Romain Karpinski
email: romain.karpinski@loria.fr

Abdel Belaïd
email: abdel.belaid@loria.fr

ZoneMapAlt: An alternative to the ZoneMap metric for zone segmentation and classification

Keywords: Performance evaluation, OCR, ZoneMap metric, String matching

This paper proposes a new evaluation metric based on the existing ZoneMap metric. The ZoneMap method, designed to perform a zone segmentation evaluation and classification, is considered in the context of OCR evaluation. Its limits are spotted, described and a new algorithm, ZoneMapAlt (ZoneMap Alternative) is proposed to solve the identified limits while keeping the properties of the original one. To validate the new metric, experiments have been made on a dataset of scientific articles. Results demonstrate that the ZoneMapAlt algorithm provides greater details on segmentation errors and is able to detect critical segmentation errors.

I. INTRODUCTION

The aim of this paper is to propose a new metric to evaluate the performances of a layout extraction (or segmentation) method. Layout extraction methods are often part of a recognition system and represent a critical step for the recognition performances. Indeed, poor layout extraction performances can lead to severe recognition errors because the information is partial or truncated. Therefore, performance evaluation is an important task that allows one to be aware of a method quality. It also can be useful when creating a new method to understand the behavior and spot errors. In the context of OCR evaluations, the evaluation of the extracted layout can be used to compare different approaches.

A segmented document is composed of objects represented by geometric shapes such as polygons or rectangles or by their set of pixels. In this paper, we consider that zones and objects are the same.

Usually, comparing two different segmentations consist of matching reference objects (the ground truth) with hypothesis objects (output of the system). This matching can be hard to perform when many errors occur and especially when these errors accumulate. Figure 1 shows all basic segmentation errors that can be spotted in documents at line level. Let h be a hypothesis zone (HZ) and r be a reference zone (RZ). Let H be the set of hypothesis zones (HZs) such as H = {h 0 , h 1 , ..., h i }, i ∈ R and R be the set of reference zones (RZs) such as R = {r 0 , r 1 , ..., r j }, j ∈ R. Regarding segmentation evaluation, a HZ h that includes several RZs is called a merge. Conversely, a RZ r that includes several HZs from H is called a split. These two types of errors can happen vertically, horizontally or both. When comparing segmentations, several class of objects may be present such as TextLine or Graphic. Therefore, their comparison with RZs can be penalized when the class expected is not equal to the class of the match. In this case, the evaluation method assess jointly the classification and the segmentation of zones. Figure 2 illustrates two examples of segmentation, Figure 2a shows RZs and Figure 2b HZs. In this output, all zones are text lines represented by their minimum bounding box (rectangles). Since all the objects belong to the same class, the classification part of the evaluation can be ignored. In Figure 2b, as illustrated by the dark rectangle (red), merging errors occurred both vertically (joining two rows of the same column) and horizontally (joining two columns of the two rows). The evaluation of this type of segmentation is difficult because several errors occur in the same area and makes it hard to match zones in this area. Recently, the ZoneMap metric [START_REF] Galibert | The zonemap metric for page segmentation and area classification in scanned documents[END_REF] has been proposed to evaluate jointly the segmentation and the classification of zones. It was developed and used for the evaluation campaign MAURDOR [START_REF] Oparin | First maurdor 2013 evaluation campaign in scanned document image processing[END_REF] that aimed to evaluate capabilities of methods on scanned document images. The ZoneMap algorithm has the following weaknesses:

• It does not take into account the intersection between reference zones. • It does not permit many-to-many matching allowing to handle multiple segmentation errors. • It groups areas that have an intersection even when their intersection area is negligible. We propose to correct these limits in a new version of ZoneMap dubbed ZoneMapALt.

The paper is organized as follows: Section II presents methods from the state of the art on performance evaluation of zone segmentation and classification. Section III describes the ZoneMap algorithm and its limits. Section IV depicts the newly created algorithm ZoneMapAlt and shows how the ZoneMap limits are considered. In section V, experiments are performed to validate the chosen metric. Finally, section VI concludes the paper and gives perspectives.

II. RELATED WORKS

Performance evaluation methods can be summarized in two categories depending on the nature of the document and ground truth availability: pixel-based or object-based. Pixel-based methods assess the class assigned to each pixel and evaluate the document segmentation either globally or sparately by object type [START_REF] Antonacopoulos | Icdar2003 page segmentation competition[END_REF]. Object-based methods seek to assess the quality of a document segmentation at a higher level (only the object and its geometric representation are considered and not its pixels). In both cases, these methods must take into account the location of pixels or objects along with their type (TextLine, Graphic, ...) and shape.

Object-based methods are often faster to compute than pixel-based methods, especially when working with high resolution images [START_REF] Garris | Evaluating spatial correspondence of zones in document recognition systems[END_REF]. In the concern of gaining efficiency, pixel-based methods often represent pixels as polygons transformed into a set of intervals [START_REF] Clausner | Scenario driven in-depth performance evaluation of document layout analysis methods[END_REF] [6] [START_REF] Antonacopoulos | Performance analysis framework for layout analysis methods[END_REF] (or uses the run-length encoding [START_REF] Seo | Performance evaluation tools for zone segmentation and classification (pets)[END_REF]). As for object-based methods, they do not consider the content of the objects (pixels) and encode only their shape represented by either polygons [START_REF] Randriamasy | Benchmarking page segmentation algorithms[END_REF] [10] or, in more precise contexts, by rectangles [START_REF] Galibert | The zonemap metric for page segmentation and area classification in scanned documents[END_REF] [4] [START_REF] Liang | Performance evaluation of document structure extraction algorithms[END_REF]. Often, the bounding box (rectangle) is used because it is simpler to process than polygon and also represents the minimum rectangle completely including the object. Other data representation exists, such as graphs. The graphs are used to match higher level representation of pixels where nodes are segments (association of several consecutive pixels having the same class), as in [START_REF] Shafait | Pixel-accurate representation and evaluation of page segmentation in document images[END_REF] or an object, as in [START_REF] Lopresti | A fast technique for comparing graph representations with applications to performance evaluation[END_REF] where the authors use the graph probing technique. This latter technique performs the comparison by counting similar nodes or as in [START_REF] Dasand | An empirical measure of the performance of a document image segmentation algorithm[END_REF], a document model composed of a hierarchy of bounding box representations is used to perform an empirical measure of matching based on the graph-like model.

Object-based methods employs object overlap to match objects [START_REF] Galibert | The zonemap metric for page segmentation and area classification in scanned documents[END_REF] [4] [START_REF] Randriamasy | Benchmarking page segmentation algorithms[END_REF] [10] [14] [15] by utilizing the intersection area as a matching criteria. They are, therefore tributary of intersections between objects which, when they are multiple and complex, can be hard to match. In the case of an object being represented by pixel intervals, the overlap of interval pairs is used [START_REF] Clausner | Scenario driven in-depth performance evaluation of document layout analysis methods[END_REF] [6] [7] [START_REF] Seo | Performance evaluation tools for zone segmentation and classification (pets)[END_REF] to generate the overlap matrix of intervals (matching or not) used to deduce segmentation errors.

To qualify segmentation errors, 5 types of segmentation errors which are the most frequent, as described in [START_REF] Randriamasy | Benchmarking page segmentation algorithms[END_REF], are: noise assimilated to an object (False alarm), object from the ground truth missed (Miss), object oversegmentation (Split), object under-segmentation (Merge), simultaneous object over-and under-segmentation (Split & Merge). Liang et al. [START_REF] Liang | Performance evaluation of document structure extraction algorithms[END_REF] use different terms to classify segmentation results based on relations cardinality which convey the same effects: one-to-one (Match), one-to-zero (Miss), zero-to-one (False Alarm), one-to-many (Split), many-to-one (Merge), many-to-many (Multiple errors).

