the state-changes from low to middle entropy. It can be seen that the edge intensity increases initially (from left to right) and remains at the maximum level at about 10–30 points subsequent to the state-change before declining. For state changes from middle to high entropy, Fig. 4b shows the edge intensity increasing steadily before the state changes. It reaches its maximum at just about 5 points subsequent to the statechange points before undergoing a steady decline. For the state-change from high to middle entropy (Fig. 4c), the edge intensity shows a small variation. For the statechange from middle to low entropy (Fig. 4d), the edge intensity seems to increase gently. To examine statistical significance of the change along the dimension of relative positions to the state-change points, these positions were divided into four regions of equal length, positions between 30 and 10, positions between 10 and 10 (state-change region), positions between 10 and 30, as well as positions between 30 and 50. The use of four regions is arbitrary; using three or five regions should give very similar conclusions. An independent samples t-test (Howell, 2001) was used to compare the difference between each two adjacent regions above. For the curve in Fig. 4a (change from low to middle entropy), the increase prior to the statechange region was highly significant. The increase subsequent to the state-change region, as well as the decrease thereafter, was also highly significant. For the curve in Fig. 4b (change from middle to high entropy), the increase prior to the stage-change region was highly significant. The subsequent decreases were
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Fig. 4. (a–d) The dotted irregular curves show the percentage of positions containing edges at each time step over the region of the adjacent positions to the state-change point. The smooth curves show the means of the percentage of positions containing edge across each 21 points. (a–d) show that information for state-changes from low to middle entropy, from middle to high entropy, from high to middle and from middle to low entropy, respectively: (a) low–middle, (b) middle–high, (c) high–middle, (d) middle–low.
both significant. For the curve in Fig. 4c (change from high to middle entropy), the increase prior to the stagechange region was significant. The subsequent changes were not significant. For the curve in Fig. 4d (change from middle to low entropy), the regions prior to and post the stage-change were not significantly different, whilst the increase from the 10–30 region to the 30–50 region was highly significant. The statistical results are summarized in Table 1.
4. Discussion 4.1. Attraction toward edges This study explores an aspect of pigeon navigation by specifically looking at the influence of ‘‘edges’’ contained in an aerial image of the landscape. We found that edges were related to homing paths and to changes in their
states of positional uncertainty. Pigeons were found to fly directly over edge-containing regions in the landscape more commonly than expected by chance. This implies either that pigeons were attracted to edge-containing features of the underlying landscape, or, perhaps, that they followed edge containing features once they happened to arrive at them. This is consistent with less formal findings that pigeons in the visually familiar area (Biro, 2002; Guilford et al., 2004), and possibly even unfamiliar areas (Lipp et al., 2004), appear to orient along linear landscape features such as roads, railways, rivers, and hedgerows even though these do not topographically constrain flight (as coastlines or mountain ranges do). Similarly, complex land features such as settlements and junctions have been thought to attract pigeons (Biro, 2002; Guilford et al., 2004; Kiepenheuer, 1993; Dornfeldt, 1982), and these too might be expected to have unusually high edge intensity.
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Table 1 The statistical results of the comparisons between regions along the dimension of relative positions to the state-change points
State-change from low to middle entropy State-change from middle to high entropy State-change from high to middle entropy State-change from middle to low entropy
Change prior to the statechange region
Change subsequent to the state-change region
Onward change
Increase: tð24:4Þ ¼ 6:92, po:0005 Increase: tð40Þ ¼ 13:00, po:0005 Increase: tð32:9Þ ¼ 2:45, po:05 No significant change: p ¼ :39
Increase: tð25:3Þ ¼ 4:02, po:0005 Decrease: tð40Þ ¼ 5:87, po:0005 No significant change: p ¼ :085 No significant change: p ¼ :095
Decrease: tð30:6Þ ¼ 3:87, po:005 Decrease: tð40Þ ¼ 6:82, po:0005 No significant change: p ¼ :72 Increase: tð40Þ ¼ 3:98, po:0005
4.2. Visual information and state changes The second analysis showed that there was a relationship between the positions of state changes and edge intensity. Pigeons generally change their navigational states over locations with higher information density. Detailed inspection of the tracks overlaid on the aerial image suggested that on many occasions the state changes were obtained over boundaries between different types of terrain, such as boundaries of woods, footpaths or roads, although there are counter-examples. One possibility is that the edge-containing features simply cause a change in orientation, and this produces a temporary increase in entropy. Alternatively, it is also possible that these edge-containing features attract the birds’ attention, causing them to fly irregularly along these details thus producing high entropic flight patterns. The edge intensity of land features changes highly significantly along the track segments adjacent to the state-change points associated with increases in track entropy (and potentially, hence, navigational uncertainty) in particular. We found sharper patterns of edge intensity changes across the range of track positions containing state-changes from low to middle entropy and from middle to high entropy than those of the other two categories of state changes. The maximum edge intensity of the latter occurred at only some 5 s after the state-change point with a higher peak, while the maximum of the former occurred some 20 s after the state-change point with a lower peak. The reason for changes of edge intensity across the ranges of track positions containing the state-changes from high to middle entropy and from middle to low entropy is unclear. It is possible that the difference in the timing of the edge intensity peak in relation to the state-change position is itself indicative of the distance at which the pigeons were responding to the visual land features. That is, the highest entropy state is triggered when birds are attending to features closely underneath them,
