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Introduction

When orienting in space and searching for food, microchiropteran bats continuously emit echolocation signals. The returning echoes are analyzed in the auditory system to perform the basic echolocation tasks of detection, localization and classification [1]. Classification of vegetation probably plays a major role in spatial orientation and in food acquisition. It is fundamental for recognizing landmarks and vegetation edges which are mandatory for the route following behavior observed in bats [2]. In addition it is also very important for finding and recognizing foraging habitats such as meadows, bushes, trees etc. which are indicators of specific food sources [3],[4]. In all of these cases the vegetation has to be classified from a relative long distance of up to a few meters. The behavior of bats in the field indicates that bats notice background structures within the so called edge space which extends up to around 6 m [5]. It has also been shown that Natterer's bats learn to discriminate conifers from broad-leaved trees and that horseshoe bats commuting along a hedge of bushes show distinct reactions in their echolocation behavior when the reflection properties of the bushes are changed by covering them with velvet (Denziger and Schnitzler, unpublished data). In addition to the classification of vegetation types, bats can also identify parts of plants like flowers and fruits. Glossophagine bats for instance, find new nectar sources by classifying the shape and texture of flower echoes [6],[7].

Plants have complex shapes that cannot be described in terms of simple geometrical primitives [8]. From an acoustical point of view, a plant can be approximated as a stochastic array of reflectors formed by its leaves. McKerrow et al. [9] removed the leaves from pot plants and discovered that the contribution of branches to the echoes is minor. In large plants the stem might also play a role. In broad-leaved plants, the reflectors are relatively flat and usually large compared to the emitted wavelengths (~0.3–1.5 cm) in a typical frequency modulated bat call. Hence, the backscatter from a broad-leaved plant typically is a superposition of reflections, with statistics determined by the characteristics of the foliage such as the size and the orientation of the leaves, along with their spatial distribution. The overall duration of the echoes is a result of these parameters too. In dense foliage, for instance, surface leaves will acoustically shadow deeper ones, thus strongly attenuating the sound waves that penetrate beyond the outer surface. These properties also apply to conifer trees, except for the fact that they possess needle-shaped reflectors that are small relative to a considerable part of the emitted wavelengths. Conifers are therefore regarded as diffuse scatterers that produce many small echo components, whereas broad-leaved plants lead to pronounced amplitude peaks in the echoes, referred to as glints.

Although the importance of classifying complex objects is well discussed in the scientific bat literature, very little is known about how bats actually perform classification. Only a few previous studies directly addressed the question of object classification using echolocation in bats, and most of them did so in the context of classifying objects with rather simple shapes [10],[11],[12], or only a few reflectors [13],[14]. The few experiments that tested the bat's ability to classify relatively complex echoes [15],[16] did not suggest an explicit mechanism to explain it. The studies that examined classification of simple objects usually assumed simple cues that could be easily recognized in the temporal, frequency or time-frequency representation of the echoes as a basis for classification such as, for instance, a certain notch arrangement in the frequency domain. This approach is hardly feasible for real plant echoes due to their complexity and the strong dependency on the angle of acquisition which makes the ad hoc identification of such features a difficult task. Another typical approach is to identify peaks corresponding to reflections from parts of the object and to compare them to stored echoes that represent known objects or known geometrical shapes (e.g., edges, corners and surfaces). The comparison can be done by measuring the difference between the echoes directly [15] or by comparing certain representative statistics [17]. Once again, these methods will face severe difficulties with complex echoes, mainly since the echoes returning from different reflectors always highly overlap and are very hard to isolate. A few studies trying to classify complex echoes such as vegetation echoes [13],[18] and Stilz and Schnitzler unpublished data relied on extracting one or several parameters (e.g. peak intensity, average intensity and etc.) from some representation of the echoes, with a subsequent selection of those parameters that best assign the plant echoes to their corresponding classes. Thus, the set of all tested parameters is determined by the experimenter beforehand. This has advantages and disadvantages: on the one hand, parameters are usually chosen according to physical or biological plausibility which simplifies their interpretation, but on the other hand strong assumptions are made by choosing a fixed set of candidate parameters since some of the important features might be overlooked.

