IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL

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1 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL Principal Component Analysis of Single-Beam Echo-Sounder Signal Features for Seafloor Classification Ali R. Amiri-Simkooei, Mirjam Snellen, and Dick G. Simons Abstract Acoustic remote sensing is a useful tool for seafloor characterization. This contribution presents the results of seafloor sediment classification using single-beam echo-sounder (SBES) data based on a phenomenological method. Basic concepts of principal component analysis (PCA) and its applicability to the sediment classification using acoustical data are studied. This mathematical tool, which retains most of the variation of the data, is applied to the SBES echo shape parameters such as total energy, time-spread, skewness and flatness on three low (12 khz), moderate (38 khz), and high (200 khz) frequencies, making 12 features in total. These parameters are dependent on sediment types and can therefore be used as attributes for seafloor classification. To decrease the statistical fluctuations of the extracted features, an averaging over a sufficiently large number of consecutive pings have been applied to the features. The SBES classification results basedonthepcaand -means clustering approach can clearly discriminate between different sediment classes. The signal at 12 khz contains information on sediment layers (5 m depth). The performance of the method and the results obtained are assessed using the following independent criteria: 1) inspection of the track crossings indicates stable feature extraction and processing strategy; 2) comparison between the class numbers of the classification results and of the grab samples shows a significant correlation coefficient of 0.90; and 3) an error matrix verifies the stability and independence of the classification results from the features considered. Index Terms Echo shape parameters, principal component analysis (PCA), single-beam echo-sounder (SBES). I. INTRODUCTION ACOUSTIC signals are widely used in many marine applications in which one measures bathymetry in shallow and deep water using single- and multibeam echo-sounders (SBES and MBES). Whereas travel time is used for the bathymetry measurements, the intensity and shape of the received signal can provide useful information on the composition of the seafloor Manuscript received August 30, 2010; revised February 02, 2011; accepted February 26, Date of publication May 12, 2011; date of current version May 27, Associate Editor: R. Chapman. A. R. Amiri-Simkooei is with the Department of Surveying Engineering, Faculty of Engineering, University of Isfahan, Isfahan, Iran. He is also with the Acoustic Remote Sensing Group, Faculty of Aerospace Engineering, Delft University of Technology, Acoustic Remote Sensing, 2629 Delft, The Netherlands ( a.amirisimkooei@tudelft.nl). M. Snellen and D. G. Simons are with the Acoustic Remote Sensing Group, Faculty of Aerospace Engineering, Delft University of Technology, Acoustic Remote Sensing, 2629 HS Delft, The Netherlands. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /JOE [1] [3]. Many studies are currently ongoing to characterize seafloor sediments using acoustical signals [4] [10]. Having available efficient algorithms for seafloor classification using acoustical data results in a significant reduction of the cost. It also provides a complete overview of the bottom composition of the surveyed area. Seafloor classification methods can be divided in two categories [11], [12]: model-based methods and empirical methods. Model-based methods translate echo signals directly into the physical properties of sediments. The advantage is that they take the physics into account to characterize the seafloor. The optimal method to modeling the acoustical signals is still subject to research. Also, parameter estimation using inversion procedures are subject to intensive research [12], [13]. Questions to be answered regard the modeling complexity required. In addition, models in general are valid only for a certain range of frequencies and sediment types [14]. Extension of these ranges might be required for certain applications. Model-based methods often require knowledge about system characteristics such as sensitivity, emitted signals, and directivity patterns. This information is not always available. Empirical methods rely on the study of certain echo signal features that are correlated with sediment properties. A few of these features are usually combined using a clustering method. Each identified cluster is then associated with a particular type of sediment. The empirical methods are easy to implement, but have the disadvantage that it is not trivial to interpret the results. Grab samples could be of use to convert the acoustical classification results to physical properties of sediment. Seafloor sediment classification using SBES signals is of particular interest because of the SBES s limited cost compared to MBES systems. Seafloor classification with SBES systems is an active field of research and there exists a broad range of approaches for which we refer to the previous work as follows. 1) Determination of the energy ratio of the first- and second-bottom return to characterize the seafloor by [15], [16]. The first echo is assumed to be representative of the sediment roughness, whereas the energy in the second return is assumed to correspond to the sediment impedance. 2) comparison between measured and theoretically modeled echo patterns in the time domain by [12], [17], and in the frequency (wavelet) domain by [18]. The former developed a sediment geoacoustic parameter estimation method that compares bottom returns with an echo envelope model based on high-frequency incoherent backscatter theory and sediment properties. 3) Seafloor characterization using artificial neural networks by [11], where a /$ IEEE

2 260 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL 2011 seafloor classification method based on the parameterization of the reverberation probability density function using computer simulations was developed. 4) Describing Quester Tangent s (QTC) software for statistical seabed classificationby[19]. This approach uses many statistical algorithms to generate over 130 statistical features and applies a principal component analysis to extract the more informative features. Another commercial system is the RoxAnn that uses the energy of the tail of the first echo (E1) and the total energy of the second echo (E2), which are dominantly related to the acoustical roughness and hardness, respectively. In [20] a comparison between the commercially available bottom classification systems RoxAnn and QTC is made. This latter one is an example of an empirical method that bases the sediment classification on signal features. There exist three families of echo parameters used in these empirical seafloor characterization methods. These include the statistical moments, the spectral moments, and the fractal dimensions [21]. The statistical moments resemble the moments associated with statistical distributions. The spectral moments are used to describe the shape of the echo envelope in the frequency domain. The fractal dimension is a statistical measure that gives an indication of how completely a fractal can fill space. A combination of these three families is used by [21] in which a principal component analysis and a clustering method are applied to discriminate between the seafloor sediment classes. This work describes an empirical sediment classification method that differs in several ways from previous work as follows. 1) We briefly present basic concepts of principal component analysis (PCA) to gain insight into the general theory of the method. Its applicability to acoustical sediment classification is assessed using simple intuitive examples. 2) We only use the statistical moments of the received echo which are the simplest and well-understood geometrical features of the received signal. This highlights the importance of using these features (commercial software companies do not disclose details of their methodtothescientific community). 