The ZoneMap algorithm [START_REF] Galibert | The zonemap metric for page segmentation and area classification in scanned documents[END_REF] and the PETS tool [8] consider objects classification errors in their metrics in addition to the layout assessment. They allow us both to evaluate jointly the segmentation and the object classification. Penalties are assigned to compared objects that do not have the same class. A more recent method [START_REF] Coteand | Layered ground truth: Conveying structural and statistical information for document image analysis and evaluation[END_REF] proposes to combine the object-based approach with the pixel-based approach by using a hierarchical structure of the ground truth. Objects are divided into sub-objects called elemental patterns (parts of objects) which allows one to assess them at pixel level and also to evaluate objects from the results of each of their elemental patterns.

The method we propose in this paper is object-based. It faces the same segmentation error types cited in [START_REF] Liang | Performance evaluation of document structure extraction algorithms[END_REF]. It corrects the limits of the ZoneMap algorithm using a new reliable matching method which considers previously matched objects to avoid counting several time the same intersection area. It also allows us to assess more complex segmentation errors by enabling many-to-many associations. The ZoneMap metric and its limits are further described in Section III.

III. ZONEMAP ALGORITHM AND LIMITS

A. ZoneMap Algorithm

Let L = {h i , r j }, i, j ∈ R be the set of links between pairs of RZs and HZs.

The ZoneMap algorithm acts in three steps: first, force links are computed between intersecting zones, then, zones are grouped based on these links. Finally, zone groups are classified by their configuration from which the error score E ZoneM ap is computed.

1) Computing Link Force: Links are computed for each intersecting zone between RZs and HZs. The link force between r i and h j is given by the equation 1: Figure 3 illustrates the link force variation for several zones configurations.

Link(r i , h j ) = ( r i ∩ h j r i ) 2 + ( r i ∩ h j h j ) 2 (1)
2) Zone Grouping: The goal of the second step is to associate RZs with HZs to form groups. Only non-zero link forces are retained. Links are sorted in decreasing order of force. For each link l which associates the zones r i and h j : If r i or h j is in a group (not both at the same time) then we insert the zone that does not belong to a group into the group of the other one. If r i and h j do not belong to a group, we create a new group that contains both.

Inserting a zone into a group can only succeed if the final group does not contains more than one RZ and more than one HZ at the same time (i.e. many-to-many matching not allowed). If a zone could not be inserted, nothing will be done. At the end of this step, zones that do not belong to any group are considered missing if it is a RZ, or falsely detected if it is a HZ.

3) Computing the E ZoneM ap : The next step is to compute the error E k of each group k in leading to the global error E ZoneM ap given by the equation 2.

E ZoneM ap = 100 × N k=1 E k area(R) with E k = (1 -α c )E s + α c E c (2)
E s is the surface error while E c is the classification error of the zone. α c ∈ [0,1] is the weight given to the classification error to adjust the influence of segmentation and classification during the evaluation. The calculation of E s and E c depends on the group configuration.

Let H k be a set of HZs and R k be a set of RZs that belong to the k th group. A set of groups is obtained where each group is in one of the following configurations:

1) False Alarm: The group contains only one HZ. It means this zone has no match with RZs, therefore the system has over-detected this zone.

E s = area(H k ) (3a) E c = E s (3b)
2) Miss: The group contains only one RZ. It means that this zone has no match with HZs, therefore the system has under-detected this zone.

E s = area(R k ) (4a) E c = E s (4b)
3) Match: The group contains only one HZ and one RZ.

E s = area(H k ∪ R k -H k ∩ R k ) (5a) E c = d(t H , t R ) × area(H k ∩ R k ) + E s (5b) d(t H , t R ) ∈ [0, 1]
is the distance between the two zone classes. 4) Split: The group contains only one RZ and more than one HZ. It means that the RZ has been segmented into several parts. α M S ∈ [0, 1] is the split/merge coefficient and

|H k | is the cardinality of H k . E s = area(H k ∩ R k ) * α M S * |H k | (6a) E c = (|H k |-1+min hj ∈H k d(t H , t R ))×area(H k ∩R k ) (6b) 5
) Merge: the group contains more than one RZ and one HZ. It means that RZs have been merged. The calculation of the fusion error is the same as for the split, but with HZ and RZ inverted. When the score E ZoneM ap is equal to zero its means that there is no error.

A E ZoneM ap score can be above 100 when there are a lot of False Alarm errors. In this case, the total erroneous surface can be superior to the sum of RZs area.

B. Limits of the ZoneMap Metric

As said in the introduction, the ZoneMap algorithm is not suited to handle complex segmentation errors (multiple split and/or merge errors). Moreover, it does not always deduce the correct type of segmentation error when there are intersections between RZs. Two limits arise. The first is about not taking into account existing reference intersections (RI L ) and assigning zones without a minimum intersection. Figure 4 illustrates the segmentation of RI L . Zones represented by letters are RZs and zones represented by numbers are HZs. The results of the ZoneMap algorithm in Table I show that h 1 merges r A and r B . This error relates an association of the zones without taking into account the associations previously carried out. Regarding h 1 and r A , their intersection is assimilated to their matching. Therefore, this intersection area cannot be used again to match with another zone for both participating zones. When trying to match h 1 with r B , one should remove from h 1 the previously used intersection area before trying to match it with r B . The dark area in Figure 4 corresponds to the intersection area of r A and r B and is responsible for the match of h 1 with r A and r B . The algorithm should match r A with h 1 and inform us that r B has been missed. The second limit describes the inability of the algorithm to perform many-to-many (M T M L ) associations. Figure 5 represents the segmentation of M T M L . Table II contains the results for this limit and shows that h 1 matches with r A and h 2 matches with r B . This result is not acceptable since all zones are interconnected. The result should translate the fact that h 1 merges r A and r B but also segments r A and r B . It should be the same for h 2 . However, the results produced by ZoneMap are far from the ideal error classification. The impossibility of making many-to-many associations limits the possible outcomes and therefore the accuracy of the evaluation. We propose to improve the ZoneMap metric by proposing a new algorithm that handles the limits previously described. The proposed approach is reported in Section IV.

IV. ZONEMAPALT

Let L = {h i , r j }, i, j ∈ R be the set of processed links (also called validated). The Algorithm 1 illustrates the proposed matching technique. The aim of this algorithm is to take care of intersection between RZs. This is done by considering compared zones only once. Considering RI L of ZoneMap, the intersection between r A and h 1 can only be counted once. Counting the intersection area only once disallows other zones to be matched with a part of a zone that has already been used in a match. Therefore, intersections between r A and h 1 should be removed from both zones for the next matches. One important characteristic of ZoneMapAlt is its ability to perform many-to-many zone alignments. Indeed, it allows the identification and analysis of complex segmentation errors that are critical for the application.

The principle of the ZoneMapAlt algorithm is as follows ((line x) is a line reference in the algorithm):

• For each link, there are 3 main conditions: 1) (line 7-12) If h j is associated with at least one RZ. In this case, the union of all r k (U r ) associated with h j is computed. Then, the intersection of h j with U r is subtracted from h j . Also, the intersection of r i with U r is subtracted from r i . 2) (line 13-17) If r i is associated with at least one HZ. In this case, the union of all h m (U h ) associated with the r i is computed. Then, the intersection of r i with U h is subtracted from r i . 3) (line 18-26) If the intersection of r i and h j relatively to r i is above a threshold β, the association is accepted. The link between the two polygons is marked with the cardinality of the relation (that is, the number of r i and h j for this relation). For each matched zones, sub-zones have been extracted to use only intersecting areas. This can lead to remaining sub-zones that have not been used at all. These sub-zones are a Miss if it is a RZ and a False Alarm if it is a HZ. To determine if a zone (target zone) has been missed or falsely detected, one can remove successively from the target zone each zone, that been matched with it. If the resulting area is above zero, then it is a remaining zone that must be added in a single group.