whereas the middle entropy state is entered as the pigeons attend to features still some distance in front of them. This interpretation may also accommodate the less clear cut finding that downward state changes have a more diffuse relationship to edge-containing features, suggesting that this finding may signal attention to features at longer and more variable distances from the birds. 4.3. Possible navigational mechanisms As with any field-based experiment which relies for its inferences solely on interpreting animals’ movement patterns, we cannot be sure that our pigeons’ tracks are the result of navigational decisions alone. Pigeons may react to landscape features for non-navigational reasons (e.g. Kiepenheuer, 1993; Dornfeldt, 1982): edge-containing features might signal potential food sources, resting places, conspecific company, safety from predators, thermal up-draught sources or triggers, or, simply, novel places for birds to explore. Nevertheless, our experience tells us that homing pigeons tend to remain in their loft almost all the time, unless encouraged out, and home immediately after displacement. Our birds rarely stop en route home (only once out of 96 releases in this current experiment), except very close to the loft, and take more direct routes with increasing familiarity (i.e. they do not show evidence of exploratory behaviour once familiar with a route), eventually forming stereotypical individual routes to which they remain faithful and which they follow with little delay after release (Biro et al., 2004; Meade et al., 2005). Pigeons predominantly use fast, powered flight, making little use of soaring, so it is unlikely that aerodynamic effects are the cause of attraction to edges. Taken together the above evidences suggests that pigeons are highly motivated to home, and that their patterns of movement are dominated by navigational decisions to this end. As the elevation achieved by the pigeons is never more than 100 m or so, it is not very likely that they have clear line of sight view
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to the home loft from ranges of several kilometres. This adds some extra credence to the hypothesis that, even in a familiar area, the pigeons must, to some extent, utilize navigational information from the landscape. We believe it is reasonable to infer that the reactions to edge-containing features found in this study indicate the use by pigeons of the navigationally relevant visual information contained within those features. 4.4. The way ahead Our findings have demonstrated that the Bayesian entropy state model of Roberts et al. (2004), which has not previously been supported by landscape evidence, does relate to behavioural characteristics of homing pigeons. We identified a systematic relationship between the classification of flight-entropy states by the model and the land features under the pigeons’ flight tracks. It is important to note that the landscape edge information was estimated independently of the computation applied to the flight tracks by the Bayesian model, and hence the existence of a relationship between the two offers some credence to our analysis and interpretations. Traditional methods using experimental manipulations and comparisons of different treatment conditions have long been applied in the investigation of homing pigeon navigation. Nevertheless, given the complexity of landscape information, extracting salient variations and correlations within the data appears too complex for traditional methods. Since it is practically impossible to manipulate the land features themselves (unlike other cues that are more easy to vary experimentally), conclusions have to be drawn from observational data. Little about these variations and correlations has been concluded objectively. This study has shown the utility of a novel approach to such a biological problem. With the help of aerial photography, GPS technology and edge detection algorithms, accurate positional data could be collected and land features could be quantified in this study, providing the basis for a bottom-up, datadriven approach as a more objective method for testing behavioural hypotheses. Rather than being restricted to particular features or configurations on the land, this study has successfully related navigational behaviour with features on the ground in a general manner. Although we have focused on edges, further studies will concentrate on modelling the aerial image of the terrain in various ways. For example, features on the ground can be segmented based on their colour composition, feature sizes and orientations. Experimental manipulations, such as repeated releases of the same birds, can be used with computationally feasible hypothesis testing. A limitation of this study was that we could not manipulate the terrain and that all our subjects belonged to the same loft. Therefore, our findings might, to some extent, reflect some
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uniqueness in the composition and structures of the terrain around our loft. It would be informative to apply the current analysis to datasets obtained from different terrains.