3) We make use of three signals, different in frequencies (low, moderate, and high frequency). The extracted features at the three frequencies, handled through PCA, is an innovation of the present contribution. This paper is organized as follows. Section II describes the principal component analysis (PCA). The applicability of the PCA to acoustical signals is studied using theoretical aspects and intuitive examples. Section III briefly describes the physical processes that could potentially influence the intensity and shape of echo-sounder bottom returns. The informative features using the echo shape parameters are treated in this section. We employ the echo shape parameters that are conceptually similar to the statistical moments. Section IV presents the numerical results. The method is applied to SBES EA 600 data collected in the Cleaver Bank area in the North Sea, north-west of the Netherlands. Data at three frequencies of 12, 38, and 200 khz will be used. It is aimed to 1) extract the features, 2) apply the PCA and a clustering analysis, 3) present and interpret the classification results. The received echo, and hence the extracted features, are subject to high statistical fluctuations, which makes the classification results very variable. The extracted features Fig. 1. Principal component analysis applied to two echo shape parameters (features) time-spread and skewness of a SBES data set. of a sufficiently large number of consecutive pings are averaged to make the clusters as separate as possible, leading to less variability in the classification results. We then make a comparison between the classification results and the ground truth information. Objective ways for obtaining ground truth classification results are provided and the conclusions are presented in Section V. II. PRINCIPAL COMPONENT ANALYSIS (PCA) PCA is a standard mathematical tool that transforms a number of different, but possibly correlated, variables into a smaller number of uncorrelated variables called principal components (PCs). Since PCA is widely used for many classification applications, we think that a thorough description of the PCA might be of interest to the underwater acoustical community. Therefore, this section presents a review to PCA and -means clustering that can potentially be of interest, but it can equally well be skipped for the readers who are familiar with the concepts. More information on the theory of PCA can be found in [22]. By means of theoretical background and simple examples, we aim to provide both an intuitive interpretation for PCA and a discussion of the topic. The method extracts relevant information from complex data sets consisting of different attributes (features). After mean centering and standardization (variance scaling) of a data set for each attribute, PCA involves the calculation of the eigenvalue decomposition of the data covariance matrix. The order of PCs is based on the amount of variations of the data they represent. The first PC has the largest variations. Each component can then be interpreted as the direction, uncorrelated to previous components, which maximizes the variance of the samples when projected onto that component. High-dimensionality of the features makes their visualization and interpretation difficult. PCA reduces the dimensionality of the data, but retains most of the variation in the features. Reduction is achieved by identifying directions (PCs) along which the variation in the data is maximal. When a complex dataset is visualized as a set of coordinates in a high-dimensional data space, PCA provides a lower dimensional picture, called a shadow

3 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 261 Fig. 2. Echo shapes of received signal acquired at three frequencies, 12 khz (left), 38 khz (middle), and 200 khz (right) in three different areas: sandy gravel (thin solid line), sand (thick solid line), and sandy mud (thin dashed line). of the object, which is viewed from the most informative viewpoint. Strictly speaking, (small) parts of the data are lost in the PCA process. A. Mathematical Background and Intuitive Examples Consider feature -vectors (with the number of data points or sample size) all collected in the data matrix, usually after standardization such that each feature is given a zero mean and unit variance. The unit variance of the features indicates that one deals with the unweighted PCA, while in case that some features are of higher or lower importance one may deal with the weighted PCA. This standardization is applied when there exists no a-priori information on the weights of the features and hence ensures that all features have equal weights. The covariance matrix of the features can be simply obtained as where the diagonal elements are the variances (here ones) of the features and the off-diagonal elements are the covariances (here correlation coefficients) among the features. The eigenvalue decomposition of the positive-definite covariance matrix is where is a diagonal matrix with diagonal entries the eigenvalues of,and is an matrix of eigenvectors, where each column corresponds to one of the eigenvalues, of.. We may partition as.,where includes the first eigenvectors of corresponding to the largest eigenvalues given in, while includes the remaining eigenvectors of corresponding to the smallest eigenvalues of. The matrix (1) (2) (3) is of size which represents the first principal components (PCs). They are used as new features to classify the seafloor and each PC contains independent information from other components. The percent of the total data set variance explained by each PC is where. 1) Example 1: Let and be two normalized features, having zero means and unit variances. They are assumed to be correlated with a correlation coefficient of,i.e. The eigenvalue decomposition of the covariance matrix (4) (5) reads where and. This decomposition indicates that the first and second PCs and are independent with the variances and, respectively. The contributions of the first and second components are and, respectively. Two special cases of this problem occur when and. For the former case the two features are uncorrelated and hence we cannot predict one from the other. We obtain unit variances both for and.forthelatter case, the two features are fully correlated indicating fully redundant features. One then has, and hence and. The variances of and are two and zero, respectively. This means that all of the variabilities have been captured by the first PC, and the second PC has no further variability. Example 1 shows how the PCA is related to the eigenvalue decomposition. This understanding leads us to a prescription for how to apply PCA in the single-beam echo-sounder data. As an (6)