A new configuration called Multiple that characterizes an area that has suffered several segmentation errors has been introduced. This case might happen depending on the segmentation algorithm performances and the structure of the surface analyzed. In order to heavily penalize this configuration, the erroneous surface is multiplied by a coefficient γ M ∈ [0; 1] as well as by the number of zones concerned. The surface error of a Multiple segmentation error zone is given by the equation 7. The classification error in this configuration is done by the equation 8

E s = area(R k ∩ H k ) * γ M * |R k + H k | (7)
E c = (|H k + R k | -2 + min h∈H k ,r∈R k d(t H , t R )) (8)
A user threshold β ∈ [0, 1] has been introduced to determine whether the intersection is important enough relatively to the RZ. It is set empirically to 0.2 and works well on text lines. When this threshold is set to 0, the algorithm maximizes the amount of associated zones. It means that an intersection of one pixel is enough to associate two zones together. The main consideration is that a zone can be responsible for several errors and the zones with the strongest links are considered to have priority over the association.

V. METRICS VALIDATION

A. Solving the Limiting Cases

To evaluate the ZoneMapAlt algorithm, we compared its result with ZoneMap on the two identified limits. The results obtained by ZoneMapAlt on Figure 4 and Figure 5 are shown in Table III and Table IV. All experiments were performed with the user threshold β equal to 0.2.

Regarding the results on both limits, the ZoneMapAlt provides more details on segmentation errors. In fact, for RI L , the r B is correctly classified as a missed zone instead of getting assigned to the group containing r A and h 1 . M T M L is more complex, more details can be observed by ZoneMapAlt algorithm. The best match (r A and h 1 ) is used as a match classification type then the next ones are classified regarding what classification was done previously. This allows penalizing heavily one zone that is at the end of the list so that it conveys the complexity of the segmentation error.

B. Real Case Example

To validate ZoneMapAlt, a real case example is discussed (see Figure 2a for its RZs and in Figure 2b for its HZs). Figure 6 shows the visual detection of the Multiple class. When many-to-many associations are possible, it means that at least one area connects the other ones (ambiguous case) otherwise it would be a split or merge. Since configuration Multiple is based on many-to-many associations, it identifies areas that are responsible for the severe errors. These errors are severe because areas involved contain not only the information concerning their line but also the adjacent lines which will make it difficult to recognize.

C. ZoneMap and ZoneMapAlt Comparison

In order to compare ZoneMap and ZoneMapAlt a common dataset is used. The goal is not to evaluate one segmentation method on a specific dataset but to compare the E ZoneM ap differences between the two methods. This is why the dataset was created locally from INIST1 collections. It is composed of 97 single-page and multicolumn articles with headers, footnotes and references. These are documents with a very simple physical structure with few output variations. They are issued by several publishers and from several sources. They represent scientific articles in French, English, German and Spanish, from several different times (from 1942 until 2000), with different fonts. To perform the experiments, the OCRopus OCR [START_REF] Breuel | The ocropus open source ocr system[END_REF] segmentation algorithm was selected.

The comparison of E ZoneM ap scores between ZoneMap and ZoneMapAlt algorithms are shown in Table V. The main difference between the two scores is that ZoneMap classifies zones as Missed and False alarmed when ZoneMapAlt classify them as Split, Merge or Multiple. This can be observed with the increase of E ZoneM ap score in the second limiting case. Indeed, for the ZoneMap algorithm on M T M L there are two Match therefore remaining areas are Missed and False alarm while ZoneMapAlt produces Match, Split, Merge and Multiple with also some Miss and False alarm. The introduction of the type Multiple can only increase the E ZoneM ap as in this case the surface error is greater than any other configuration types. On the other hand, as shown by the first limiting case, missed RZs that are touching other RZs will no longer be assigned to their adjacent neighbors as long as the overlapping ratio between zones (Algorithm 1 line 18) is above β. In this case, the E ZoneM ap will decrease because a Missed is less severe than a Split. number of matched zones is maximized. When β = 1, the number of matched zones is minimized. One can observe that when β increases the number of Multiple errors decreases, which means that the remaining intersection between two zones is not sufficient to associate them together. Moreover, when the number of matches decreases, the number of false alarms and misses increase. It does not increase for the same amount of error because when a zone has a missed and a match part, when the match is removed the number of miss stay the same.

D. Influence of β Parameter

VI. CONCLUSION

In this paper, we proposed a new metric ZoneMapAlt based on the ZoneMap metric. This metric allows one to perform the evaluation of a segmentation algorithm. It takes into account the segmentation and classification of zones jointly. A user threshold β is introduced to control the matching sensitivity of the algorithm which makes the algorithm flexible. A new segmentation error type called Multiple is used to qualify the zones responsible for several errors and allows many-to-many matches. The experiments show that ZoneMapAlt provides more information on segmentation errors than ZoneMap, classifies them more accurately and is able to find zones that produce critical errors.

In the future, we plan to combine the ZoneMapAlt matching process with hierarchical pixel-based methods to allow even more precise evaluations.

Figure 1 :

 1 Figure 1: Segmentation errors at line level. HM is horizontal merge. HS is horizontal split. VM is vertical merge. VS is vertical split.

  (a) Ground truth segmentation at line level (b) System segmentation at line level

Figure 2 :

 2 Figure 2: Example of (a) ground truth segmentation and (b) system segmentation.

Figure 3 :

 3 Figure 3: Example of link force values depending on the configuration of the zones.

Figure 4 :

 4 Figure 4: ZoneMap RI L . In green, RZs. In red, HZs

Figure 5 :

 5 Figure 5: ZoneMap M T M L . In green, the RZs. In red, the HZs

begin

  Compute links L Sort links by descending order forL k ∈ L do hj ←-L k .h ri ←-L k .r if ∃ r | {L k .h, r} ∈ L then // Remove reference association Ur ←-∀r k |{L k .h,r k }∈L r k hj ←-hj -(hj ∩ Ur) ri ←-ri -(ri ∩ Ur) Conf.M erge ← card(∀r k | {L k .h, r k } ∈ L ) end if ∃ h | {h, L k .r} ∈ L then // Remove hypothesis association U h ←-∀hm|{hm,L k .r}∈L hm ri ←-ri -(ri ∩ U h ) Conf.Split ← card(∀hm | {hm, L k .r} ∈ L ) end if (area(hj ∩ ri)/area(ri)) > β then if not Conf.Split & not Conf.Merge then Conf.M atch ←-1 end ComputeError(conf ,ri,hj) L k ∈ L end end end Algorithme 1 : ZoneMapAlt AlgorithmTable III: ZoneMapAlt results on RI L . Group # Reference zone(s) Hypothesis zone(s

Figure 6 :

 6 Figure 6: ZoneMapAlt result on a real example showing Multiple segmentation error class.

Figure 7

 7 Figure7shows the number of classification errors depending on the β parameter value. When β = 0, the

Figure 7 :

 7 Figure 7: Number of match, miss, false alarm, split, merge and multiple errors for the whole range of value of β.

Table I :

 I Results of ZoneMap on RI L .

	Group # Reference zone(s) Hypothesis zone(s) Segmentation type
	1	A, B	1	Merge

Table IV :

 IV ZoneMapAlt results on M T M L .

	Group # Reference zone(s) Hypothesis zone(s) Segmentation type
	1	A	1	Match
	2	B	1,2	Split
	3	A,B	2	Merge
	4	A,B	1,2	Multiple

Table V :

 V Average comparison of ZoneMap and ZoneMapAlt algorithms on 97 documents.