In this paper, we propose a new approach to complex echo classification. We use a linear classification technique that comes originally from the field of machine learning. We use this technique to operate directly on the raw spectrogram magnitude of the echoes, without the intermediate step of specifying some set of potentially relevant parameters or features. With this approach we take advantage of the statistical structure of the data itself in order to identify the best features to classify it. Thus, the technique allows for the exploration of a wide range of features simultaneously, and often finds simple ones. This comes at the price that the obtained results are slightly harder to interpret on first sight, but we will provide a thorough analysis of the features that are extracted from the data. Our classifiers are trained on a large database of natural plant echoes, created with a bat-like ultrasonic frequency modulated signal. We show that the trained classifiers are able to classify echoes from previously unseen plants with high accuracy. At the same time, our method provides a systematic analysis of all linear features in the echo spectrograms of the database in terms of their relevance for classifying the underlying plant species. More over our approach enables classification of vegetation echoes using a single echo. This coincides with recent work [14] that showed that bats can classify a complex 3D object using a single ensonifying position, without the need to integrate the information from echoes over different acquisition angles. The presented approach provides many insights regarding the task of plant echo classification and is sufficiently general to be applied to other types of complex echoes, for instance from food sources or landmarks.

Results

General Results

A linear SVM classifier is able to distinguish between any of the five tested plant species and any other species or group of species, based on a comparison between two single echoes, one from each class. For the classification task of discriminating one species from the rest already a simple linear classifier achieves very high percentage of discrimination (80–97%, see Table 1 for details). The classification of spruce or corn from the other species is almost perfect whereas the classification of the three broad-leaved trees, and especially the beech, from the rest was the most difficult. For the pairwise classification (Table 2) the relatively poor result for the classification of beech vs. blackthorn, both broad-leaved trees, stands out. The relatively high standard deviation in this case implies that a larger data set might improve performance. Comparing the task of pairwise classification in general to the task of one species vs. the rest reveals that the latter is the more difficult one. This is expected since a group of species always contains much more intrinsic variation that the classifier has to learn, but even with this difficulty, our linear classifiers performed surprisingly well. In the next sections we will mainly discuss the task of classifying one species against the rest, except for cases in which the pairwise comparison reveals more interesting phenomena.

Table 1. Area under the ROC curve for the five classification tasks of one species vs. the other four.

doi:10.1371/journal.pcbi.1000032.t001

Table 2. Area under the ROC curve for the ten classification tasks of one species vs. another one.

doi:10.1371/journal.pcbi.1000032.t002

The Decision Echo

The weights of the normal vector to the separating hyperplane , i.e., the decision echo, has the same dimensionality as the data, and can assist in better understanding the features that are used by our machines for classification. Since we are using linear machines, the class of an echo is actually determined by the sign of the inner product of the preprocessed echo and the decision echo, after adding the offset. This means that the regions of the decision echo that have high absolute (depicted dark or bright in the figures) values have more influence on the decision. In order to interpret the decision echo, we present the decision echoes of the classification tasks of spruce vs. the rest and corn vs. the rest together aside an image of the difference between the average spectrograms of the two classes (Figures 1 and 2). Comparing the decision echoes and the spectrogram differences (Figures 1C and 1D, 2C and 2D) it becomes clear that in both classification tasks our classifiers are actually emphasizing the areas in which the differences between the spectrograms are most salient. The comparison of the differences between the decision echoes of the two tasks shows that in the task of classifying spruce from the rest, the classifier performs a combination of a frequency domain analysis and a time domain analysis. In the early parts of this task's decision echo, low frequencies are inhibitory (with negative values) while the high frequencies are excitatory (with positive values). In the later parts (~ after 10 ms) the entire decision echo is excitatory (excluding regions with larger attenuation as will be explained below). Therefore, classification of spruce can be generally described as a measurement of the difference between the high and low frequencies intensities in the spectrogram's early parts (frequency domain analysis) and as a measurement of all intensities in the later parts (time domain analysis). The classification of the corn field is mainly a time domain analysis. Here the regions in the decision echo which are compatible with the first and second rows of the field (compare with the corn spectrogram in Figure 2A) are excitatory, while the gaps between these rows are inhibitory. The effect of the frequency dependent atmospheric attenuation of sound waves is expressed in all of the decision echoes. According to this attenuation, the higher the frequency of the wave is, the faster its intensity decreases with the distance. This gives the decision echoes a triangular shape, meaning that the higher the frequency, the less the later parts of the spectrograms are used for classification (gray regions in Figures 1 and 2).

