Estimating the number of sperm whale (Physeter macrocephalus) individuals based

on grouping of corresponding clicks

Carlos de Obaldıa Pastor, Gediminas Simkus, Udo Zolzer

Abstract

An automated Passive Acoustic Monitoring (PAM)method for the detection and differentiation of spermwhale individuals is proposed. Various methods bene-fit from the correlation of multi-channel recordings toidentify active whales. However, the proposed approachemploys audio recordings from a single hydrophone anduses a correspondence analysis to differentiate betweenactive individuals. Segments of a click are obtained bythresholding the RMS envelope of the Teager-Kaiser en-ergy operator’s output. Possible click reflections aredetected by an iterative comparison of extracted click-like segments with each other. Corresponding clicks aregrouped by comparing extracted click features and thecross-correlation of sequential time-segments of the clicksegments with one another. Signal characteristics whichdescribe time and spectral signatures of clicks are em-ployed to derive rules for an effectual correspondence be-tween the click segments. Corresponding clicks are thengrouped to determine the number of active sperm whales,hence identifying plausible signatures for individuals. Re-sults with real-world recorded signals confirm that suchcorrespondences can be used for further applications. Forinstance, intra-species classification in monaural record-ings.

Introduction

Anthropogenic noise contamination of underwater envi-ronments affect marine life and is a growing concern.Marine mammals are extremely affected, since sound isused underwater as a primary sense for communicationand foraging. Changes in the acoustical environment ofcetaceans can thus bring behavioral and health problemsin populations and individuals.

Toothed whales use pulse-like sounds, or clicks, to per-form echolocation tasks. Sperm whales (Physeter macro-cephalus) produce such clicks using their acoustic organ,the spermaceti organ, which is located on their head andis filled with a substance with a lower density than water.Each of these clicks can be characterized by a multi-pulsestructure [1, 2]. The multi-pulse structure is a result ofthe reflection of a generated pulse between the frontal anddistal air sacs in the acoustic organ of a sperm whale. In[3] the authors are able to estimate the size of a spermwhale based on their click structure.

In order to reduce the emission of noise in underwaterenvironments, Passive Acoustic Monitoring (PAM) tech-niques are used to detect the presence of marine mam-mals. If animals are present, noise sources should bemitigated. In this work, a PAM system for grouping

Pre-

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Figure 1: Proposed PAM system. The signal is pre-segmented in transient groups. Reflections are identified onthis segments based on a comparison of features. For clickcorrespondence, features for each click are used to collect thesegments in groups of corresponding clicks for each individualin the waveform.

corresponding clicks of different active sperm whale indi-viduals is presented. Estimation of the number of whalesin the waveform is based on the number of individualsidentified with the algorithm.

Proposed PAM System

Passive Acoustic Monitoring (PAM) in aquatic environ-ments refers to the use of hydrophones to detect, mon-itor and localize vocalizing marine mammals. Methodsfor wildlife monitoring have been traditionally driven byvisual observation but are also developed in combinationwith acoustic surveys [4].

In Fig. 1 the proposed monitoring system for groupingclicks in individuals is presented. A signal recorded bya single hydrophone is segmented into blocks of variablelength which would contain a direct-path click. Similari-ties in the feature set of these segments are then used toarrange them into groups which would correspond to dif-ferent individuals. The physical characteristics of whalesare sufficient to differentiate them using rule-based algo-rithms. A pair-wise comparison of clicks was preferred tosupervised learning solutions due to the unavailability ofground-truth labeled data, and to unsupervised learningalgorithms [5] which assume an invariant feature set.

Click Segmentation

To detect the echolocation clicks, the signal is pre-segmented into blocks of variable length. These segmentsare analyzed to remove possible reflections caused by theunderwater channel.

Click segmentation is performed in two steps. First, inthe pre-segmentation, the transients which conform theclick are detected and plausible boundaries for each clickare set in the signal. Such delimited segments would

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contain clicks and click reflections. The second step is toselect just the click segments by enforcing a set of ruleswith the extracted features, so that reflections due tounderwater channel conditions could be discarded.