4 262 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL 2011 application of Example 1 we now present the following example to intuitively explain the goal of PCA. 2) Example 2: The echo-shape parameters extracted from the SBES received signal [cf. Section III-B] are used to illustrate how PCA can be used to represent features with a smaller number of variables. The basic concepts can be explained with simple geometrical interpretations of the data. To allow for such interpretations, we consider the normalized features time-spread and skewness that are obtained from the signal shape [cf. Fig. 1; see later on Section IV-A]. These two features are correlated as. PCA identifies the PCs, which are linear combinations of these original features. The first component is expressed in terms of the original variables as, while the second component is, with and, the time-spread and skewness, respectively. We can therefore reduce the dimensionality of the two-dimensional data set to a single dimension by projecting the data onto the PC1. The variability of the data is the maximum value of 72% (PC2 is responsible only for the minimum value of 28% of the variability). PC1 is thus considered to have more discriminatve power than the other directions. Remarks on Applicability of PCA Although running a PCA is an easy task, interpreting the results can be difficult. A few guidelines are provided that can be used when applying the PCA to acoustical data. They could be because of the use of the principle of PCA in general or because of the use of acoustical data in particular. They are itemized in the following. The principal components (PCs) are dependent on the units used to measure the original features as well as on the range of values they assume. Therefore, one should always standardize the data prior to using PCA. A common standardization method is to transform all the data to have a zero mean and a unit variance. One usually deals with a challenge to decide how many and which components to use in the subsequent analysis. Because the PCs are uncorrelated, they represent different aspects of the features. One may for instance think of different acoustical characteristics and physical properties of seafloor sediments. The very highly correlated data could be excluded in the analysis as they provide little independent information and artificially raise the variance of the PCs. Such increase of the variance can hardly increase the discrimination power. Parts of the variation in data from state-of-the-art echosounder systems can be because of unmodeled systematic effects, resulting in dominant PCs that correlate with artifacts. For example, the depth-dependent effects (if not corrected) can introduce such systematic effects. This might, for instance, imply that the second and third PCs are more preferred than the first PC. Therefore, the erroneous data that are discriminating sediment types are discarded. Because the total number of PCs used are (much) smaller than the total number of features, parts of the data will be lost. This information loss is made minimal by PCA. The lost information has less discriminative power but this does not indicate that they are of lower value. The number of PCs applicable for seafloor classification mainly depends on correlations among the features. The higher these correlations are, the smaller the number of PCs will be [23]. In an extreme case, for features, when the correlation among features are all zeros, this number is (no reduction of PCs is possible). In another extreme, when the correlation among features are all ones, this number is one (maximum reduction of PCs is possible). When the relation among the original features are of nonlinear nature, the linear transformation because of PCA makes the statistical interpretation difficult. Therefore, the classification results based on PCA can hardly be statistically interpreted. Each PC explains a percentage of the total variability of the original data. The first PC is more highly correlated with the original features than the second, the second is more correlated than the third, and so on. One can therefore determine the correlation of each PC with the original features. It enables one to find outliers and allows one to reduce the dimensionality of the problem by eliminating some features if they are not really helping to explain the PCA process. B. -Means Clustering Method PCA does not generate separate clusters for discovering unknown groups. PCA can be used as a first step before clustering or classification. It is designed to identify directions with the largest variation and not directions relevant for separating classes of samples. ThePCsarefedtothewell-known -means clustering algorithm for which we refer to [24]. The term -means was firstusedby[25].thesimplestform of clustering is based on partitioning a given data set into disjoint subsets (clusters) such that specific clustering criteria are optimized. The -means algorithm partitions a data set by minimizing the clustering error. Clusters are represented by centers of mass of their members. Each cluster in the partition is therefore defined by its member objects and by its centroid, or center. The centroid for each cluster is the point to which the sum of distances from all objects in that cluster is minimized. It finds a partition in which objects within each cluster are as close to each other as possible, and as far from objects in other clusters as possible. Different distance measures can be used, depending on the kind of data available for clustering. For each point, -means computes its squared distance from the corresponding cluster center and takes the sum of distances for all points in the data set. The algorithm initially adopts a number of random centers in the parameter space. It then moves objects between clusters while it minimizes the variability within clusters and maximizes the variability between different clusters. -means uses an iterative algorithm to minimize the sum of distances from each object to its cluster centroid, over all clusters. This algorithm moves objects between clusters until the sum cannot be decreased further. The result is a set of clusters that are as compact and well-separated as possible.

5 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 263 Fig. 3. Geology of surface sediments for part of North Sea extracted from historical map in 1987, which has been made using grab samples of many years taken by Hamon grab. Selected area, indicated by black rectangle, contains part of Cleaver Bank area in which SBES data were collected in 2004; depth at this area rangesfrom25to65m. III. SBES SIGNAL FEATURES Acoustic seafloor classification is a useful tool for many marine applications such as marine geology, hydrography, marine engineering, environmental sciences, military sonar, and fisheries. The ultimate goal of acoustical remote sensing techniques is to remotely map the bottom composition of the seafloor. The shape and intensity of the received signals contain information on the sea or river bottom composition. Fig. 2 shows the normalized shape of the received echo at three different frequencies for different sediment types. At each frequency, normalization is done over the mean energy in three different sediment types. The fact that the shape of the received echo changes from one sediment to another can be used to discriminate between different sediment types. We investigate how well relative simple features of the acoustical signals, received after reflection at the seafloor, can be used to discriminate between different sediments. Several features of the received signal such as its shape and energy are extracted. For better understanding of the seafloor composition, the systematic effects because of water depth variations are to be eliminated. A. Data Corrections The shape of the received signal is used to extract a few features [cf. Section III-B]. Due to the nature of the acoustical signal and its propagating medium, several factors influence the received signal and hence the extracted features. The intensities at each time sample need to be corrected for spherical spreading and footprint effect. The correction because of the spherical spreading is (7) where is the absorption coefficient in db/m and is the (one-way) slant range, with the sound speed in water and the two-way travel time. The signal footprint effect is The second correction is the time-spread correction. It scales the echoes in time recorded at a depth to a reference depth in the following manner: This correction compresses signals in time from a depth greater than the reference depth and prolongs signals from a depth smaller than the reference depth. The reference depth can be chosen as an arbitrary number of 1 m, or an average depth value. We note that the linear compression/prolongation applied is an approximation of the actual physical phenomena [26]. While the time spreading because of backscatter inside the footprint is geometrically proportional to the water depth, other causes of spreading such as 1) the transmitted pulse duration, which adds to the physical received echo duration (not for the data considered in this paper), 2) the trail because of sediment-volume penetration, which is limited by the absorption coefficient in the seafloor, and 3) the time spreading because of interface roughness, which is an intrinsic property of the interface, are independent of the water depth. B. Feature Extraction The recorded single-beam signals of the Kongsberg Simrad EA 600 echo-sounder at frequencies 12, 38, and 200 khz are available. The following issues are highlighted. (8) (9)