Figure 1. Decision echo analysis for the classification task of spruce vs. the rest.

(A) Average spectrogram of the raw data of spruce. (B) Average spectrogram of the raw data of all the plants except spruce (i.e. the rest). The color bars for both (A) and (B) are in dB. (C) The difference of the preprocessed spectrograms of spruce and the rest. (D) The normal vector (decision echo) to the separating hyperplane calculated for this classification task. In both (C) and (D) black represents negative values, white represents positive ones, and gray is zero.

doi:10.1371/journal.pcbi.1000032.g001

Figure 2. Decision echo analysis for the classification task: corn vs. the rest.

(A) Average spectrogram of the raw data of corn. The color bars for both (A) and (B) are in dB. (B) Average spectrogram of the raw data of all the plants except corn (i.e. the rest). (C) The difference of the preprocessed spectrograms of spruce and the rest. (D) The normal vector (decision echo) to the separating hyperplane calculated for this classification task. In both (C) and (D) black represents negative values, white represents positive ones, and gray is zero.

doi:10.1371/journal.pcbi.1000032.g002

Generation of Artificial Hybrid Spectrograms and Echoes

An alternative interpretation of the decision echo is the direction in the high-dimensional input space along which the changes between the two classes are maximal. In other words, for a pair of species it represents the transition between the two. Inspired by Macke et al. we calculated for each pair of species the average spectrogram, and then added the decision echo multiplied by a positive or negative factor η. By doing this we actually move along the direction of the maximum change from a mean representation of the two plants in the directions of each one of them. We used this method to generate 1000 artificial spectrograms that are hybrids of different ratios of the apple vs. corn pair (500 on each side of the hyperplane see Figure 3).

Figure 3. The results of generating hybrid sepctrograms of apple and corn.

Only (B) and (D) were artificially generated. Color bars are not presented, but the data are in the spectral power scale. (A) Average spectrogram of apple. (B) The decision echo multiplied by η = 0.07 added to the average spectrogram. (C) The average spectrogram of corn and apple. (D) Same as B, but with η = −0.07. (E) Average spectrogram of corn. (F) The decision echo calculated for this task used to create (B) and (D). Dark intensities depict negative values, while white depict positive ones. (G) Classification performance of echoes created from artificial hybridized spectrograms as a function of the η factor. To measure performance we divided the spectrograms of each species into 10 groups, each containing 50 spectrograms with a similar η. The units of η are relative, such that η = 1 corresponds to an artificial spectrogram that is as distant to the hyperplane as the most distant original spectrogram. The performance is measured in the percentages of echoes that were correctly classified according to the expected classification.

doi:10.1371/journal.pcbi.1000032.g003

To generate echoes from the hybrid spectrogram, we propose to use the random phase method described in the Materials and Methods section. We did so in order to verify our method, and the resulting echoes lead to a consistent classification behavior, i.e., higher classification performance for larger absolute values of η (see Figure 3 for more details)

Support Vectors

To determine the separating hyperplane, the SVM uses only a limited number of data points (the ones that are closest to the hyperplane) which are termed support vectors. The importance of the ith support vector is weighted by a constant α_i. Adding up the support vectors on each side of the hyperplane separately, with the proper weighting, provides another view on the classification rule. For an arbitrary pair of two species, a weighted sum of the support vectors on one side of the hyperplane can be intuitively understood as the most similar this species can acoustically be to its pair in the limits of our data set. The spectrograms of the weighted support vectors for the pair of apple tree and corn field reveals how in some cases an apple tree can acoustically resemble a corn field and vise versa (Figure 4).

Figure 4. Spectrograms of the weighted support vectors on each side of the hyperplane.

The color bars are in dB. (A) The apple spectrograms used as support vectors added up according to their weights. (B) Same as A for corn. Examining the two weighted spectrograms, the idea of the support vectors, being the most difficult data points to separate in the limits of the data set, becomes clearer.