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Journal of Theoretical Biology 239 (2006) 71–78 www.elsevier.com/locate/yjtbi
An edge-detection approach to investigating pigeon navigation Kam-Keung Laua,, Stephen Robertsa, Dora Birob, Robin Freemana, Jessica Meadeb, Tim Guilfordb a
Machine Learning Research Group, University of Oxford, UK Animal Behaviour Research Group, University of Oxford, UK
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Received 10 May 2005; received in revised form 21 July 2005; accepted 25 July 2005 Available online 29 August 2005
Abstract This study brings together work in pattern recognition and animal behaviour. By applying algorithms in pattern recognition, we examined how visual landscape information influences pigeons’ homing behaviour. We used an automated procedure (Canny edge detector) to extract edges from an aerial image of the experimental terrain. Analysis of pigeons’ homing routes recorded using global positioning system (GPS) trackers showed that the chosen homing paths, as well as changes in the birds’ navigational states, tended to coincide with these edges. This study demonstrates that some edge-containing land features attract homing pigeons and trigger changes in their navigational states. r 2005 Elsevier Ltd. All rights reserved. Keywords: Navigation; Homing pigeon; Vision; Pattern recognition; Edge detection
1. Introduction The orientational abilities of homing pigeons (Columba livia) have long attracted the attention of researchers. Several decades of investigation have identified a number of mechanisms and information sources that pigeons utilize whilst orienting within unfamiliar as well as familiar areas (see Wallraff, 2001; Wiltschko and Wiltschko, 2003 for recent reviews). According to the ‘‘Map-and-Compass’’ model first proposed by Kramer (1953), a pigeon displaced to an unfamiliar site would first attempt to locate its position relative to the home loft based on locally available cues (the ‘‘map phase’’)—these cues are thought primarily to be olfactory (Papi, 1992; Wallraff, 2001, 2004), with the possible involvement of magnetic information still under debate (Walker, 1998; Wallraff, 1999; Haugh et al., 2001; Reilly, 2002). A bearing appropriate for the loft is Corresponding author. Department of Engineering Science, Parks Road, Oxford OX1 3PJ, UK. Tel.: +44 1865 273000; fax: +44 1865 273907. E-mail address: [email protected] (K.-K. Lau).
0022-5193/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2005.07.013
then calculated and assumed (the ‘‘compass phase’’) with the aid of a time-compensated sun-compass (Kramer, 1953, 1961) or a magnetic compass (Walcott and Green, 1974; Ioale, 1984; Wiltschko et al., 2001). Within familiar areas, visual cues are known to contribute to orientation (Braithwaite and Guilford, 1991; Burt et al., 1997; Biro et al., 2003). The finding that birds deprived of both olfactory and correct suncompass information are capable of assuming homeward oriented flight paths suggests that they are able to extract directional information from visual landscape cues alone (Gagliardo et al., 1999), and tracking of clock-shifted birds supports this view, because birds can show direct homeward routes at least under some conditions (Holland et al., 2000; Bonadonna et al., 2000). This represents an alternative to map-andcompass navigation in the sense that it operates independently of a compass, and is often referred to as ‘‘pilotage’’ (Baker, 1984). Until recently, experimental methods aimed at testing behavioural hypotheses have concentrated on manipulating pigeons’ normal perception of navigational information. Pigeons were either deprived of or misled
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about olfactory, magnetic, sun position, and/or even visual information according to the experimental designs (Wallraff, 2001; Wiltschko and Wiltschko, 2003). Studies have also focused on the influence of particular visual land features (e.g. Biro, 2002; Guilford et al., 2004; Kiepenheuer, 1993; Dornfeldt, 1982; Lipp et al., 2004, etc.). Nevertheless, conclusions in these studies were made based on observation of pigeons’ flight paths in relation to subjectively identified features, rather than based on objective measures. The success of these studies has been limited by the precision of available tracking methods. Vanishing bearings and homing speed provide only very limited information about the homing; radio-tracking and following by aircraft cannot provide accurate position data (Meade et al., 2005; Wiltschko and Wiltschko, 2003). On-board compass heading recorders, developed in the late eighties (e.g. Bramanti et al., 1988; Bonadonna et al., 1997; Holland et al., 2000), give more detailed track information, but are inherently error prone. More recently, the development of miniature global positioning system (GPS) tracking devices for pigeons (von Hunerbein et al., 2000; Steiner et al., 2000) has led to the provision of precise positional information (4 m accuracy) for the detailed investigation of the influence of visual terrain on pigeons’ choice of flight path (Guilford et al., 2004; Roberts et al., 2004; Biro et al., 2004; Meade et al., 2005; Lipp et al., 2004). In this paper, rather than focusing on individual landscape features, we apply pattern recognition methodologies to explore how pigeons make use of general visual landscape for navigation. We will look specifically at the influence of ‘‘edges’’ contained within an aerial view of the landscape on the birds’ behaviour. There are three reasons to consider edges as the examined variable in this study. First, image processing theories suggest that edges capture crucial information in an