6 264 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL 2011 the skewness, and 4) the flatness at three different frequencies (12 features in total). They are conceptually similar to the first, second, third, and fourth statistical moments. The received echo signals are subject to (high) statistical fluctuations even for a homogeneous seabed. We apply an averaging over the features of 100 successive pings to reduce such fluctuations and to obtain more precise results. The features provide different information but they are probably statistically correlated. They contain (independent) information regarding the physical properties of the seabed and hence provide useful tools for classification. Because the features are correlated, one can apply PCA to obtain possibly a smaller number of uncorrelated components for subsequent clustering analysis. We now provide the mathematical formulation of the features. The total energy is (10) Fig. 4. Maps of normalized (zero mean, unit variance) echo shape parameters (features) of SBES data: total energy (top-left), time-spread (top-right), skewness (bottom-left), and flatness (bottom-right). In each frame, subframes top, middle, and bottom correspond to frequencies 12, 38, and 200 khz, respectively. where is the truncated return pulse duration and is the water-depth corrected intensity as a function of time. In practice one has to be satisfied with discrete evaluation of the integral. The total energy is an important parameter as it directly relates to the hardness and roughness of the seabed. As a second-order moment, the time-spread is (11) where is the echo center of mass and is given as (12) As a third-order moment, the skewness is (13) As a measure of the asymmetry, the skewness is typically positive for all seafloor echoes. This indicates that the echo shape is right-skewed, meaning that the mass of the shape is concentrated on the left hand side. The fourth-order moment, the flatness or kurtosis, is Fig. 5. PCA applied to echo shape parameters of SBES data: total energy (top-left), time-spread (top-right), skewness (bottom-left), and flatness (bottom-right). In each frame, subframes top, middle, and bottom correspond to first PC, second PC, and classification map based on -means clustering method, respectively. Proper echo shape parameters suitable for discrimination between various seafloors need to be defined. In [21] six energetic, statistical, spectral, and fractal echo parameters are shown to carry useful information for seafloor characterization. We introduce and use only the first two types. The features are 1) the total energy, 2) the time-spread, 3) (14) which is a measure of the peakedness of the echo shape. An echo shape with high kurtosis (less flatness) tends to have a distinct peak near the mean and to have heavy tail(s). But an echo with low kurtosis has a flat top near the mean rather than a sharp peak, with short tail(s). Henceforth, the word flatness is used as a measure for the kurtosis parameter. Note that the argument time in the preceding equations is the time reference introduced in (9), which makes the extracted features independent of the depth effects. We highlight that the normalization of the time-spread, skewness, and flatness by the total energy makes them purely shape parameters.

7 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 265 Fig. 6. PCA and -means clustering applied to 12 extracted features of echo shape parameters at 12, 38, and 200 khz. (a) Correlation coefficients among different features; (b) variance proportion of principal components; (c) the first three principal components versus position; (d) scatter plot of PC1 versus PC2 when -means method is applied to the first three PCs; and (e) histogram of the first PC for clustered data. Also, the skewness and flatness are independent of echo duration because they are normalized by the third and fourth power of, respectively. IV. RESULTS AND DISCUSSIONS One data set from an SBES Kongsberg Simrad EA 600 is used. The experiment was carried out in the Cleaver Bank area located in the North Sea [cf. Fig. 3]. This part of the North Sea has been the subject of extensive geological surveys and is of particular interest because of its variability in sediment types. The experiment was done in November The SBES was mounted on the Luymes ship in this trial. The SBES system used is operated at three frequencies 12, 38, and 200 khz. The beamwidths used are 15.5, 9.6, and 7.2 degrees at 12, 38, and 200 khz, respectively. The corresponding pulse lengths are 1000, 256, and 256. Ping rates typically are 5 Hz, while the maximum ping rate is 20 Hz. The time structure of echo envelopes depends on the beamwidth and sidelobes. Therefore the features extracted are not intrinsic to only the seafloor but to the combination of seafloor and echo-sounder. Because the sonar characteristics do not change for the entire survey, the differences among the features are because of the seafloor characteristics. We also note that the low frequency signal at 12 khz presumably concerns physical phenomena such as specular coherent reflection and in-sediment propagation (similar to a subbottom profiler), while the high frequency signal 200 khz describes backscatter from the seafloor roughness, with a limited amount of sediment volume scattering. Independent information about the seafloor composition is availablefortheareain which the SBES data set were recorded: the grain size distribution of the analyzed grab samples is employed as ground truth for checking the results obtained from analyzing the SBES signals. A. Feature Extraction The four echo shape parameters, discussed in Section III-B, of the SBES data set are computed. Each of these features has been calculated for individual pings. To make the features independent of the artifacts because of the depth, all depth-dependent corrections introduced in Section III-A have been applied to the measured signals. To decrease the statistical fluctuations of the extracted features an averaging over the features of consecutive pings is needed. The number of pings used should be large enough to significantly reduce such fluctuations. This number was set to 100 for the results presented in this study, corresponding to the spatial resolution of 100 m. Each feature

8 266 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL 2011 Fig. 7. The classification maps based on the first three PCs and clustering analysis (number of clusters was set to three); all 12 features used (a, option I), only nine pure shape parameters used (b, option II). is then normalized to have a zero mean and a unit variance. This standardization ensures that the features have equal weights in the next analysis steps. The normalized features at the three frequencies are plotted versus position in Fig. 4. Several mechanisms play a role in the formation of the SBES echo. Specular reflection, determined by the impedance contrast between water and sediment, is of importance for the signal part returning from angles close to normal incidence. Often, use is made of the Kirchhoff cross section to describe the signal return in this angle range, where also the roughness of the sediment is taken into account. For the signal part that corresponds to returns at angles away from normal incidence, scattering at the sediment interface roughness and the backscattering of sound from inhomogeneities within the sediment volume, are the main mechanisms governing the echo formation [12], [17], [27], [28]. In general, the energy in the echo is expected to increase for increasing mean grain sizes, as both the sediment roughness (often expressed as the spectral strength) and the impedance contrast increase. When not accounting for volume scattering, the increased roughness is expected to result in increased timespreads for coarser sediment. The increased contribution of the volume scattering parameter for the finer sediments is also expected to increase time spreads. Consequently, the time-spread is expected to be a somewhat ambiguous parameter showing a minimum for the medium grained sediment [29]. For the skewness and flatness considerations as above are more cumbersome. It should be stressed, however, that the limited beamwidths of the SBES systems might result in the features showing different behavior than described above. The limited opening angle makes the SBES insensitive to returns from angles away from nadir. This can, for example, result in signal energies lower than expected for the coarse sediments. It should also be noted that Fig. 8. The classification maps based on the first three PCs and clustering analysis of all 12 extracted features: (a) four clusters, (b) five clusters, (c) six clusters, and (d) seven clusters. the beamwidths differ for the three different frequencies considered in this paper. 