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Frequency vs. Time Information

From the decision echoes we learned that both time and frequency information are used for classification and that in higher frequencies the earlier parts of the spectrograms are preferred for classification, probably due to atmospheric attenuation. Here we test whether classification is possible when only parts of the spectrogram's information are used. We divided the spectrograms into squares of 5 kHz by 5 ms, and for each square, we trained and tested SVMs for all the classification tasks in the same manner described above. We found that already the information contained in one of the limited squares within the spectrogram is sufficient for classification with very high (~0.9) performance in all cases except for beech (Figure 5). However, the exact position of this limited sensitive region in the time-frequency space can be significantly different for different classification tasks. In spruce classification for instance the low frequencies in the beginning of the echo provide the best classification performance. In blackthorn on the other hand the later parts of the spectrogram are better for classification, and there is a wide range of frequencies and times that can be used with almost equal performance.

Figure 5. Classification performance of four classification tasks when using partial data of the spectrograms for classification.

Each pixel represents the performance when using a square from the spectrogram with a frequency band of 5 kHz and time duration of 5 ms. The color denotes the area under the ROC curve (AUC) when classifying using only this square of information from the spectrograms. The classification tasks presented are: (A) Spruce vs. the rest; (B) Blackthorn vs. the rest; (C) Beech vs. the rest; (D) Corn field vs. the rest.

doi:10.1371/journal.pcbi.1000032.g005

Generalization over Different Angles

Our classifiers generalized over different aspect angles. This can already be learnt from the basic experiments since we trained them by using data from all angles, and then tested them with high success on data from all angles (Tables 1,2). In a different version of the one species vs. the rest experiment we trained machines using training data recorded from all angles except for the tested one and then tested on data points from only the tested angle. The classification performance in these experiments stayed as high as in the ones in which data from all angles were used to train and test the machines with no significant difference (Two way ANOVA, F_2,60>0.86, P<0.45).

The Effects of Preprocessing on Performance

In order to examine the sensitivity of the performance of our machines to the preprocessing of the data, we used a cross-validation approach to estimate the performance while changing the parameters of the preprocessing steps. This was done on the training data set as explained in the methods section for two procedures: the effect of cutting out the echoes in the time domain, and the effect of the time-frequency resolution (i.e., the DFT window length used to calculate the spectrogram).

To test the effect of cutting the echo out in the time domain, we changed the threshold according to which the cutting points were determined. Cutting the echo improved the classification performance by a non significant average of 0.02 (Two way ANOVA, F_2,60>1.78, P<0.18) We attribute this slight improvement to the registering effect that this procedure has on the echoes. Applying a threshold is closely equivalent to recognizing the first wave front of the echoes and this aligns them before any further processing. The two different cutting criteria (10 or 20 times above noise level) showed no difference what so ever.

To determine the effect of the DFT window length we varied it and kept the percentage of the overlap between sequential windows constant (Figure 6). The extent of the spectrograms in the temporal direction decreased with window length whereas the extent in frequency increased such that the overall information remained constant. Up to a certain window length (1000), representing a time bin of 1ms (with 80% overlap) the window length had no significant influence on classification performance. Above this length however, for the 2000 window, there was an overall significant decrease (0.07 on average) in classification performance (2-way ANOVA, F_3,80>18.5, P<0.0001). This decrease mainly affected the three classification tasks blackthorn vs. rest (0.25 on average, 1-way ANOVA, F_3,16>24.8, P<3⁻⁶), beech vs. rest (0.13 on average, 1-way ANOVA, F_3,16>6.5, P<0.005) and corn vs. rest (0.03 by average, 1-way ANOVA, F_3,16>2.85, P<0.07) while the performance of the other two tasks did not change. The decrease is probably a result of the loss of time information due to excessive smoothing. In general, the most suitable window length depends on the specific classification task.

Figure 6. Effect of the DFT window length on classification performance.

(A) The area under the ROC curve (AUC) for four different window lengths ranging from 250–2000 µs. Average results are presented together with the blackthorn classification case, in which the effect was most clear. The difference between a 2000 µs window length and the other lengths is significant (P<0.05), whereas the difference between the three other lengths is not. (B) Average spectrograms for a window length of 2000 µs (first row) and a 250 µs one (second row) for the classification task of blackthorn vs. the rest. It can be seen how time information is decreased (i.e. smeared) for the 2000 µs window (first row). This makes separation between the two classes easier with the 250 µs window (second row) even when only examining them visually.

doi:10.1371/journal.pcbi.1000032.g006

Discussion

General Conclusions

In this work we analyzed the characteristics of a database containing vegetation backscatter from five plant species ensonified with a bat-like ultrasonic pulse from different aspect angles. We used a linear classification technique to find discriminative features in the backscatter spectrograms that were able to differentiate between different plant species independent of aspect angle. In contrast to previous approaches, we did not derive these features from biological or practical plausibility assumptions. Instead, discriminative features were learned from the statistical regularities found in our database. When we tested our classifiers on a single echo from a new, previously unseen specimen from one of the species in the database, classification performance was surprisingly high, ranging between 0.8–0.99. This indicates that the echoes created by a frequency modulated ultrasonic sweep can be highly informative about the plant's species membership. This forms a possible explanatory basis for some of the observed abilities of bats in classifying complex objects such as landmarks or vegetation as indicator for food sources [3],[4].