Pre-segmentation

A pre-segmentation method similar to the proposedone in [6] based on the Teager-Kaiser energy operator(TKEO) [7] is employed to detect click transients. TheTKEO is applied on the discrete time signal x(n) as:

Ψ(x(n)) = x2(n)− x(n+ 1)x(n− 1). (1)

After applying the energy operator, all the peaks ofΨ(x(n)) which lie above a certain threshold ΓTK arefound. The threshold ΓTK is defined as:

ΓTK (x(n)) = µ (x(n)) + h · σ (x(n)) , (2)

where µ(·) and σ(·) denote the mean and the standard de-viation of the signal. The constant h in Eq. 2 is a weightfactor for setting the peak threshold lower or higher.This threshold is exploited in [6] to find significant peaks,group them, and segment the signal in clicks. However,in this way a segment could be formed by joining con-secutive groups of clicks if the clicks are too near to eachother. Also, if the peaks of a single click are too far awayfrom each other, the click will be divided.

To overcome this drawback an approach based on sig-nal smoothening by calculating the RMS envelope is em-ployed. The RMS envelope is applied as in [8] to Ψ(x(n))with a window length of 20ms and a hop size of 4 sam-ples. Peaks are then found on the RMS envelope ofΨ(x(n)). Preliminary boundaries for the segments ofclicks are set at the first minima before and after eachpeak. The RMS envelope (red) in Fig. 2 is calculatedfrom the TKEO signal (blue) of a particular click (black).

A Hamming window is then applied to a signal seg-ment within the time positions given by these preliminaryboundaries. The TKEO is again applied to the windowedsegment and peaks are found inside such boundaries. Fol-lowing experimental results, the beginning of a segmentof a click starts at 0.5ms before the first TKEO peakand ends at 5ms after the last TKEO peak. The offsetis necessary to prolong the segment as the click endingdecays slowly in time and in amplitude. An example sig-nal with its corresponding segment and click positions isshown in Fig. 3. The difference of the time positions ofthe segments is defined as the inter-segment interval.

Click Extraction

In ocean environments the speed of sound is a function oftemperature, pressure and salinity. Therefore, in under-water acoustic channels, click and reflection power varieswith time due to its multi-path characteristics. A reflec-tion may thus achieve a slightly larger power level thanthe direct-path click signal. Although reflections behindthe direct-path signal are plausible in underwater channelconditions, in the presented work only forward reflectionsare considered, i.e. the reflected segments are assumedto be after the detected segment.

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Figure 2: A RMS peak surrounded by two minima. TheRMS envelope (red) is calculated on the TKEO signal (blue).

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Figure 3: Detected click positions after pre-segementation.

In applications with a single hydrophone it is usually as-sumed that the reflected clicks propagates through mul-tiple paths, thus making the reverberated click to bestretched in time[9]. This however depends on the whaleposition with regard to the hydrophone and on the qual-ity of the signal. For consecutive clicks the second clickmay be falsely detected as a reverberated click of the firstwhale.

An iterative approach to detect reflections is introduced.Segments are compared in a sequential way. Let κm beeach of the detected segments in the pre-segmentationstep, and m the segment position, where m = [1, . . . ,M ]and M is the number of detected segments in x(n). Re-flections are searched to the right of κm. The segmentis checked against a set of rules with the next segmentκm+1. If κm+1 is not an apparent reflection then m isincreased. If on the other hand, κm+1 is a click reflectioncandidate, the segment is flagged and skipped in the nextsearch.

Reflected segments are identified based on a set of rules.Two groups of reflections are defined. A high power re-flection is considered to have a short interval between twosegments (< 35ms), high negative magnitude of cross-correlated segments, and matching inter-pulse distances.Low power reflections on the other hand may have a largeinterval between segments (> 35ms), the negative abso-lute magnitude of cross-correlated signal is higher thanthe positive magnitude, and usually a click followed by anecho has a significantly higher amplitude. After discard-ing reflections, the resulting set of κm segments shouldcontain only segments with single direct-path clicks.