1) Echo Energy: The (normalized) echo energy is an important parameter for the discrimination of various sediments. Discarding the effect of the limited beamwidth it is expected to increase for increasing sediment grain sizes. The results are given in Fig. 4 (top-left frame) (a) at the three frequencies 12, 38, and 200 khz. For all three frequencies, low energy values are found in the sm area and high values are found in the sg area, as expected and explained above. However, for the S area a more ambiguous behavior is seen. For the 12 khz data, signal energies in this region are comparable to those in the sg area, whereas for the 38 and 200 khz data the energies are more like those for the sm area. The high energies in the S area for the 12 khz data can be because of the larger penetration of sound in the sediments at 12 khz, resulting in a higher volume scattering contribution. And, at 38 and 200 khz, the comparable energies in the S and sm regions are likely because of the limited beamwidths of the SBES

9 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 267 Fig. 9. Shape of received echo at 12 khz for two areas of orange (dark dashed line) and red (light solid line) in Fig. 8. (a) Normalized intensity, (b) zoom-in over tail of signal, and (c) components of skewness in (13) normalized by total energy and time-spread. TABLE I COEFFICIENTS OF THE FIRST PC AND SECOND PC IN TERMS OF ORIGINAL FEATURES EXTRACTED AT FREQUENCIES 12, 38, AND 200 khz systems, making the SBES less sensitive to sound impinging at angles away from nadir. Still, based on these results, three distinct areas can be seen. The areas are sandy mud (sm), sand (S), and sandy gravel (sg). These results are well comparable with the historical map presented in Fig. 3 [cf. [30]), and the groundtruth information (see later on Section IV-C]. 2) Time-Spread: The time-spread is considered to be a pure shape parameter and independent of the energy.asexplained above, the time-spread is expected to exhibit a minimum for intermediate grain sizes. Increased time-spreads are expected for small grain sizes because of the increased volume scattering. Also, for the coarser sediments the time spreads are expected to increase because of the increased roughness. This behavior is clearly visible for the 12 khz data and to a lesserextendalsoforthe38khzdata [Fig. 4 top-right frame (b), subframes top and middle]. For the 200 khz data, values for the time-spread are highest for the sm area, as expected. However, the time-spread for the sg area is now lower than for the S area. Again the time-spreads indicate the presence of three distinct areas. 3) Skewness and Flatness: The skewness and flatness are shown in the bottom frames in Fig. 4. Because they are normalized by the third and fourth power of the time-spread, the echo duration has no influence on these features. At 38 khz, both features discriminate reasonably well between the three main sediment types sm, S, and sg. For the 200 khz data the two features are found not to discriminate well between S and sg. At 12 khz, the results of skewness and flatness are different. The skewness is larger in the sm area than the S and sg areas. Interpretation of this behavior is rather difficult since they are affected by both the transducer sensitivity and the normalization by echo energy and time-spread in (13) and (14). For the flatness (also partly seen in the skewness), new areas with high flatness values appear within the sg area, indicating the presence of heavy tails in the received echos. Since the flatness contains information on the far-end tail of the signal [cf. Section IV-B], these results might indicate that sediment layers of variable thickness are present in these areas. Both for the skewness and flatness, the difference between the mapsfor12khzand38khzissignificant, whereas the change in frequency is only a factor of three. However not only the frequencies but also the beamwidths are different for the two transducers; it is 15.5 degrees for the 12 khz and 9.6 for the 38 khz. Consequently, the 12 khz sounder is more sensitive to soundcominginfromanglesawayfromnadirandpotentially contributingtothefar-endtailofthe echo. The far-end contributions are reflected in the skewness and flatness (see the next section). This difference between the SBES transducers prevents a physical interpretation of the variations of these parameters as a function of frequency. B. Principal Component Analysis The principal component analysis (PCA) of Section II is applied to the 12 extracted features (four features at three frequencies). Depending on the number of features used, the first two (or three) PCs are then used for a cluster analysis based on the

10 268 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL means clustering method [24]. Choosing the number of clusters using the clustering algorithms is often a tricky exercise. Basedontheinspectionofthefirst two (or three) principal components, the number of clusters with similar acoustical properties was set to three. This agrees with the historical map presented in Fig. 3. The results on the PCA and the classification using the -means clustering approach are presented in the following three steps: 1) Individually to each feature at all frequencies: The PCA has been applied to each individual normalized feature (e.g., total energy) at the three frequencies 12, 38, and 200 khz. Three possibly dependent features have been converted to three independent components. For the total energy, the first and second PCs are responsible for 71.9% and 23.2% of the variability, respectively. These values for time-spread, skewness, and flatness are 88.7% and 9.4%, 73.4% and 17.8%, and 61.8% and 28.4%, respectively. The PCs are linear combinations (through matrix )of original features. For total energy one then has the first PC as,where,, 2, 3 are the column entries of (one column per component). These coefficients are given in Table I for the first and second PCs of each feature. The first PC is not far from being just the sign-corrected average of the features, where it removes most of the redundancy. The second PC is mainly dominated by the effects of the low, moderate, or high frequency signals. Fig. 5 corresponds to Fig. 4 in which each frame represents one feature at the three frequencies. In each frame, the first PC (top subframe) and second PC (middle subframe) along with the classification map (bottom subframe) based on the -means clustering method are presented. The classificationresultsbasedonthefirst three features (energy, time-spread and skewness) can clearly discriminate between the three sediment types, namely sm, S, and sg. The results of the flatness is somewhat different. The point is that the second PC cannot discriminate between S and sg area, but instead can discriminate within the sg area a smaller area (the third PC can discriminate between S and sg). This small identified area is because of the use of a low-frequency signal of 12 khz that provides information on the sediment layers. A softer sediment is likely present underneath the sg layer. 