Once a linear classifier is trained, it can also be used as a generative model. This means that the learnt features can be used to generate new artificial examples of the data. In our case we could create new echoes of a certain plant species or of a combination of species (Figure 3). In the future we hope to use this type of artificially generated echoes in behavioral experiments in order to test the correlation between our linear functions and bat classification performance.

What Did the Classifiers Actually Learn?

As described in the methods, we designed our preprocessing procedure in such a way as to minimize the species-specific noise (due to external or internal recording parameters) to prevent the classifiers from using it for classification. The probability that such artifacts still retain some influence on our results is quite low considering the actual information that leads to a classification decision as depicted in the decision echoes. All decision echoes (see examples in Figures 6 and 7) give a higher weight to regions of the spectrogram where the signal of at least one of the classes is high above the noise level. Regions with lower signal intensities, i.e. later in time and higher in frequency, tend to have values close to zero in the decision echoes. As an additional test, we repeated the same classification experiments, but this time after preprocessing the echoes with a Wiener filter [19], which uses the noise spectrum in order to filter out the noise from the entire signal, not only from the low amplitude regions. The noise spectrum for each echo was estimated in the same way as described in the methods. There was no significant difference in the classification performance of the classifiers with and without Wiener denoising (F_1,48>1.6, P<0.22). The results after denoising appear to be slightly (but not significantly) better which implies that the measurement noise does not contain species-specific artifacts that could be erroneously used by the algorithm for classification. When examining the decision echoes it seems that some of them (e.g. corn classifiers, see Figure 2) use the time structure of the echoes more than the frequency content, while others (e.g. spruce classifiers, see Figure 1) use the frequency content more than the time structure. In general, in all cases both time and frequency information was used for classification. Regarding the best features of the plants used for classification, it seems that our classifiers neither use the overall extent, nor the fine texture of the spectrogram. Instead they rely on intermediate scale structures, such as the representative frequency content in a certain time interval or a characteristic time structure for certain frequencies. In most cases we could identify a small region in the spectrogram which is already sufficient for classification. However, the exact position of this decisive region in the time-frequency plane can significantly change between the different classification tasks. This means that if nothing is known about the classified plant species beforehand, a large proportion of the spectrogram is required to achieve a good performance over all tasks. Thus, a call with a large frequency bandwidth, as is observed in frequency modulating bats, is preferable from the classification point of view.

Figure 7. The area under the ROC curve (AUC) for all of the broad-leaved trees pair-wise classification, when using partial information from the spectrograms, limited to frequency bands of 10 kHz.

The graphs show a relative preference for the low frequencies information, but the exact slope is task-specific.

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Figure 8. The correlation between the distance from the separating hyperplane and the fourth moment of the echoes.

o – regular data point, * – support vectors. Correlation values are indicated in rectangles in upper right corner. (A) The comparison for the task of classifying apple and spruce reveals a high correlation between the distance and the fourth moment. (B) The comparison for the task of classifying beech and blackthorn reveals no correlation between the distance and the fourth moment, implying that the fourth moment cannot be used to classify the two. This figure also visualizes how the task in (A) is easy for the SVM compared to the one (B).

doi:10.1371/journal.pcbi.1000032.g008

A plant is a complex object comprised of many reflectors (mainly the leaves). Although the spatial arrangement of the different plant species contributes to the echo structure, it can be helpful to regard the plant leaves as an array of independent, rather simple reflectors to understand the differences in the frequency content of species. In our study we found that the most suitable frequencies for classification are not necessarily the ones with the best signal to noise ratio (SNR). The highest SNR was usually attained around 50 kHz, whereas the frequencies with the best classification performance were in most cases lower, indicating that the echoes vary more in the lower frequency range between species.