image, albeit in a relatively more abstract manner than the original image itself (Russell and Norvig, 2003). Second, edge detection is both practically possible and objective, making any experimental results produced here reliable. Edges defined by lines or curves on an image across which there are significant changes in brightness, have long been a topic of investigation in pattern recognition studies; here we attempt to investigate directly their influence on pigeon homing behaviour. Established algorithms have been developed to detect edges on images (Heath et al., 1998). Third, previous studies of route choice in pigeons navigating within their familiar area (and perhaps even beyond) have discussed circumstantial evidence that birds are attracted to linear features of the landscape (roads, rivers, railway lines, forest edges, field boundaries, hedgerows) and may utilize these as navigational aids (Biro, 2002; Guilford et al., 2004; Biro et al., 2004; Lipp et al., 2004). Such linear features are likely to have high edge content. If visual
cues do affect pigeons’ navigational strategies and edges capture sufficient information in the visual landscape, we would expect to see a significant relationship between the pigeons’ flight path and the edges on the image, although this relationship may vary among individuals’ tracks and across different navigational states within the tracks. In this study, we will first look at the edge intensity under the tracks compared to their adjacent regions. More importantly, we will examine the Bayesian latent state model applied to bird tracks as discussed in Roberts et al. (2004) and Guilford et al. (2004). The previous study described in these papers applied a measure of flight track complexity and broke down short-distance (1–4 km) homing of pigeons into three (or two in some cases) classes of discrete navigational states with a sophisticated time-series model (Hidden Markov Model). The degree of complexity at each track point was calculated based on the irregularity of the track segment containing this track point. With this modelling, a homing track in this study consisted of many time points (at a sample rate of one per second) and typically contained about 5–10 navigational state changes from one state class to another. It has been argued that these state changes represent changes in navigational strategy caused by pigeons’ observations of the terrain (refer to Roberts et al. (2004) for technical details and Guilford et al. (2004) for biological implications). Here, we will look at the quantitative difference in edge intensity between locations under those state-change points and locations under other parts of the pigeons’ tracks.
2. Methods 2.1. The data set The data consisted of homing tracks with positions in latitudes and longitudes recorded at 1 Hz using GPS trackers (24 g) between June and August 2003. A total of 96 tracks were recorded from 12 adult homing pigeons released singly from 8 different sites, located at distances ranging from 3.0 to 7.1 km around the loft. Prior to the recorded flights, each pigeon was accustomed to carrying a tracker attached to its back by Velcro (see Biro et al., 2002, 2004) and familiarized with each site through four unrecorded releases. The Universal Transverse Mercator formula was used to convert latitudes and longitudes to actual physical positions (Crossley, 1999). 2.2. Detecting edges on aerial images The edge image was produced by running a Canny edge detection on the aerial image covering the region of interest, provided by Getmappings plc. Canny edge
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detection was developed by John F. Canny in 1986 (Canny, 1986) and is currently considered as the best edge detection method for general purposes (Heath et al., 1998). The analysed image covering the area of interest was first scaled to a manageable size of 2000 2000 pixel2, with each pixel representing an area of 6.67 times 6.67 m2 on the land. To apply the edge detection, the original colour image of the landscape was first converted into a greyscale image; Canny edge detection with various thresholds was then applied to the image to produce the edge images. Canny edge detection involves successive smoothing of the greyscale image at a variety of scales, followed by application of a pair of twodimensional convolution masks (one vertical and one horizontal) over the image. This produces the vertical and horizontal gradients (change of intensity) of the grey level image. By combining the these two gradient maps an edge image is created. Full details of the Canny edge detection process may be found in standard texts on image processing, e.g. (Fisher et al., 1996). Figs. 1a and b show an example of Canny edge detection. 2.3. Analysis 1: edge attraction Edge content below the tracks was compared with that over areas adjacent to the tracks. The presence of edges below each track point over an area of 3 3 pixel2 was examined. For each track, a percentage of track points containing edges was computed. Fig. 2 shows an example, in which points on a track are classified as with or without associated edge content edges over areas of 3 3 pixel2. Tracks were then randomly shifted 30 times within a small range (a maximum distance of about 50 pixels). To prevent the result generated at the original position from being compared with itself, a minimum shifting of 6 pixels was also used. The percentage of a track at the original position was compared to the mean percentage of the same track at the 30 randomly shifted positions. We note that the conclusions inferred from these comparisons are not sensitive to the precise values of the above randomizing parameters.