2) All 12 features (option I): Fig. 6(a) shows the correlation coefficient (correlation matrix) among the 12 features presented in Fig. 4. Because the features are statistically correlated, it is more useful to combine all of the features for the PCA process. The first PC accounts for 60.3% of the variability, the second PC carries 19.6% of the variability and the third one 9.4% [cf. Fig. 6(b)]. Together, the first three PCs accounted for about 90% of the variance and hence will be used for further analysis. The PCs are linear combinations of the original variables according to. Table II lists the first three columns of corresponding to the first three PCs. The relative contributions of the echo features to the first PC are of comparable magnitude. This component is thus not far from being just the sign-corrected average of the features, which TABLE II COEFFICIENTS, OF THE FIRST (PC1), SECOND (PC2), AND THIRD (PC3) PCS INTERMS OF ORIGINAL FEATURES. THE FEATURES,, AND ARE THE ECHO ENERGY AT 12, 38, AND 200 khz, RESPECTIVELY;,, AND ARE THE CORRESPONDING VALUES FOR TIME-SPREAD,,, AND ARE THE CORRESPONDING VALUES FOR SKEWNESS, AND,, AND ARE THE CORRESPONDING VALUES FOR FLATNESS removes 60.3% of the redundancy. The second PC is influenced significantly by the total energy at 38 and 200 khz along with skewness and flatness at 38 khz. The third PC is dominated significantly by the skewness and flatness at low frequency of 12 khz. Subsequent components (4 to 12) become less important, which are reflected by their variance [cf. Fig. 6(b)]. The first three PCs are plotted versus longitude and latitude [cf. Fig. 6(c)]. The first PC discriminates between sm area and S and sg areas (top subframe), whereas the second PC discriminates between S area and sg area (middle subframe). PC3 provides more discriminative information within the three areas. The first three PCs are fed to the -means clustering algorithm to assign a class number to each measurement. Obtaining the optimum number of clusters is not a trivial task. Based on the results from grab samples and inspection of the first two PCs, this number was set to three. The three-type partitioned data are plotted versus PC1 and PC2 [cf. Fig. 6(d)] in which three colors represent three acoustical classes. Fig. 6(e) shows the histogram of the first PC for these three-type partitioned data. A clear distinction between the blue histogram and the green and red ones is an indication for a high discrimination between sm area and S and sg areas [cf. Fig. 6(c), top subframe]. The clustered PCs are now plotted versus longitude and latitude to make the classification map [cf. Fig. 7(a)]. Three acoustical classes, namely sm (blue), S (green), and sg (red) can clearly be discriminated. These results are consistent with the geological map presented in Fig. 3, and also with the results obtained by analysis of multi-beam echo-

11 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 269 sounder data given in [4] for the same area. In Section IV-C we groundtruth the results using other independent measures. Motivated by the fact that the first three PCs provides more information than the three classes, we attempted to increase the number of acoustical classes. The number of clusters (and hence acoustical classes) was thus set to four, five, six, and seven. Fig. 8 shows the classification results (frames a to d). Within each of the three classes in Fig. 7(a) we can see now subclasses (though they are now more scattered than when we have less number of classes). This raises an important question that cannot be fully answered in the present contribution: whether the classified map represents information only on the surficial sediment or it also consists of information on the sediment layers. We hypothesis that it also provides information on the sediment layers. For example, the red area, which appeared after having at least four classes [class # 4 in Fig. 8(a)] is because of the skewness and flatness parameters at low frequency. This area can be seen in the skewness and flatness at 12 khz rather than at 38 and 200 khz [cf. Fig. 4], which contains information on the deeper sediment layers. The dark blue in the frames Fig. 8(b) (d) is likely because of finer sediment (e.g., mud) in the sm area. To further explain the comment on the effect of sediment layers, the normalized shape of the received echo at 12 khz for the two areas of orange and red [classes 3 and 4 in Fig. 8(a)] is presented. The averaged intensity over a large number of pings are given in Fig. 9. Comparing the two curves in frame a, at the first instant, may indicate that they look alike. A zoom-in on the (far-end) tail of the received signal along with the components of skewness in (13), i.e.,, normalized by the total energy and time-spread, are provided in frames Fig. 9(b) and (c), respectively. There is a clear distinction between the two curves from the time samples (time epochs) of 25 to 50, corresponding to the average depth of 5 m in sediment. In other words, the tail of the signal in the red area is heavier indicating higher skewness and flatness parameters. 3) All nine purely shape features (option II): For this analysis, we exclude the total energy features at the three frequencies. This makes nine features time-spread, skewness, and flatness at the three frequencies. Though we have corrected for all depth-dependent effects to calculate the total energy, we aim to understand how sensitive the results are to the purely shape parameters. We then again use the first three PCs and apply the -means clustering method. The classification results are given in Fig. 7(b). The results are consistent with those obtained when considering all 12 features given in Fig. 7(a) (in the next subsection a comparison is made using an error matrix). The importance of this statement relies on the fact that this option uses purely shape parameters that are independent of all possible unmodeled effects (e.g., depth-dependent ones) influencing the total energy. This is an indication that the depth-dependent effects have been corrected to a large extent. Also, the results are independent of the amplitude calibration re- Fig. 10. Classification results versus grab sample classes. A correlation coefficient of 0.9 is observed. Because many samples are on top of each other, for better presentation, samples are plotted on a circle of which data refer to its center. TABLE III ERROR MATRIX OF CLASSIFICATION RESULTS (OPTION I VERSUS OPTION II), WITH ALL NUMBERS EXPRESSED AS PERCENTAGES. OVERALL ACCURACY IS quirements source level variations for instance which are challenging even for simple systems such as SBESs. C. Groundtruthing Results A common question regarding all remote sensing methods is: How accurate are the classification results? Visual inspection of a classified area is not usually a quantitative measure. There has been extensive research on classification accuracy assessment methods on the general remote sensing theory over the last decade. To ground truth the classification results, three kinds of assessment are addressed in this study. 1) Cross Trackings: To understand how sensitive the classification results are to the tracks taken, a few cross tracks (perpendicular tracks) have been used. A robust processing strategy and reliable classification method should be independent of the track directions of the ship. We may therefore study the classification results closely at locations where the vessel has crossed previous tracks. If the color is stable in both directions, it is an indication that the classification results are consistent. Close inspection of the track crossings in Fig. 4(a), Figs. 6 8 indicates stable color appearance and hence stable classification methodology and processing strategy. Although this cannot be considered as a real ground truth for the classification, it assures us that the methodology employed gives consistent results.