Some reason for these preferred frequency bands can be found in radar theory [20]. The cross section of a reflector depends on the geometry of the reflector in relation to the wavelength of the sound pulse. For a simple spherical reflector, the intensity of the echo depends on the ratio between the sphere's circumference and the wavelength of the emitted signal. This ratio defines three regions: (1) The Rayleigh region - if the circumference is smaller than the wavelength the intensity of the reflections decreases rapidly when decreasing the radius of the sphere. (2) The resonance region - if the wavelength is of the same order as the circumference (up to ~10 times larger) the intensity of the reflection oscillates depending on the ratio mentioned above. (3) The optic region - if the circumference is much larger than the wavelength the intensity of the reflection is equal in all frequencies. This division into three domains exists also in reflectors with a more complex shape, but then the cross section will also depend on the angle of ensonification. The borders of these regions when considering the extreme frequencies of our emitted signal (25 and 120 kHz) are such that reflectors larger than 14 cm will be in the optic region for all frequencies, and reflectors smaller than 0.03 cm will be in the Rayleigh region for all frequencies. The reflectors in between will be in all three regions depending on the frequency. From the point of view of classification, it is clear that the Rayleigh region is the most advantageous since at a given frequency, the intensity of the reflection changes with the circumference, therefore providing direct information about the reflectors size. Clearly, this presupposes that the intensity is high enough to be perceived. The optic region on the other extreme provides no frequency information that could be used for classification, since the reflections in all frequencies are redundant. Obviously, the time structure can still be different. The resonance region shows a more complex interdependence between frequency and reflector size than both extremes, but a suitable classifier might be able to use this information.

In order to relate this theoretical framework to our data, we have to provide some approximation of our reflector's circumference. This is not easy, for the leaves on plants comprise of a range of many sizes, and they are not simple spheres. In the case of spruce, its needles prevent us from doing this, but it is safe to assume that it's very small radial dimension (up to a few millimeters) is equivalent to relatively high frequencies, above 100 kHz, and therefore most of its reflectors will behave according to the Rayleigh domain. Corn leaves on the other extreme are very long, and will therefore probably mainly behave according to the optic domain. As for the three broad-leaved trees, we use the roughly approximated average leaf length (calculated by measuring a variety of leaves) in order to estimate the relevant wavelength range. Apple and beech trees exhibit the largest leaves among the three, with an average length of around 8 cm. This is equivalent to a wavelength of a few kHz. Its reflectors should therefore behave according to the resonance domain when the emitted signals have frequencies of up to a few dozens of kHz, and according to the optic domain with higher frequencies. Blackthorn trees exhibit smaller leaves, with an average length of about 3 cm. This is equivalent to a wavelength of roughly 10 kHz, resulting in its reflectors being in the resonance domain for most of the frequencies of the signals emitted in this research.

Spruce classification is probably easiest to explain by to this approach. Its many reflectors in the Rayleigh region result in lower intensities in the low frequencies of its echoes (Figure 2). This means that it can be well classified by its lack of low frequency content. Indeed, as can be seen in the decision echo and time-frequency classification performance (Figures 3C and 7A), the information in low frequencies provide the best classification performance for spruce.

Corn field in contrast should not contain much frequency information, and truly its decision echo doesn't seem to be using any obvious frequency information (Figure 2D), and so does the time-frequency classification performance graph imply (Figure 5D).

In the case of the three broad-leaved trees (apple, beech and blackthorn) the effects of frequency are less obvious. We therefore examined the classification performance of each pair when only using parts of the spectrograms with a limited bandwidth of 10 kHz while retaining the entire time information. For all pairs, classification was best at low frequencies (Figure 7). For beech vs. blackthorn and apple vs. blackthorn, all frequency bands between 25–80 kHz lead to a similar classification performance, whereas in beech vs. apple, performance begins to drop already at the 30–40 kHz band. These could be explained by the above argumentation: all three plants exhibit leave sizes in a considerable large range such that for our emitted call all three species probably have reflectors both in the resonance and in the optic regions. Apple and beech trees, however, have bigger leaves than blackthorn and thus should have more reflectors in the optic region and less in the resonance region, particularly at higher frequencies. As a consequence, apple and beech should be harder to discriminate in this frequency range.

Are the Extracted Discriminative Features Available to the Bat Brain?