Fig. 1. (a, b) An example of applying the Canny edge detection: the edges of the aerial image in (a) were detected as shown in (b).
2.4. Analysis 2: state-change regions The second analysis involved first replicating the previous work on Bayesian latent state modelling, and second a statistical comparison of edge intensity. To apply the state modelling, each track was first computed with the ‘‘embedding space decomposition’’ method to produce a value of entropy (measuring stochastic complexity) for each position on the track. These values were then entered into a hidden Markov model (variational learning optimization algorithm) for classification into different entropy states which may relate to different underlying navigational states or strategies The
Fig. 2. An example showing points on a track being classified as with or without edges over areas of 3 3 pixel2.
details of this entropy-state-classification method, and its interpretation can be found in (Roberts et al., 2004; Guilford et al., 2004).
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Three putative classes of navigational states were identified in the computation: high, middle and low entropic states, and so there are four categories of state changes: from low to middle entropy, from middle to high entropy, from high to middle entropy and from middle to low entropy. We have hence separated our edge analysis allowing for different categories of state changes. With the state-change points generated for each track in the computation, the difference in edge intensity between these state-change points and their adjacent track points was analysed. Then similar calculations were done for points, which were one time-step, two time-step, three time-step, etc. before and after the statechange points. This built up a distribution of percentage before and after the state changes which was then examined statistically.
3. Results 3.1. Analysis 1: edge attraction
Percentage of positions containing edges
Clear results were shown in all of our analyses. The first analysis examined the difference in edge intensity under the flight paths compared to the adjacent areas. Fig. 3 shows the percentages of track points with edges underneath (an area of 3 3 pixel2). The edge intensity of the tracks at the original positions was larger than that in the randomized positions for all 8 release sites studied. A statistical comparison with two-way repeated-measures ANOVA was used (Howell, 2001). The first factor was a between-group factor with 2 levels: original position and randomized positions. The second factor, a repeated-measures factor, was site, with the site
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Fig. 3. The percentage of positions containing edges for the pigeon tracks at the original positions and at randomized positions The error bars show the ranges of 71 standard deviation from the means.
reference numbers as the factor levels. It was found that the edge content under pigeons’ flight tracks was significantly higher than that of the random adjacent areas (F ð1; 22Þ ¼ 3014, po:0005), showing that there was a general tendency for pigeons to fly over regions with higher-than-average edge density. 3.2. Analysis 2: state-change regions The dotted irregular curves in Figs. 4a–d show the edge intensity across regions along the relative positions of the state-change points. The x-axis represents the position on the track in relation to the state change and is in seconds. Negative numbers are prior to the state change. To reduce the effect of any random fluctuation at each individual time-step, temporal smoothing was applied to the dotted irregular curves in Fig. 4a–d. This was done by taking moving averages of each 21 consecutive positions sequentially along the dimension of the relative position to the state-change point. The choice of a 21-point filter is arbitrary; we note that the conclusions inferred from the data are not sensitive to its precise value. The smooth curves in Figs. 4a–d show the smoothed distribution of the dotted irregular curves. Fig. 4a shows the edge intensity over the range of positions containing the state-changes from low to middle entropy. It can be seen that the edge intensity increases initially (from left to right) and remains at the maximum level at about 10–30 points subsequent to the state-change before declining. For state changes from middle to high entropy, Fig. 4b shows the edge intensity increasing steadily before the state changes. It reaches its maximum at just about 5 points subsequent to the statechange points before undergoing a steady decline. For the state-change from high to middle entropy (Fig. 4c), the edge intensity shows a small variation. For the statechange from middle to low entropy (Fig. 4d), the edge intensity seems to increase gently. To examine statistical significance of the change along the dimension of relative positions to the state-change points, these positions were divided into four regions of equal length, positions between 30 and 10, positions between 10 and 10 (state-change region), positions between 10 and 30, as well as positions between 30 and 50. The use of four regions is arbitrary; using three or five regions should give very similar conclusions. An independent samples t-test (Howell, 2001) was used to compare the difference between each two adjacent regions above. For the curve in Fig. 4a (change from low to middle entropy), the increase prior to the statechange region was highly significant. The increase subsequent to the state-change region, as well as the decrease thereafter, was also highly significant. For the curve in Fig. 4b (change from middle to high entropy), the increase prior to the stage-change region was highly significant. The subsequent decreases were