12 270 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL ) Grab Samples: We now compare the classification results with the grab samples. The ultimate goal of SBES data analysis is to transform the signal feature classification results into estimates of seafloor sediment properties such as mean grain size. The goal of the sediment grab sampling and grain-size analysis is to evaluate the potential correlation between the mean grain size and the results from classification. Grab samples were taken by a grab sampler at 50 positions in the (larger) surveyed area, butthereareonly16samplesintheareawherethesbesdata were taken. The grab samples were washed, dried, and sieved through a series of mesh sizes to analyze the grain size distribution. Based on the mud, sand, and gravel percentages, the grab samples were classified using a Folk scheme [31]. The classification indicated that five seafloor types are present in the area, i.e., sandy mud (sm), muddy sand (ms), sand (S), gravelly sand (gs) and sandy gravel (sg). To make the comparison easier we, respectively, assign the class numbers 1, 1.5, 2, 2.5, and 3 to the above folk classes based on their mean grain sizes, sorted from fine to coarse sediment. We do not directly estimate the mean grain sizes using the acoustical data. But, to highlight the high potential capability of the proposed method for seafloor characterization, the preceding numbers are correlated to the acoustical class numbers 1, 2, and 3inFig.7(a).Theclassification results show overall good agreement with the ground truth information of the grab samples [cf. Fig. 10]. The dependence of acoustical results on sediment class numbers may also be examined using the sample Pearson correlation coefficient. Significant correlation coefficient is observed between these two samples. The only mismatch is because of one grab sample that belongs to the boundary region of two classes. Removing the only bad sample from the analysis leads to a high correlation coefficient of.ifone considers five acoustical classes, and hence five Folk classes as, the correlation coefficient will reduce to. 3) Error Matrix: Two options were previously used to make the classification results [cf. Fig. 7(a) and (b)]. Visual inspection indicates consistent results using these two options. To obtain a quantitative measure, we produce an error matrix by comparing the two classification results [cf. Table III]. We can then obtain the overall accuracy of the classification results. The actual accuracy of classification results is unknown because it is impossible to perfectly assess the true class of every sample point because of the lack of actual ground truth. The columns and rows of the error matrix represent the classification results based on options I and II, respectively. The overall classification accuracy can be computed as the total number of correct class predictions (the sum of the diagonal error matrix) divided by the total number of sample points. The overall classification accuracy is. D. Generalization of Method To generalize the utility of this method for a wider range of oceanic engineering readers, a few issues are addressed. In practice, the SBES source levels might vary over the course of the survey. In general, these variations are recorded and consequently variations in source levels can be corrected in the analysis. For the analysis presented here the source levels were kept constant during the survey; this is also revealed by the fact that the classification is equally good using just the shape parameters (time-spread, skewness, and flatness), indicating that the results are not affected by source level variations. Also variations in pulse length can be accounted for in the analysis and such variations during a survey, therefore, will not severely affect the classification. Whereas the frequency and beamwidth in general will not vary for a single SBES system, they will be different for different SBES systems. The signal features cannot be corrected for changes in beamwidth and frequency. This prevents a comparison of feature values obtained by different systems. Variations in these parameters might also affect the discriminating performance of the different systems, and care should be taken when comparing classification maps taken by different sonar systems. The use of modeling that allows for predicting the received echo shapes, and consequently signal features, as a function of sediment type and SBES characteristics is expected to provide insight in the classification performance of different SBES systems. V. SUMMARY AND CONCLUSIONS We applied the general theory of PCA to SBES data for seafloor classification. Echo shape parameters of the received signal such as total energy, time-spread, skewness, and flatness change from one sediment type to another and can therefore be used as attributes for seafloor classification. This method was applied to a SBES data set at the three frequencies of 12, 38, and 200 khz, thereby resulting in 12 features. Echo shape parameters were extracted for individual pings at these three frequencies. To reduce the statistical fluctuations, we averaged over the features of a sufficiently large number of adjacent pings. The PCA was applied to decorrelate the correlated echo shape parameters and to reduce the dimensionality of the data. Optimized linear combinations of these features using PCA were shown to clearly discriminate between different sediment classes. Application of the -means clustering method to the first three principal components resulted in a clear discrimination between different acoustical classes. This is an indication that there exist different sediment classes in these research areas. Three clusters, corresponding to three main acoustical classes, were identified. The results were in agreement with the grab samples collected. A significant correlation coefficient was observed between the class numbers of the classification results and of the grab samples. We applied the method to the purely shape features, which are independent of possible unmodeled systematic effects like depth-dependent ones. Similar results to what we observed using all of the features were obtained. This shows the consistency of the classification results, which was also verified by means of an error matrix. Further, it was attempted to increase the number of acoustical classes. Different consistent acoustical classes were identified. The new classes partly present more information (as subclasses) of the surficial sediment within the sandy mud, sand, and sandy gravel areas and partly present information on the sediment layers because of the use of low frequency signal.