	Method	E ZoneM ap	Match	Miss	False Alarm	Split	Merge	Multiple Total Error
	ZoneMapAlt	15,42	3 120 647	99 738	186 214	1 543	215 783	24 640	527 918
	ZoneMap	14,57	3 120 647 111 926	216 526	4 484	176 033	0	508 969
	ZoneMapAlt -ZoneMap	0,85	0	-12 188	-30 312	-2 941	39 750	24 640	18 949

Institute for scientific and technical information, Nancy, France


Michael Reinwald
email: michael.reinwald@upmc.fr

Quentin Grimal
email: quentin.grimal@upmc.frc

Jacques Marchal
email: jacques.marchal@upmc.frd

Stefan Catheline
email: stefan.catheline@inserm.fre

Lapo Boschi
email: lapo.boschi@upmc.fr

Bone-conducted sound in a dolphin's mandible: Experimental investigation of elastic waves mediating information on sound source position

Mammals use binaural or monaural (spectral) cues to localize acoustic sources. While the sensitivity of terrestrial mammals to changes in source elevation is relatively poor, the accuracy achieved by the odontocete cetaceans' biosonar is high, independently of where the source is. Binaural/spectral cues are unlikely to account for this remarkable skill. We study bone-conducted sound in a dolphin's mandible, investigating its possible contribution to sound localization. Experiments are conducted in a water tank by deploying, on the horizontal and median planes of the skull, ultrasound sources that emit synthetic clicks between 45-55 kHz. Elastic waves propagating through the mandible are measured at the pan bones and used to localize source positions via either binaural cues or a correlation-based full-waveform algorithm.

Exploiting the full waveforms and, most importantly, their reverberated coda, we can enhance the accuracy of source localization in the vertical plane, and achieve similar resolution of horizontal-vs. vertical-plane sources. Our results need to be substantiated by further experimental work, accounting for soft tissues and making sure that the data are correctly mediated to the internal ear. If confirmed, they would favor the idea that dolphin's echolocation skills rely on the capability to analyze the coda of biosonar echoes.

INTRODUCTION

The acoustic environment of marine mammals is very different from that of humans and other terrestrial mammals. Water is much denser than air, and sound travels five times faster through water than through air and is less strongly attenuated; the energy carried by acoustic waves is more efficiently transferred to bone tissue from water than from air; presumably because they would be disadvantageous from the point of view of locomotion in water, marine mammals have lost pinnae through evolution; their ear canals are typically filled with cellular debris and appear to play no functional role in hearing [START_REF] Ketten | Structure and function in whale ears[END_REF].

Marine mammals use echolocation to navigate and hunt. For about two centuries [START_REF] Hunter | Observations on the structure and oeconomy of whales[END_REF], they have been known to complete such tasks with remarkable accuracy and efficiency. The contribution of dolphin's anatomy to audition-related tasks was first evaluated by Kenneth Norris in a suite of groundbreaking studies (Norris, 1964 , 1968a , b; Norris and Harvey, 1974). A dolphin's mandible is very thin, almost "translucent," at its posterior end (0.5 mm to 3.0 mm thickness, depending on the species), and is overlain by an oval fatty volume, which connects the posterior jaw bone, also named pan bone, with the tympano-periotic complex (TPC). Norris suggested that sound propagates through the thin pan bone, entering the fats which possibly act as a low-impedance wave guide that directs sound towards the inner ear. This is still the most widely accepted theory of the sound propagation pathway for hearing in cetaceans [START_REF] Au | The sonar of dolphins[END_REF][START_REF] Au | Principles of marine bioacoustics[END_REF][START_REF] Brill | Assessment of dolphin (tursiops truncatus) auditory sensitivity and hearing loss using jawphones[END_REF][START_REF] Mooney | Hearing in cetaceans: from natural history to experimental biology[END_REF] and is supported by experimental [START_REF] Brill | Behavioral evidence for hearing through the lower jaw by an echolocating dolphin (tursiops truncatus)[END_REF][START_REF] Norris | Sound transmission in the porpoise head[END_REF] and numerical [START_REF] Aroyan | Three-dimensional modeling of hearing in delphinus delphis[END_REF] results. Norris' "jaw-bone theory" has been further developed in more recent studies: While high-frequency sounds could propagate through the jaw bone, low-frequency sounds (below 30 kHz) could propagate through bonefree fat channels just below the eyes and posterior to the lower jawbone [START_REF] Brill | Assessment of dolphin (tursiops truncatus) auditory sensitivity and hearing loss using jawphones[END_REF][START_REF] Ketten | Functional analyses of whale ears: adaptations for underwater hearing[END_REF][START_REF] Popov | Localization of the acoustic window at the dolphins head[END_REF]. Cranford et al. simulated sound propagation in the head of a Cuvier's beaked whale and introduced the idea of a "gular pathway" for sound reception [START_REF] Cranford | Acoustic pathways revealed: simulated sound transmission and reception in cuvier's beaked whale (ziphius cavirostris)[END_REF], with sound entering the head from below and between the mandibular walls rather than through the posterior mandible. Some studies propose that the teeth play an important role in sound reception; due to their periodic placement, they could act as an acoustic metamaterial, resonating and amplifying sound for specific frequencies [START_REF] Dible | On the role of periodic structures in the lower jaw of the atlantic bottlenose dolphin (tursiops truncatus)[END_REF][START_REF] Graf | Acoustic modelling of dolphin sound reception and implications for biosonar design[END_REF]. Others suggest that the morphology of the mental foramens found in the mandible helps sound enter the fatty tissues [START_REF] Ryabov | Role of the mental foramens in dolphin hearing[END_REF]. Møhl et al. [START_REF] Møhl | Dolphin hearing: relative sensitivity as a function of point of application of a contact sound source in the jaw and head region[END_REF] measured the auditory brainstem evoked potential for an Atlantic bottlenose dolphin by placing suction cups on various positions on the animal's head and emitting acoustic click stimuli via embedded piezoelectric transducer elements. Their results suggest that the area of maximum sensitivity is slightly forward of the pan bone area. This does not contradict Norris' jaw bone theory since the outer mandibular fat channel extends forward to the skin and towards the area where Møhl et al. found sensitivity to be highest.

It has been suggested by experiments [START_REF] Blauert | Spatial hearing: the psychophysics of human sound localization[END_REF][START_REF] Moore | Interaural time and intensity difference thresholds in the bottlenose dolphin (tursiops truncatus)[END_REF][START_REF] Renaud | Sound localization by the bottlenose porpoise tursiops truncatus[END_REF] that dolphins locate sound sources via binaural cues known to be employed by terrestrial animals, i.e. interaural time differences (ITD), which describe the delay of a signal arriving at the two ears at two different times, and interaural level differences (ILD), which describe the difference in intensity between the signals perceived at the two ears.

While ITD are relatively easy to reproduce theoretically, ILD effects are more complex, as they cannot be modeled by simply accounting for differences in source-receiver distance: they are importantly affected by sound shadowing due to the impedance mismatch between the subject's head and the surrounding propagation medium [START_REF] Mooney | Hearing in cetaceans: from natural history to experimental biology[END_REF], while a significant fraction of acoustic energy traveling from one ear to the other is diffracted by the head's surface, thus following a complex propagation path. In any case, binaural cues are only relevant as long as a sound originates from somewhere else than the median plane.

Because median-plane sources are equidistant from both ears, no phase or amplitude (if the subject's anatomical features are symmetric with respect to the median plane, as they most often are) differences exist between the signals perceived at the two ears, i.e. zero ITD and ILD (e.g. [START_REF] Butler | Binaural and monaural localization of sound in two-dimensional space[END_REF][START_REF] Hartmann | How we localize sound[END_REF]. ITD and ILD are naturally nonzero whenever the source is not on the median plane, so that the ears lay at different distances from the source.

The only (rare) cases of median-plane sources generating nonzero ITD/ILD are species characterized by asymmetrically positioned ears, e.g., the barn owl [START_REF] Keller | Head-related transfer functions of the barn owl: measurement and neural responses[END_REF].