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Ref. click

Corr. click

Other click

Figure 4: Correlation example. The black signal is the auto-correlation of a selected whale click. The red signal is thecross-correlation of two corresponding clicks. The blue signalis the cross-correlation of clicks from different whales. Dottedlines represent the peak correlation level for each signal.

Feature Extraction

Since the characteristics of the generated click dependon the trajectories inside the acoustic organ of the spermwhale, it can be implied that individual characteristicsare to be found by analyzing the nature of the clicks [10].In this sense, feature sets for each click are analyzed tofind individual-specific characteristics. For example, thereflection of the pulses inside the acoustic organ charac-terize the impulse response of the sperm whale’s head[11]. Assuming thus that the acoustic response in thespermaceti is characteristic of each individual, the clickduration and the inter-pulse distance (IPD) are then con-sidered as features.

Different acoustic characteristics of each individual areconsidered by evaluating the inter-segment interval, clickduration and IPD, click correlation level, low frequencyspectrum, and Linear Frequency Cepstral Coefficients(LFCC).

By calculating the auto-correlation of each segment andby cross-correlating the segments it is also possible to finda correspondence between the spectral energy content oftwo or more clicks. Fig. 4 shows the peak correlation levelof a corresponding and a not corresponding segment of aclick.

A cesptral smoothed spectrum is calculated for each clicksegment as in [8]. Liftering is done with a cut-off que-frency at 1

8 times the cepstral length. The spectrum wastruncated between 0.2 and 0.4 of the Nyquist frequencyto demise irrelevant features. The spectral content ofclicks appears to be clearly differentiable in this range.Fig. 5 shows the spectral envelope for two correspondingclicks sampled at 44.1 kHz.

The cepstrum is a good technique to determine time-invariant filter characteristics. This can also be helpfulsince the nature of a click is steady over a short period oftime, and reflections due to channel-related phenomenaare not characteristic of the click itself. A linear filterbank is then used to extract 12 LFCCs, from which thelast 11 coefficients are used as features.

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Reference click Corresponding click

Figure 5: Spectrum of a reference and a corresponding click.

(a) Iteration 1

(b) Iteration 2

Figure 6: Iterative grouping example for corresponding clicksegments. Filled boxes show a positive correspondence. Foreach iteration one click group is found. Each group belongsto different whales.

Click Grouping

Decision rules are used to derive similarity between theclick segments κm. Each feature set is exploited to de-velop a rule-based click grouping method.

Click grouping is done in an iterative fashion as depictedin Fig. 6. A segment κm is compared with the next seg-ment κm+1. If the segments correspond, κm+1 is addedto the group and the comparison continues with the nextclick. If segments do not match, the segment is left asidefor a next iteration. This process is repeated until nomore clicks are left, or the ratio of remaining clicks tototal clicks is very low. Depending on the amount anddistance of matching features, clicks can have a strong,good, or low correspondence. A rule set is derived us-ing inter-segment interval values, cross-correlation levels,IPD, and spectral and cepstral features.

The physical characteristics portrayed by the click fea-tures of the previous section do not take into account thetime-variant characteristics of the underwater acousticchannel, nor the movement of the whale. To overcomefeature variability, a time window Tw = 10 s is used tofind correspondences. Groups of clicks in different timewindows can then be merged using the same set of rules,or a derivation of them.

Results and Evaluation

During evaluation 24 signals of sperm whale recordingswhere used. The provided signals contain different num-

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Figure 7: Original signal (gray), detected clicks (light blue),and grouped clicks for 4 detected individuals.

ber of active individuals, as well as a different amountof clicks and are recorded in different environments. Thenumber of individuals in the signals where previously es-timated by an experienced listener. The signals are ofdifferent duration, from several locations, recorded at dif-ferent depths and sampling rates. Only one channel oneach signal is used for evaluation.