13 AMIRI-SIMKOOEI et al.: PCA OF SBES SIGNAL FEATURES FOR SEAFLOOR CLASSIFICATION 271 The method has already been tested on two different data sets; the results of a second experiment is documented in [32]. The set up (three frequency, four features) used seems to be optimal as they both provided promising results. Further improvement of the method by including more frequencies and/or features are likely possible. This method can therefore be used as an alternative to the QTC commercial software, which is not theoretically available to the scientific underwater acoustics community. Also, model-based methods can definitely benefitfromthe results presented. We may use such results to groundtruth the model-based results. In addition, combination of model-based methods and the method described here might provide sediment parameters for each cluster. ACKNOWLEDGMENT The authors would like to acknowledge the valuable comments of the associate editor and three anonymous reviewers that significantly improved the presentation of this paper. REFERENCES [1] J.A.Goff,H.C.Olson,andC.S.Duncan, Correlationofside-scan backscatter intensity with grain-size distribution of shelf sediments, New Jersey margin, Geo-Marine Lett., vol. 20, pp , [2] J. S. Collier and C. J. Brown, Correlation of sidescan backscatter with grain size distribution of surficial seabed sediments, Marine Geol., vol. 214, pp , [3] V.L.FerriniandR.D.Flood, Theeffectsoffine-scale surface roughness and grain size on 300 khz multibeam backscatter intensity in sandy marine sedimentary environments, Marine Geol., vol. 228, pp , [4] D. G. Simons and M. Snellen, A Bayesian approach to seafloor classification using multi-beam echo-sounder backscatter data, Appl. Acoust., vol. 70, no. 10, pp , [5] A. R. Amiri-Simkooei, M. Snellen, and D. G. 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R. Jackson and K. Briggs, High-frequency bottom backscattering: Roughness versus sediment volume scattering, J. Acoust. Soc. Amer., vol. 92, no. 2, pp , [28] T. T. Lied, M. Walday, F. Olsgard, K. E. Ellingsen, and S. Holm, SEABEC A single beam echo sounder seabed classification system, in Proc. Conf. Ocean 04 MTS/IEEE Techno-Ocean 04: Bridges Across the Oceans, 2004, vol. 4, pp [29] M. Snellen and D. G. Simons, J. Papadakis and L. Bjorno, Eds., Modeling single beam echo sounder signals for sea and river bed classification, in Proc. Int. Conf. Underwater Acoust. Measurements: Technol. Results, Heraklion, Crete, Greece, 2007, pp [30] Rijks Geologische Dienst and British Geological Survey, Holocene en Oppervlaktesedimentkaart 1987, ser. Indefatigable sheet 53 N-02 E. 1: [31] R. L. Folk, The distinction between grain size and mineral composition in sedimentary-rock nomenclature, J. Geology, vol. 62, no. 4, pp , [32] A. R. Amiri-Simkooei, M. Snellen, and D. G. Simons, T. Akal, Ed., Seafloor classification using multi-frequency single-beam echo-sounder echo shape parameters, in Proc. 10th European Conf. Underwater Acoust., Istanbul, Turkey, Jul. 2010, vol. 1, pp Ali R. Amiri-Simkooei graduated from the Mathematical Geodesy and Positioning Group at the Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands. His research area focused on least-squares variance component estimation with applications to GPS data. He has also been a Postdoctoral Researcher at the Acoustic Remote Sensing Group, Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands. His research area focuses on seafloor classification using multi- and single-beam echo-sounders. He is currently an Academic Staff Member of the Department of Surveying Engineering, Faculty of Engineering, University of Isfahan, Iran.

14 272 IEEE JOURNAL OF OCEANIC ENGINEERING, VOL. 36, NO. 2, APRIL 2011 Mirjam Snellen received the M.Sc. degree in aerospace engineering from the Delft University of Technology, Delft, The Netherlands, in 1995 and the Ph.D. degree in geoacoustic inversion from the University of Amsterdam, Amsterdam, The Netherlands, in She was a Research Scientist at The Netherlands Organization for Applied Research (TNO), where she was working in the group of underwater acoustics and in the group of aeroacoustics until Currently, she is the Assistant Professor in the Acoustic Remote Sensing Group at the Faculty of Aerospace Engineering, Delft University of Technology, Delft, The Netherlands. Dick G. Simons received the M.Sc. degree in physics and the Ph.D. degree from the University of Leiden, Leiden,TheNetherlands,in1983and1988,respectively. His Ph.D. research topic involved the development of an imaging gas scintillation spectrometer for X-ray astronomy. In 1990, he joined the Underwater Acoustics Group of the Physics and Electronics Laboratory of the Netherlands Organization for Applied Scientific Research (TNO), The Hague, The Netherlands. In 2003, he was appointed Part-Time Professor at Delft University of Technology, holding the Chair Seafloor Mapping at the Faculty of Aerospace Engineering. In 2006, he became Full Professor at the same faculty, holding the Chair Acoustic Remote Sensing. He is involved in several extensive research projects characterized by a strong international cooperation and major field experiments at sea. His current research comprises the mapping of seafloor topography and composition, and its dynamic behavior, using all kinds of sonar systems, such as single- and multibeam echo sounders, low-frequency active sonar, and seismic systems. He also works on geoacoustic inversion with global optimisation methods such as genetic algorithms, both using active sound sources and ambient noise. Prof. Simons is member of several committees, among which the scientific committee of the European Conferences on Underwater Acoustics (ECUA). He is Associate Editor of the IEEE JOURNAL OF OCEANIC ENGINEERING for the areas bathymetry surveys, mapping, remote sensing, and sonar image processing.