Since the intent of our study is to test which features of plants echoes might enable bats to classify the plants, we have to examine if the information used by our classifiers is – at least in principle – available to the bat brain.

After the preprocessing of the received echoes our classifiers were trained to recognize plant species based on the magnitude of their spectrograms. This information is easily accessible to the bats through the spectro-temporal decomposition of the echo in the cochlea [21]. We ignored the phase information which to date has not unequivocally been proven to be used by bats. We also did not cross-correlate the recorded echoes with the emitted signal. This is often done in echolocation studies, thus revealing the impulse response (IR) of the ensonified object, although it is not known whether bats can actually use the IR. Finally, we use a time resolution of about 1ms which is far above the minimum time resolution which has been reported for bats [22],[23]. Thus it seems highly probable that the information used by our classifier is available to bats. Experimental evidence suggests that bats can extract information with a much higher resolution than required (see [23] for a summary).

Do the Results Extend to More General Natural Scenes?

The classifiers were able to classify a plant correctly at acquisition angles that were not present in the training set, i.e., our classifiers generalize to a certain degree over the angle of acquisition. This result was unexpected, since in acoustics, as opposed to vision, a slight change of the acquisition angle can result in a very large change in the echo, as has been shown for plants [9],[11]. However, we noted above that our classifiers use intermediate-scale features which probably vary more slowly over the angle of acquisition. Moreover, most of the species in our database contain leaves in all orientations such that the local statistics do not change significantly with acquisition angle, even when the individual echoes vary considerably.

An issue that was not tested in this work is the generalization over distance, i.e. the ability to use the same classifiers on objects that were ensonified from different distances. The two main limiting factors regarding this generalization are the attenuation of the echoes and the change of the beam width. The attenuation affects the echoes in two ways: 1) The SNR of the entire echo deteriorates, in a frequency dependent manner. 2) The geometric attenuation increases with the square of the distance, and therefore the attenuation rate within the echo will change when it returns from different distances. The first problem of the overall SNR could be dealt with, up to a limit, by increasing the intensity of the emitted signal. In addition, our classifiers do not require the fine texture of the spectrograms for classification, and therefore can probably tolerate a certain deterioration of the SNR without a significant drop in performance. The second problem could be overcome – at least in principle – by using the absolute distance as measured by the arrival time of the echo to compensate for the attenuation differences within the echo.

As for the beam, its width will widen the further the emitter is from the plant, thus increasing the ensonified region. The larger the emitter distance, the more reflectors will contribute to the echoes. Taking into account the intermediate features used by our classifiers, we hypothesize that as long as our beam is wide enough to capture them, classification performance will stay high. A too wide beam, however, could introduce new echoes from other reflectors, which leads to a smearing effect due to the arrival of more reflections at close instants in time, and thus to a slow deterioration of classification performance. Although bat beams are usually much wider than the one used by us, it is clear that there exists a distance range in which the echo statistics are similar to our setting.

Relation to Behavioral Studies

In one of the few reported works dealing with the bat's ability to classify complex echoes, Grunwald et al. [14] found that bats can distinguish the fourth moment of artificially created echoes. They conclude that bats might be using the changes in the fourth moment to facilitate navigation guided by echolocation. We tested this conclusion in the light of our results for two pair-wise classification tasks. To this end we calculated the fourth moment of each echo and compared it to its distance from the hyperplane (see methods). The results (Figure 8) show that in the rather simple task of classifying a conifer tree (spruce) from a broad-leaved tree (apple) the distance from the hyperplane of each echo is linearly correlated with its fourth moment (R~ = 0.64, P<0.00001). However, since we were using only linear machines, our classifiers have no access to higher order statistics such as the fourth moment. This means that information sufficient to classify the two trees is also available in the low order statistics of the echoes. In the case of a difficult classification task (blackthorn vs. beech) on the other hand, we found a close to zero linear correlation between the distance from the hyperplane of the echo and its fourth moment (R~ = 0.1, P<0.00001). Moreover when examining the data (Figure 8B) it is obvious that only the fourth moment is not a sufficient statistic for discriminating between these two broad-leaved tree species. In contrast, the SVM is able to find features that are sufficient for reliable classification of this pair already by relying on simple first- and second-order statistics.