Other species, including humans, are not very effective at differentiating sound source positions within the median plane [START_REF] Butler | Monaural and binaural localization of noise bursts vertically in the median sagittal plane[END_REF][START_REF] Heffner | Evolution of sound localization in mammals[END_REF][START_REF] Van Opstal | The auditory system and human sound-localization behavior[END_REF], or, more generally, within a "cone of confusion" (e.g. [START_REF] Van Opstal | The auditory system and human sound-localization behavior[END_REF]. Their (limited) ability at this task must be explained in terms of non-binaural cues (e.g., acoustical clues not simply related to a difference between right and left signals). It has been suggested that sound-localizing animals learn to interpret certain acoustical cues associated with their anatomy in order to solve this ambiguity [START_REF] Batteau | The role of the pinna in human localization[END_REF][START_REF] Blauert | Sound localization in the median plane[END_REF]Hart-mann, 1999;[START_REF] Macpherson | Vertical-plane sound localization with distorted spectral cues[END_REF][START_REF] Van Opstal | The auditory system and human sound-localization behavior[END_REF]. Anatomy can be thought of as a spectral filter (the head-related transfer function, or HRTF), which will change depending on source position: because the back of our head is different from our face, it interacts differently with an incoming wave field, which consequently sounds different to our ears.

The HRTF associated with a human skull has been found to provide, in principle, sufficient information for a source to be localized with fairly high accuracy, independent of the location of the source, even when data from only one ear are used [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF]; yet, psychoacoustics studies [START_REF] Van Opstal | The auditory system and human sound-localization behavior[END_REF] have shown that the performance of the, e.g., human ear-brain system at localizing median-plane sources is relatively poor: we are much more effective at discriminating sources within the horizontal plane. Other terrestrial species show the same limitations. It has also been found experimentally that humans are relatively poor at source localization tasks if only one ear is used; subjects with unilateral hearing loss apparently learn to function with one ear only, but their performance at sound localization has been found to remain significantly poorer than that of subjects with no hearing loss [START_REF] Agterberg | Improved horizontal directional hearing in bone conduction device users with acquired unilateral conductive hearing loss[END_REF][START_REF] Van Opstal | The auditory system and human sound-localization behavior[END_REF]. It is inferred that, while humans and other terrestrial species certainly use HRTF information in sound-localization tasks, they exploit only a subset of the information provided by the HRTF itself. The consensus is that the only monaural cues that they are actually capable of using are certain "notches" of the frequency spectrum perceived by the ears, or "spectral cues," whose amplitude, and location along the frequency axis, are controlled by the complex shape of the pinnae and depend on the position of the source (Van Opstal, 2016, Chapter 7).

Cetaceans are also characterized by a salient HRTF [START_REF] Aroyan | Three-dimensional modeling of hearing in delphinus delphis[END_REF][START_REF] Au | Hearing by whales and dolphins[END_REF][START_REF] Supin | Direction-dependent spectral sensitivity and interaural spectral difference in a dolphin: Evoked potential study[END_REF]; how and to what extent they make use of it, is still unclear. Simple physical considerations suggest that anatomical features characterized by relatively strong density contrasts with respect to the surrounding medium (water) most significantly contribute to characterizing the HRTF, and thus to sound localization. Since the density of soft tissues found in marine mammal bodies is close to that of water [START_REF] Norris | Sound transmission in the porpoise head[END_REF][START_REF] Reysenbach De Haan | Hearing in whales[END_REF], it is inferred that features such as the mandible, the cranium or small air sacs play the most important roles, similar to the external ears of terrestrial mammals [START_REF] Aroyan | Computer modeling of acoustic beam formation in d elphinusdelphis[END_REF][START_REF] Song | The influence of airfilled structures on wave propagation and beam formation of a pygmy sperm whale (kogia breviceps) in horizontal and vertical planes[END_REF][START_REF] Wei | The role of various structures in the head on the formation of the biosonar beam of the baiji (lipotes vexillifer)[END_REF]. One important difference in the sound localization performance of terrestrial mammals vs cetaceans is the latter's ability to localize sound sources within the median plane with a very high accuracy [START_REF] Renaud | Sound localization by the bottlenose porpoise tursiops truncatus[END_REF]. This can be quantified by the minimum audible angle (MAA), i.e., the minimum angular distance between two sources of sound, still allowing to discriminate them as two different sources. Signals emitted by two sources separated by an angle smaller than the MAA are perceived as coming from only one source. The MAA changes depending on the azimuth and elevation of the sources, and on the nature of the emitted signal. By studying the behavior of live dolphins when exposed to sound coming from different locations, their MAA in the median plane has been estimated around 0.7 • for broadband clicks. Similar values are observed for sources positioned on the horizontal plane [START_REF] Au | Principles of marine bioacoustics[END_REF][START_REF] Nachtigall | Biosonar and sound localization in dolphins[END_REF]. In comparison, psychoacousticians estimate the MAA of human subjects at around 7 • in the vertical plane, as opposed to only ∼ 1 • in the horizontal one [START_REF] Nachtigall | Biosonar and sound localization in dolphins[END_REF], while other terrestrial mammals perform more poorly than humans (Heffner and Heffner, 2016, Figure 3). It can be inferred from these observations that, when echolocating, dolphins are capable of extracting from their HRTF more information than terrestrial mammals in sound localization tasks [START_REF] Branstetter | Sound localization by cetaceans[END_REF]. The acoustic environment of cetaceans would indeed favor animals capable of localizing sound, whether it be emitted or reflected from prey or predators, regardless of their position in space. Dolphins' MAA grows to 2.3 • -3.5 • for narrow-band signals [START_REF] Au | Principles of marine bioacoustics[END_REF][START_REF] Nachtigall | Biosonar and sound localization in dolphins[END_REF], which do not mimic typical echolocation clicks.

This study addresses the question of how a dolphin's head inner anatomy may contribute to sound localization, and in particular to echo-localization, by means of a suite of physical acoustics experiments conducted on one skull specimen of short-beaked common dolphin (Delphinus Delphis). The HRTF of the short-beaked common dolphin has so far only been addressed in a limited number of studies. Most of our previous knowledge results from numerical models; Krysl and Cranford carried out vibroacoustic simulations on a CT scan of a full head of a common dolphin showing single-frequency HRTFs for 5.6 kHz, 22.5 kHz and 38 kHz [START_REF] Krysl | Directional hearing and head-related transfer function in odontocete cetaceans[END_REF]. In their work, single-frequency HRTFs were equivalent to amplitude or intensity variations with respect to the source position. They simulated sound pressure levels at two virtual positions on the surface of the TPCs (one dorsal, one ventral), caused by monochromatic plane waves traveling along a suite of different azimuths and elevation angles. Strong variations in modeled data were found between the dorsal and the ventral receiver positions. The spatial pattern of the HRTFs was also found to depend strongly on the source frequency used. The results were not conclusive as to what extent the calculated asymmetries in the receiving pressure pattern were due to the inexact placement of the receivers, versus asymmetries in the specimen's anatomy. Another, similarly minded study [START_REF] Aroyan | Three-dimensional modeling of hearing in delphinus delphis[END_REF] showed that the mandible and its surrounding fats focus acoustic waves toward the TPC, therefore playing an important role in sound conduction through the head. Receptivity patterns at two virtual ear positions showed high asymmetry and complexity, and varied significantly depending on which parts of the head were simulated.