Results using the presented click grouping method cor-rectly estimated the reference number of individuals inthe evaluation signals. The plurality of individuals inthe waveform is also found by analyzing the variability ofthe inter-segment interval of all waveforms. An unsteadyinter-segment interval will indicate that more than oneactive individual is clicking.

Fig. 7 shows a click grouping result for an example sig-nal. Signals are arranged in separate plots by groups ofcorresponding clicks. The reference information of theoriginal signal indicates that three individuals are activein the given signal. The total number of whales which aredetected is four. However, only three whales are activeat once during the time slot between 58 s and 75 s.

Conclusion

The proposed Passive Acoustic Monitoring (PAM) tech-nique for abundance estimation of sperm whales (Phy-seter macrocephalus) achieve good estimates of the num-ber of active sperm whales in recorded signals. Abun-dance estimation is achieved by grouping the correspond-ing clicks according to the similarity of their feature sets.Rule-based decisions are used to perform grouping of theclick segments. Such a rule set is derived by relating the

physical characteristics of the clicks with the estimatednumber of individuals labeled in the signals. Characteris-tics found between correspondent clicks in the evaluatedrecordings suggest that a signature is present on clicks fordifferent sperm whale individuals. The method could alsobe adapted for abundance estimation of other species.

References

[1] B. Møhl, M. Wahlberg, P. T. Madsen, A. Heerfordt,and A. Lund, “The monopulsed nature of spermwhale clicks,” The Journal of the Acoustical Soci-ety of America, vol. 114, no. 2, p. 1143, 2003.

[2] R. Antunes, L. Rendell, and J. Gordon, “Measuringinter-pulse intervals in sperm whale clicks: consis-tency of automatic estimation methods.,” The Jour-nal of the Acoustical Society of America, vol. 127,pp. 3239–47, May 2010.

[3] V. Teloni, W. M. X. Zimmer, M. Wahlberg, andP. T. Madsen, “Consistent acoustic size estimationof sperm whales using clicks,” Journal of CetaceanResearch and Management, vol. 9, pp. 127–136,2004.

[4] J. Barlow and B. Taylor, “Estimates of sperm whaleabundance in the northeastern temperate Pacificfrom a combined acoustic and visual survey,” Ma-rine Mammal Science, vol. 21, no. July, pp. 429–445,2005.

[5] X. Halkias and D. Ellis, “Estimating the Num-ber of Marine Mammals Using Recordings of Clicksfrom One Microphone,” Proc. of the 2006 IEEEInt. Conf. on Acoustics Speech and Signal Process-ing Proceedings, vol. 5.

[6] V. Kandia and Y. Stylianou, “Detection of spermwhale clicks based on the Teager-Kaiser energy op-erator,” Applied Acoustics, vol. 67, pp. 1144–1163,Nov. 2006.

[7] E. Kvedalen, “Signal processing using the Teager en-ergy operator and other nonlinear operators,” Mas-ter, University of Oslo Department of Informatics,no. May, 2003.

[8] U. Zolzer, DAFX: Digital Audio Effects: SecondEdition. John Wiley & Sons, 2011.

[9] E. b. P. Strumillo, F. Benard, H. Glotin, and P. Gi-raudet, “Highly defined whale group tracking bypassive acoustic stochastic matched filter,” in Ad-vances in Sound Localization, InTech, 2011.

[10] L. Rendell and H. Whitehead, “Do sperm whalesshare coda vocalizations? Insights into coda us-age from acoustic size measurement,” Animal Be-haviour, vol. 67, 2004.

[11] B. Møhl, “Sound transmission in the nose of thesperm whale Physeter catodon. A post mortemstudy,” Journal of Comparative Physiology A: Sen-sory, Neural, and Behavioral Physiology, vol. 187,June 2001.

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