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Fig. 4. (a–d) The dotted irregular curves show the percentage of positions containing edges at each time step over the region of the adjacent positions to the state-change point. The smooth curves show the means of the percentage of positions containing edge across each 21 points. (a–d) show that information for state-changes from low to middle entropy, from middle to high entropy, from high to middle and from middle to low entropy, respectively: (a) low–middle, (b) middle–high, (c) high–middle, (d) middle–low.
both significant. For the curve in Fig. 4c (change from high to middle entropy), the increase prior to the stagechange region was significant. The subsequent changes were not significant. For the curve in Fig. 4d (change from middle to low entropy), the regions prior to and post the stage-change were not significantly different, whilst the increase from the 10–30 region to the 30–50 region was highly significant. The statistical results are summarized in Table 1.
4. Discussion 4.1. Attraction toward edges This study explores an aspect of pigeon navigation by specifically looking at the influence of ‘‘edges’’ contained in an aerial image of the landscape. We found that edges were related to homing paths and to changes in their
states of positional uncertainty. Pigeons were found to fly directly over edge-containing regions in the landscape more commonly than expected by chance. This implies either that pigeons were attracted to edge-containing features of the underlying landscape, or, perhaps, that they followed edge containing features once they happened to arrive at them. This is consistent with less formal findings that pigeons in the visually familiar area (Biro, 2002; Guilford et al., 2004), and possibly even unfamiliar areas (Lipp et al., 2004), appear to orient along linear landscape features such as roads, railways, rivers, and hedgerows even though these do not topographically constrain flight (as coastlines or mountain ranges do). Similarly, complex land features such as settlements and junctions have been thought to attract pigeons (Biro, 2002; Guilford et al., 2004; Kiepenheuer, 1993; Dornfeldt, 1982), and these too might be expected to have unusually high edge intensity.
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Table 1 The statistical results of the comparisons between regions along the dimension of relative positions to the state-change points
State-change from low to middle entropy State-change from middle to high entropy State-change from high to middle entropy State-change from middle to low entropy
Change prior to the statechange region
Change subsequent to the state-change region
Onward change
Increase: tð24:4Þ ¼ 6:92, po:0005 Increase: tð40Þ ¼ 13:00, po:0005 Increase: tð32:9Þ ¼ 2:45, po:05 No significant change: p ¼ :39
Increase: tð25:3Þ ¼ 4:02, po:0005 Decrease: tð40Þ ¼ 5:87, po:0005 No significant change: p ¼ :085 No significant change: p ¼ :095
Decrease: tð30:6Þ ¼ 3:87, po:005 Decrease: tð40Þ ¼ 6:82, po:0005 No significant change: p ¼ :72 Increase: tð40Þ ¼ 3:98, po:0005
4.2. Visual information and state changes The second analysis showed that there was a relationship between the positions of state changes and edge intensity. Pigeons generally change their navigational states over locations with higher information density. Detailed inspection of the tracks overlaid on the aerial image suggested that on many occasions the state changes were obtained over boundaries between different types of terrain, such as boundaries of woods, footpaths or roads, although there are counter-examples. One possibility is that the edge-containing features simply cause a change in orientation, and this produces a temporary increase in entropy. Alternatively, it is also possible that these edge-containing features attract the birds’ attention, causing them to fly irregularly along these details thus producing high entropic flight patterns. The edge intensity of land features changes highly significantly along the track segments adjacent to the state-change points associated with increases in track entropy (and potentially, hence, navigational uncertainty) in particular. We found sharper patterns of edge intensity changes across the range of track positions containing state-changes from low to middle entropy and from middle to high entropy than those of the other two categories of state changes. The maximum edge intensity of the latter occurred at only some 5 s after the state-change point with a higher peak, while the maximum of the former occurred some 20 s after the state-change point with a lower peak. The reason for changes of edge intensity across the ranges of track positions containing the state-changes from high to middle entropy and from middle to low entropy is unclear. It is possible that the difference in the timing of the edge intensity peak in relation to the state-change position is itself indicative of the distance at which the pigeons were responding to the visual land features. That is, the highest entropy state is triggered when birds are attending to features closely underneath them,