In our experimental study, we attempt to evaluate the specific contribution of bone conduction to sound localization. To this goal, we conduct experiments on a dolphin's skull specimen immersed in water, in the absence of soft tissues. It has been suggested (e.g., [START_REF] Aroyan | Three-dimensional modeling of hearing in delphinus delphis[END_REF][START_REF] Mccormick | Sound conduction in the dolphin ear[END_REF][START_REF] Song | Inducing rostrum interfacial waves by fluid-solid coupling in a chinese river dolphin (lipotes vexillifer)[END_REF][START_REF] Wei | A numerical evidence of biosonar beam formation of a neonate yangtze finless porpoise (neophocaena asiaeorientalis)[END_REF] that bone conduction affects significantly the dolphin's HRTF. Bone conduction seems to be a driving force for hearing mechanisms in baleen whales [START_REF] Cranford | Fin whale sound reception mechanisms: skull vibration enables low-frequency hearing[END_REF]. Despite the isolation of the skull from the TPC, Ketten also theorized some influence of bone conduction in dolphin hearing, i.e., on sound reception pathways [START_REF] Ketten | Cetacean ears[END_REF]. Cranford et al. suggested that a complex wave propagation pattern including flexural waves along the mandible bone of a Cuvier's beaked whale might contribute to the received pressure at its two ears [START_REF] Cranford | Acoustic pathways revealed: simulated sound transmission and reception in cuvier's beaked whale (ziphius cavirostris)[END_REF]. In summary, while it is likely that the mandible plays an important role in this context, the exact nature of its contribution to sound localization remains to be determined.

Using accelerometers glued to the pan bone, we measure elastic waves traveling through a mandible specimen immersed in water; we record the signal generated by different sound sources, positioned at many different locations within a large water tank; we measure the ITD and ILD (binaural cues) resulting from such recordings and estimate their potential performance as source-localization cues. Finally, we study in much detail how the wave-(known in physical acoustics as "acoustic time reversal" [START_REF] Fink | Time-reversed acoustics[END_REF]) to numerically reconstruct the location of sources via full-waveform data. In this endeavour, we take the standpoint of physicists, attempting to quantify the information carried by our data, independent of how these would be received and processed by the auditory system of a living organism. Our main goal is to contribute some new information on the potential contribution of certain features of dolphins' skulls (in particular, their mandible) to sound localization performance.

II. EXPERIMENTAL SETUP & DATA ACQUISITION

All our experiments are conducted on the skull (cranium and mandible) of a male adult short-beaked common dolphin, shown in Figure 1a. The skull is ∼50 cm long and ∼20 cm wide. The specimen was acquired on loan from the French National Museum of Natural His-

c(t) = sin [φ 0 + 2πf t] w(t), (1)
where φ 0 denotes the initial phase of the signal, f =45 kHz and w(t) is a Tukey window [START_REF] Harris | On the use of windows for harmonic analysis with the discrete fourier transform[END_REF], which has a total duration of 100 µs and tapers the first and the last 15 µs of the signals, to ensure their smooth on-and offset;

2. a linear chirp

c(t) = sin ϕ 0 + 2π(f 0 t + k 2 t 2 ) w(t), (2)
with minimum frequency f 0 =45 kHz, maximum frequency f 1 =55 kHz, chirpyness (i.e., rate of frequency change across the chirp) k= f 1 -f 0 t , and w(t) the same Tukey window as above.

The The entire experiment was repeated three times, including setup and wiring, in order to check consistency and minimize the effect of random errors. All measurements presented in the following are obtained by averaging the outcomes of the three experiments, for each combination of source and receiver positions. The associated standard deviation is used as an estimate of measure uncertainty. Throughout this study, we dub "direct" signal the waveform defined by Equations 1 or 2, as it is recorded at the accelerometers after having propagated through water and bone, and being accordingly attenuated. We dub "reverberated" the signal recorded after the direct signal, refracted, reflected, diffracted by and through bone tissue. The so defined reverberated signal is, alone, always longer than Au et al.'s estimate of ∼250 µs for a dolphin's integration time [START_REF] Au | Detection of complex echoes in noise by an echolocating dolphin[END_REF]. For the sake of simplicity, we neglect reverberations occurring before the end of the direct signal;

visual inspection (e.g., Figure 4) shows that their effect is indeed minor, compared to the complex, relatively long coda.

III. ITD-AND ILD-BASED SOURCE LOCALIZATION

We define ITD as the onset time of the direct signal measured at the left accelerometer minus the onset time of the same signal, measured at the right accelerometer. We measure the ITD associated to all our recordings of horizontal-and median-plane sinusoidal sources (Equation 1). This is done by means of a matlab routine that identifies the shape of the source signal in the recorded signal through cross correlation. We show in Fig. 5 the results of this exercise, as functions of source azimuth (if the source is on the horizontal plane) or elevation (if on the vertical plane). For median-plane sources, the ITD should be approximately zero; measured values of ITD accordingly never exceed 6 µs, corresponding to an error of 0.9 cm in space. For horizontal-plane sources, by simple geometrical considerations and neglecting HRTF-related diffraction effects (which is reasonable given the absence of soft tissues in our experiment), ITD is expected to approximately coincide with

ITD(ϕ) = (a/c) sin(ϕ), (3)
where a is inter-receiver distance and c the speed of sound in water. Again, Figure 5 shows a good agreement between our data and theoretical predictions. Importantly, our measure of ITD should not be taken as an estimate of ITD as perceived by live dolphins, which might be significantly affected by the presence of soft tissues and other anatomical features.

We define ILD as the ratio of the maximum amplitudes (Figure 6) of the direct signal as recorded by left vs. right receivers, in dB, i.e., where, for the sake of clarity, the signal s is explicitly written as a function of source azimuth and elevation, and receiver position (its only possible values being r L , r R for left and right receiver, respectively). Although other definitions of ILD have been proposed, e.g. in the field of robotics [START_REF] Youssef | Towards a systematic study of binaural cues[END_REF], Equation 4has been used in similar bioacoustic research [START_REF] Moore | Underwater localization of pulsed pure tones by the california sea lion (z alophuscalifornianus)[END_REF] and can be interpreted similarly to peak values of electrophysiological audiograms [START_REF] Mulsow | Interaural differences in the bottlenose dolphin (tursiops truncatus) auditory nerve response to jawphone click stimuli[END_REF][START_REF] Supin | Direction-dependent spectral sensitivity and interaural spectral difference in a dolphin: Evoked potential study[END_REF]. We cannot relate our ILD observations to a simple theoretical model as for the ITD, because of (i) the inherent complexity of waveforms resulting from multiple reverberations within the pan bone, and

ILD(ϕ, ϑ) = 20 log 10 max [s(ϑ, ϕ, r L , t)] max [s(ϑ, ϕ, r R , t)] [dB], (4)
(ii) our neglect of anatomical features, other than the mandible and skull bones, including cranial air sacks, the albuminous foam (which separates the middle and inner ear from the skull) and acoustically functional fats, that are likely to contribute to ILD [START_REF] Ketten | The marine mammal ear: specializations for aquatic audition and echolocation[END_REF][START_REF] Supin | Direction-dependent spectral sensitivity and interaural spectral difference in a dolphin: Evoked potential study[END_REF] and, interestingly, introduce significant dispersion [START_REF] Aroyan | Three-dimensional modeling of hearing in delphinus delphis[END_REF]. Also, because our setup does not account for such complexity, our data cannot be directly compared to experimental data or realistic numerical ILD models. Figure 7 shows our measures of ILD, derived from waveform data via Equation 4, as a function of source azimuth and elevation.

As expected, ILD values associated with median-plane sources are close to 0, with fluctuations of less than 2 dB. For horizontal-plane sources, the ILD ranges between 18 dB and -18 dB, changing most rapidly directly in front of the dolphin's beak, at ϕ between -10 • and 10 • . In this range of ϕ, ILD decreases from 13 dB down to -12 dB, losing more than 1 dB per degree. This is an effect of sound shadowing by bone tissues, as the receiver at x L loses direct acoustic sight of the sound source when this is rotated to the opposite side of the mandible. At larger, positive or negative, azimuths, the ILD grows less rapidly, at a rate of less than 1 dB per degree, and fluctuations (standard deviation) up to ±2 dB.