Wichmann et al. have shown the relevance of a hyperplane calculated from the data to human categorization performance [24],[25]. They compared SVM-based classification with human performance on a task of image gender classification, and found that SVMs are able to capture some of the essential characteristics used by humans for classification. Furthermore, Wichmann and Macke were able to show that the distance from the separating hyperplane could be used to predict the certainty with which these decisions are made. Despite the fact that it is known that the brain can perform classification of nonlinear data, these works always used linear machines just as we did. In the future we would like to use the SVM as echo generators in order to test the relevance of our calculated hyperplanes to performance of the bat brain.

Final Conclusion

We have found that the highly complex echoes created by ensonifying plants with a frequency modulated bat like signal contain vast species specific information that is sufficient for their classification with high accuracy. From the point of view of a bat, we prove that it can use a single echo received by one ear, with a surprisingly simple receiver, having a relatively low time resolution and no access to the impulse response, to extract the information required for classification. We also demonstrate how it can then apply a basic linear hyperplane that could be easily implemented by a neuronal apparatus, in order to classify the vegetation echoes. These findings could explain some of the abilities observed in natural bat behavior such as using landmarks for navigation, and finding food sources on specific vegetation.

Materials and Methods

Data Acquisition

A biomimetic sonar system consisting of a sonar head with three transducers (Polaroid 600 Series; 4-cm-diam circular aperture) connected to a computer system was used to create and record vegetation echoes. The sonar head was mounted on a portable tripod. Its central transducer served as an emitter (simulating the bat's mouth) and the two side transducers functioned as receivers (simulating the ears). Backscatter received from the emitted signal was amplified, A/D converted, and recorded by a computer. The emitted signal resembles a typical frequency modulated bat call in terms of its duration and frequency content (Figure 9A). It comprises a four millisecond linear down-sweep from 140 to 25 kHz. We excited the emitter with a constant amplitude, but due to the speakers frequency response an uni-modal response function was created with a maximum around 50 kHz, providing an intensity of 112 dB (SPL) at the maximal frequency in a distance of 1m from the emitter. Most of the signal energy was contained in the frequency band between 25–120 kHz. The combined frequency response of our emitter and receivers resulted in a frequency response that resembles the one of a typical frequency modulated bat call. In contrast to bats our emitted sound pulse had a rather narrow beam width, with its first null for 50 kHz occurring around 15°, much lower than known for bat calls [26].

Figure 9. Summary of the materials and methods.

(A) The basic setup of the experiments, in which a sonar head on a tripod was used to ensonify plants. The emitted signal's spectrogram is presented with the time signal under it and the frequency dependent intensity curve on the right. (B) An example of a time domain back scatter recorded from a single apple tree. The amplitude is in arbitrary units. (C) The spectrogram of the time domain signal of B, created after cutting the echo out of the time signal. The spectrogram's frequency range was cut between 120–25 kHz, and it was threshold leaving only the regions that are high above noise. (D) An illustration of the classification by SVMs. Following PCA, each spectrogram is represented by a 250-dimentional data point (shown in the figure as a 2-dimentinal point) belonging to one of two classes (circles or rectangles). The SVM then learns the best hyperplane for the training data. The data points that are closest to the hyperplane (denoted as full shapes) are called the support vectors and define the orientation of the hyperplane.

doi:10.1371/journal.pcbi.1000032.g009

The recorded back scatter or echo (both terms will be equally used in this paper, Figure 9B) was digitized at a sampling rate of 1 MHz and with a 12-bit resolution. The length of the recorded echo was very long (40 ms corresponding to 6.8 m). It included a long tail of noise after the part with echoes returning from the target. This enabled exact estimation of the noise for each recording.

All recordings were performed in the field with real plants as targets. Five plant species were chosen, representing a variety of the common species available in the local bats environment. The species were:

• Apple tree (Malus sylvestris) – This species has large leaves, in a spacious arrangement. The trees were covered with fruit.

• Norway spruce tree (Picea abies) – This was the only conifer tree that was ensonified. Its branches are spread homogenously and evenly covered with needles. Will be referred to as spruce throughout the paper.

• Common beech tree (Fagus sylvatica) – This species is characterized by large flat leaves that are on each branch usually arranged in the same plane. Will be referred to as beech throughout the paper.

• Blackthorn tree (Prunus spinosa) – This species has smaller leaves than the other broad-leaved trees, without any specific orientation. This species was usually found in a formation of a hedge rather then as a sing