whereas the middle entropy state is entered as the pigeons attend to features still some distance in front of them. This interpretation may also accommodate the less clear cut finding that downward state changes have a more diffuse relationship to edge-containing features, suggesting that this finding may signal attention to features at longer and more variable distances from the birds. 4.3. Possible navigational mechanisms As with any field-based experiment which relies for its inferences solely on interpreting animals’ movement patterns, we cannot be sure that our pigeons’ tracks are the result of navigational decisions alone. Pigeons may react to landscape features for non-navigational reasons (e.g. Kiepenheuer, 1993; Dornfeldt, 1982): edge-containing features might signal potential food sources, resting places, conspecific company, safety from predators, thermal up-draught sources or triggers, or, simply, novel places for birds to explore. Nevertheless, our experience tells us that homing pigeons tend to remain in their loft almost all the time, unless encouraged out, and home immediately after displacement. Our birds rarely stop en route home (only once out of 96 releases in this current experiment), except very close to the loft, and take more direct routes with increasing familiarity (i.e. they do not show evidence of exploratory behaviour once familiar with a route), eventually forming stereotypical individual routes to which they remain faithful and which they follow with little delay after release (Biro et al., 2004; Meade et al., 2005). Pigeons predominantly use fast, powered flight, making little use of soaring, so it is unlikely that aerodynamic effects are the cause of attraction to edges. Taken together the above evidences suggests that pigeons are highly motivated to home, and that their patterns of movement are dominated by navigational decisions to this end. As the elevation achieved by the pigeons is never more than 100 m or so, it is not very likely that they have clear line of sight view
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to the home loft from ranges of several kilometres. This adds some extra credence to the hypothesis that, even in a familiar area, the pigeons must, to some extent, utilize navigational information from the landscape. We believe it is reasonable to infer that the reactions to edge-containing features found in this study indicate the use by pigeons of the navigationally relevant visual information contained within those features. 4.4. The way ahead Our findings have demonstrated that the Bayesian entropy state model of Roberts et al. (2004), which has not previously been supported by landscape evidence, does relate to behavioural characteristics of homing pigeons. We identified a systematic relationship between the classification of flight-entropy states by the model and the land features under the pigeons’ flight tracks. It is important to note that the landscape edge information was estimated independently of the computation applied to the flight tracks by the Bayesian model, and hence the existence of a relationship between the two offers some credence to our analysis and interpretations. Traditional methods using experimental manipulations and comparisons of different treatment conditions have long been applied in the investigation of homing pigeon navigation. Nevertheless, given the complexity of landscape information, extracting salient variations and correlations within the data appears too complex for traditional methods. Since it is practically impossible to manipulate the land features themselves (unlike other cues that are more easy to vary experimentally), conclusions have to be drawn from observational data. Little about these variations and correlations has been concluded objectively. This study has shown the utility of a novel approach to such a biological problem. With the help of aerial photography, GPS technology and edge detection algorithms, accurate positional data could be collected and land features could be quantified in this study, providing the basis for a bottom-up, datadriven approach as a more objective method for testing behavioural hypotheses. Rather than being restricted to particular features or configurations on the land, this study has successfully related navigational behaviour with features on the ground in a general manner. Although we have focused on edges, further studies will concentrate on modelling the aerial image of the terrain in various ways. For example, features on the ground can be segmented based on their colour composition, feature sizes and orientations. Experimental manipulations, such as repeated releases of the same birds, can be used with computationally feasible hypothesis testing. A limitation of this study was that we could not manipulate the terrain and that all our subjects belonged to the same loft. Therefore, our findings might, to some extent, reflect some
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uniqueness in the composition and structures of the terrain around our loft. It would be informative to apply the current analysis to datasets obtained from different terrains.
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