The results in Figures 5 through 7 are not new or surprising per se, but confirm some simple, well known properties of all binaural auditory systems. Importantly, the left-right symmetries of our data and the fit between data and a simple ITD model confirm that our setup is correct, and adequate to the applications that follow.

IV. CORRELATION-BASED SOURCE LOCALIZATION

Waves that interact with a complex HRTF carry a great wealth of information, that could in principle be exploited to localize their sources. Both binaural and monaural cues discussed so far only exploit a small portion of such information. While it has been established that humans and other terrestrial species localize via those cues alone, the echolocation performance observed in dolphins suggests that their auditory system might include a more sophisticated localization mechanism. We implement a simple algorithm to localize sources, based on the time-reversal concept developed by Mathias Fink and co-workers (e.g., [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF][START_REF] Fink | Time-reversed acoustics[END_REF].

A. Accuracy of source localization by correlation

We conduct a "time-reversal" exercise based on the theoretical formulation developed in the appendix. Specifically, we implement the right-hand side of Equation A.5 and study its effectiveness as a source-localization algorithm. As explained in detail in the appendix, in the context of echolocation "time reversal" as defined e.g. by Catheline et al. [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF] is equivalent to a simple correlation of each newly perceived signal with a library of echoes previously heard and "stored." Accordingly, pairs of traces s(r R , r A , t), s(r R , r B , t) recorded at r R as described in Section II, are cross-correlated to one another, for all possible pairs of source locations r A , r B . The same is done for traces recorded at r L . As a result, for each source location r B , we obtain the correlation between the corresponding recorded signal and the signal associated to all other possible sources (r A ). Because it is closely related to how sharply a time-reversed wave field would focus at r B (see appendix), we dub it "focusing function". Since, in this study, we are looking at sources on the horizontal and median planes only, the focusing function depends on either ϑ or ϕ only; by definition, it is exactly 1 when both ϑ and ϕ are the same as those of the actual source.

For the sake of simplicity (and speed), cross correlation is implemented by first shifting each pair of signals to have zero lag, and then calculating the correlation between the shifted traces. Intensity differences between the two correlated signals are also irrelevant, as the convolution product is normalized so that the auto-correlation at zero lag equals 1.

We next visualize how well a source is localized by our algorithm as a function of its true location. This is shown in Figure 8 through 11 where the horizontal and vertical axes of each plot correspond to the azimuth ϕ 0 or elevation ϑ 0 of the true source and of all recorded sources (ϕ i ,ϑ i ). Specifically, focusing functions obtained based on the chirp-like source in the median plane are plotted in Figure 8, while Figure 9 shows the corresponding results for the sinusoidal source. By definition, values on the diagonal of all panels in both figures are 1; near the diagonal, correlations decrease monotonously in all panels; some relevant fluctuations are then observed in both figures for ϑ i far from ϑ 0 when both direct and reverberated signals are correlated, but not when the reverberated signal alone is considered. In the latter case, the focusing function is much sharper, particularly in the -50 • to 20 • elevation range, and its sharpness does not seem to depend on source elevation ϑ 0 .

To study how the resolution of our algorithm depends on the true source position in the median plane, we visualize (Figure 10a for the chirp-like source function, Figure 10b for the sinusoidal source function) the increment in ϑ needed for the focusing function to decrease to 70% of its maximum, i.e. the -3 dB width of the focusing function, which is a rule-of-thumb criterion frequently used in time-reversal acoustics [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF][START_REF] Ing | In solid localization of finger impacts using acoustic time-reversal process[END_REF][START_REF] Kim | Robust time reversal focusing in the ocean[END_REF]. The smaller the value of the -3 dB width, the higher the resolution, and the performance that can be expected in identifying the true source location. The value of 3 dB is of no particular physical or biological significance: it is only chosen in analogy with the mentioned studies. This is adequate to our goals, as we are not attempting to performance of our algorithm, as applied to a particular setup, via a suite of experiments.

The setup consists of two accelerometers installed on the mandible of a dolphin skull, fully immersed in a large water tank, and recording signals similar to a dolphin's echolocation "clicks."

We quantify the performance of our algorithm via the width of the the focusing function, or, in other words, the rate at which correlation decreases, as an observed signal is compared with library signals associated with sources increasingly far from the true one. We find that this width is significantly reduced (the rate of correlation loss is accelerated) when the direct signal, which is simply an attenuated version of the original chirp/sinusoidal burst, is subtracted from the recorded waveform before cross correlation. This way, only the reverberated coda, most strongly affected by the shape and properties of the skull, is actually employed in localization: localizing by reverberated signal alone (rather than the entire wavetrain) sharpens source resolution.

The spatial accuracy of source localization by dolphins has been observed, through behavioral experiments, to be equally accurate independent of source azimuth and elevation, i.e., it has approximately constant resolution over the entire solid angle [START_REF] Nachtigall | Biosonar and sound localization in dolphins[END_REF].

This property of dolphins is counter-intuitive, if one considers that humans and other species have presumably evolved pinnae to help determine the elevation of sound sources (Section I), while cetaceans have actually lost them. We infer that, to achieve such performance, the dolphin's auditory system might make use of a unique, and currently unknown localization tool, particularly effective for sources in the median plane or along the "cone of confusion."

Our results do not directly constrain the nature of the sound localization system implemented in a dolphin's brain; yet, they do show that signal reverberated within the dolphin's skull (with the mandible playing the most prominent role) varies significantly as a function of (that is to say, is very sensitive to) source location. The "direct" signal, i.e. signal without reverberation, appears to be much less sensitive to source location. We have shown that reverberated signal contains sufficient information to discriminate median-plane sources, and that this could be achieved by simply cross-correlating any newly perceived sound with a library of previously recorded data.

While our model shares with dolphins some relevant features, we are hardly reproducing the signals that would be perceived by actual, live specimens. Importantly, we conduct our experiments on the skull alone, neglecting the effects of muscles, fats, and other soft tissues.

While we plan to surpass this limitation in our future work, at this point we consider it to be partly justified, first, by the fact that acoustic waves propagate through soft tissues at about the same speed as through water (e.g., [START_REF] Gray | In vivo ultrasonic attenuation in cetacean soft tissues[END_REF][START_REF] Soldevilla | Cuvier's beaked whale (ziphius cavirostris) head tissues: physical properties and ct imaging[END_REF], which limits wave-propagation effects. Mandible and skull, on the contrary, provide a strong wave speed contrast (a factor of about two) resulting in significant diffraction, reverberation, etc. Cranford et al. show that the amplitude of perceived signals is significantly affected by the anatomical features of soft tissues in the head [START_REF] Cranford | Acoustic pathways revealed: simulated sound transmission and reception in cuvier's beaked whale (ziphius cavirostris)[END_REF], but we speculate that phase, more than amplitude, is relevant to source localization (correlation being mostly sensitive to phase). Secondly, the neglect of soft tissues allows us to isolate the specific effects of bone-conducted waves, before additional experiments are conducted on whole heads. In future studies, the issue of a dolphin's resolution of the fine features of acoustic signals with respect to time will also need to be addressed, taking into account e.g. the concept of cochlear integration time as defined by Au et al. [START_REF] Au | Detection of complex echoes in noise by an echolocating dolphin[END_REF]. Finally, we envisage to extend our analysis to a broader frequency range, whether by numerical modeling, or new experiments relying on better, currently unavailable hardware.

In summary, our results indicate that, within a good approximation, a one-to-one correspondence exists between the waveform of the bone-conducted, reverberated coda as recorded at a dolphin's ear locations, and the locations of the source (or, in principle, the reflecting target) that originally generated (or reflected) the signal. While we have no ulate that bone-conducted, reverberated sound could contribute to explaining the peculiar, poorly understood accuracy of sound localization in odontocete cetaceans.

its sign reversed (e.g. [START_REF] Fink | Time-reversal acoustics in complex environments[END_REF].

It is inferred that the Green's function between r A and r B can be reconstructed from an impulse emitted at r B and recorded at a set of points r that sample ∂V , by (i) time-reversing the signal G(r, r B , ω) emitted by r B and recorded at r; (ii) convolving the time-reversed signal G * (r , r B , ω) with the impulse response G(r A , r, ω) between r and r A ; (iii) iterating over all receivers r; (iv) summing the resulting signals. This procedure is usually referred to as "acoustic time reversal," because the wave field so obtained is essentially a time-reversed, backward propagated version of the original impulse response G [START_REF] Fink | Time-reversal acoustics in complex environments[END_REF]; as such, it

will naturally focus at the original source location, where it will show a very prominent maximum. An important consequence of this is that time reversal can be used as a source localization tool: if a signal generated by a source at an unknown location r B is recorded by an array of receivers forming a closed surface ∂V , by implementing numerically steps (i) through (iv) above and looking for the maximum of the resulting numerical wave field, the source location can be determined.

While in principle G is accurately reconstructed (the time-reversed wave field focuses at the original source location) only if recordings made at a dense, uniform array of receivers are time-reversed and backward propagated, many studies have shown that focusing can also be achieved using a much smaller receiver array, provided that the medium of propagation has some relevant 3-D structure, and that this structure is known and properly accounted for when modeling wave propagation. In particular, it was shown [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF] that a pair of receivers, deployed at ear locations on a human skull, are enough for the Note that the products at the right-hand side of Equation A.5 can be interpreted, in the time domain, as both the convolution of s(r L,R , r A , t) with the time-reversed counterpart of s(r L,R , r B , t), and the cross correlation of s(r L,R , r A , t) and s(r L,R , r B , t) [START_REF] Derode | Recovering the greens function from field-field correlations in an open scattering medium (l)[END_REF][START_REF] Draeger | One-channel time-reversal in chaotic cavities: Theoretical limits[END_REF]. As opposed to Equation A.4, the right-hand side of Equation A.5

does not allow one to reconstruct, from the data, the signal as originally emitted at r B (because (sr R,L , r A ) are unknown and cannot be computed). Equation A.5 can be relevant, however, if the time function h(t) is known, while the location of the source is to be determined. This applies, for instance, to echolocating species, that identify and analyze echoes of signals that they have themselves emitted. Echolocation can presumably be learned by training, which is equivalent to forming a "library" of observed echoes s(r R,L , r A ) associated with a given emitted signal and known target locations r A : each time a relevant signal is perceived, the echolocating agent would then systematically compare it to all recorded traces s(r R,L , r A ), each corresponding to a different value of r A eventually covering the entire solid angle. Imagine that this comparison be implemented via cross correlation: this is equivalent to implementing the right-hand side of Equation A.5, and the same equation implies that cross correlation should be maximum when r A =r B ; the sharpness of focusing at the source, and thus the accuracy of source localization, is strictly related to how well a timereversed, backward propagated wave field would focus at the original source. Importantly, however, the proposed algorithm does not involve any wave propagation modeling, but is based entirely on signal processing of measurements at two receivers.

  FIG. 1. (Color online) (a) Photograph of the sample (cranium and mandible) used in this study. (b)

  FIG. 3. (Color online) Source signals and their frequency spectra. The Tukey window function

  FIG. 4. (Color online) Examples of (top) signal as emitted at the source; (bottom) the same signal,

FIG. 5

 5 FIG. 5. (Color online) Measured ITD from our binaural recordings of sources deployed on the

FIG. 6

 6 FIG. 6. (Color online) Maximum amplitudes recorded at the left (black) and right (red) receivers

FIG. 7

 7 FIG. 7. (Color online) ILD in both planes. Mean ILD (solid lines) and their standard deviation

FIG. 8

 8 FIG. 8. (Color online) Focusing functions in the median plane using the chirp-like source function

FIG. 11

 11 FIG. 11. (Color online) Focusing functions in the horizontal plane, i.e. ϕ defines the azimuth,

ACKNOWLEDGMENTS

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 641943 (ITN WAVES). We are grateful to Christine Lefèvre, and to the Collection of Comparative Anatomy at the French National Museum of Natural History, for providing the skull specimen on which all our experiments were conducted. We are likewise grateful to the editor W. W. L. Au and two anonymous reviewers, for their insightful comments to our manuscript.

skull as the respective receiver. Interestingly, the -3dB width is similar to that extrapolated from Figures 8&9,i.e. our algorithm is about equally sensitive to changes in azimuth vs elevation of the source.

V. SUMMARY AND CONCLUSIONS

We have developed a source localization algorithm (Section IV) based on the cross correlation of an observed signal with a library of known signals, each corresponding to a different source location. We have implemented the algorithm in the context of a biosonar application (Equation A.5 and related discussion), and "source" should be interpreted here as synonymous with biosonar "target" (or "secondary" source). We have substantiated our source-localization metric from a theoretical standpoint, by drawing an analogy between cross correlation and the theory of acoustic time reversal. We have evaluated the

APPENDIX: TIME-REVERSAL THEORY AND CROSS CORRELATION

It is well known that, if attenuation is neglected, the imaginary part ( ) of the acoustic Green's function (i.e., impulse response) G associated with a source at r A and a receiver at r B (or vice-versa) can be obtained by the frequency-domain relationship

(e.g., Boschi and Weemstra, 2015, Equation (103)), where G is the 3-D Green's function, ∂V is an arbitrary closed surface surrounding r A and r B , and ρ, c, ω denote density, speed of sound and frequency, respectively. * stands for complex conjugation, so that the integrand at the right-hand side of Equation A.1 is the Fourier transform of the time-domain cross correlation of G(r, r B , t) and G(r, r A , t).

Think now of r B as the location of an acoustic source (e.g., [START_REF] Boschi | Stationary-phase integrals in the cross correlation of ambient noise[END_REF]; G(r, r B , ω) is the Fourier-transform of an impulse generated at r B and recorded by a receiver at r; G * (r, r B , ω) is the Fourier transform of the same signal, reversed in time. Imagine that the time-reversed signal be then emitted from r and recorded at another point r A : this amounts to convolving (in the frequency domain, multiplying) the time-reversed signal with the Green's function G(r A , r, ω). Eq. (A.1) then shows that by repeating time reversal and propagation ("backward in time") for all points r on ∂V , and summing all the resulting traces at r B , the imaginary part of the Green's function between r B and r A is obtained.

Note that the imaginary part of the frequency-domain G coincides, in the time domain, with the inverse Fourier transform

time-reversed, backward-propagated signal to sharply focus at the source; since our setup is essentially the same, we can reasonably expect two-receiver time reversal to perform about equally well in our case. Equation A.1 can thus be simplified to

where, for the sake of simplicity, and since we are only interested in finding the maxima of the expressions in question, we have dropped absolute amplitude information. Equation A.3 is only valid for impulsive signals, but it is straightforward to generalize it to an arbitrary signal s(ω). Write s as the convolution s(x 1 , x 2 , ω) = h(ω)G(ω, x 1 , x 2 ), with h an arbitrary "source time function" independent of the source and receiver positions x 1 and x 2 . If one multiplies both sides of Equation A.3 by h * (ω),

The convolution of s * with G at the right-hand side of Equation A.4 should be interpreted, again, as backward propagation of the time-reversed recorded signal s; Equation A.4 stipulates that, by this procedure (in the assumption that sufficient information about the wave field be recorded by a pair of receivers alone), a source of arbitrary complexity (with respect to time) can be reconstructed: the time-reversed signal will focus at the source, where a receiver would approximately record the original source time function h(t), reversed in time.

We take here a slightly different approach [START_REF] Catheline | Acoustic source localization model using in-skull reverberation and time reversal[END_REF]