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Skip to main content. Log In Sign Up. We characterize seafloors by a set of empirical distributions estimated on texture responses to a set of different filters.
Moreover, we introduce a novel similarity measure between sonar textures in this feature space. Our similarity mea- sure is defined as a weighted sum of Kullback—Leibler divergences between texture features.
The weight setting is twofold. First, each filter is weighted according to its discrimination power: The computation of these weights are issued from a margin maxi- mization criterion. Second, an additional weight, evaluated as an angular distance between the incidence angles of the compared texture samples, is considered to take into account sonar-image acquisition process that leads to a variability of the backscattered value and of the texture aspect with the incidence-angle range.
A Bayesian framework is used in the first algorithm where the conditional likelihoods are expressed using the proposed similarity measure between local pixel statistics and the seafloor prototype statistics. The second method is based on a variational framework as the minimization of a region-based functional that involves the Fig. Index Terms—Active regions, angular backscattering, feature selection, level sets, maximum marginal probability MMPseg- mentation, sonar images, texture.
The characterization of these high- resolution sonar images is important for a number of practical applications such as marine geology, commercial fishing, off- shore oil prospecting, and drilling —. The segmentation and the classification of sonar images with respect to seafloor types rocks, mud, sand.
This task, however, raises two major difficulties.
The first task is to deal with texture in these images. Previous methods are generally Fig. BS evolution with the incidence angles for the three seafloor types of Fig. These first-order statistics are not sufficient when high-resolution sonar images involve textures, Manuscript received January 4, ; revised May 20, and August 11, First published February 6, ; current version published which is the case gateaix most sonar images Fig.
The other important issue arising in seabed texture charac- I. Boucher are with the Department of Signal terization is a built-in feature of sonar observation: In addition Digital Object Identifier Sonar fateaux composed of sand ripples.
Rock texture for two angular sectors. We first state the segmentation issue sonar image composed by sand ripples and rocks, respectively, as a Bayesian pixel-based labeling according to local texture for two angular sectors: The steep grazing angle reduces the backscatter of an energy criterion involving global-region-based seafloor differences between facing and trailing slopes, while at low statistics.
The seafloor similarity sonar shadow. A similar loss of contrast is observable in the measure imdne introduced in Section II. The Bayesian segmentation rock samples Fig. The region-based segmen- angles has been of wide interest for sonar imaging , —. Experiments are Parametric and nonparametric techniques have been proposed reported and discussed in Section V, and conclusions are drawn to model sonar-image behavior with respect to the incidence in Section VI.
The effect of the incidence angle on the BS has also been explored as a discriminating feature for seafloor recognition , , . However, no studies have proposed II. Recently, in the images. To our knowledge, the effects of the incidence angle on field of texture analysis, features computed as statistics of local textured seabed features have not been addressed for segmen- filter responses have been shown to be relevant and discriminant tation issues.
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Only some studies were interested in simulating texture descriptors —. Motivated by these studies, we the behavior of oriented and textured seafloor types —. Each seafloor and were restricted to synthetic images or to real sonar images type denoted by Tk is characterized by a set Qk composed of involving only one seafloor type. The following conditions are issued. The proposed incidence-angle-and-texture- coefficient computed for different bands we used three based similarity measure is exploited to develop two different wavelet types: Haar, Daubechies, and Coiflet.
Jits filter responses es- timated on the J angular domains. Note that f accounts Fig. J and a given seafloor type Tk as follows: F are the feature weights such that Fig. F are exploited on cooccurrence distributions can be noticed. In a supervised con- values in the image of sand ripples leads to unimodal distribu- text, the weights are estimated from a training set T composed tion.
For cooccurrence distributions related to rock samples, a of N -labeled texture samples: F are issued from the To deal with this problem, we propose to define angular maximization of the global margin defined as follows: It are then approximated as the fraction of time the Markov chain has been shown that the MMP estimation criterion is more spends in state k for each class k and each pixel s.
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The MAP estimate assigns the same cost to every incorrect 1 Simulation of Tmax realizations of x1x2. As shown in , the MMP procedure is equivalent to maximizing the marginal of the class labels. F estimated according to a Parzen estimation A. Functional Terms method , within a square window Ws centered at s. K is evaluated as the log-likelihood of a given window size that we denote by TW is set by the user according partition with respect to texture models.
It is evaluated as the to texture coarseness. We solve for the minimization of the functional E using The derivatives of the energy terms E2 and E3 are directly a gradient-descent technique.
The evolution equation related to E1 is more complex, since it The explicit implementation of the curve evolution according involves computations over the spatial support of each region. As detailed in the front. This could be avoided by introducing the level-set method Appendix, it leads to proposed by Osher and Sethian .
K  composed of two terms. This term is always negative or null. In previous work on Brodatz textures , , we remarked that Gabor and wavelet filters were selected for oriented textures, whereas cooccurrence distribu- tions, which, in addition to the detection of texture structures, Fig. Test images and their manual segmentation in black line. In previous work, we have tested the method on various For the five test images, three segmentation algorithms are optic textures Brodatz textures.
The method was compared compared. Here, we evaluate the proposed ML. We Several analysis-window sizes are compared: Image I1 is composed of three seafloor types: For I2 and I3, the angular 3 The region-based variational segmentation described in variability of the sefloors, particularly marl ripples for I2 and Section IV that we denote by V ar. Table I summarizes the different error classification rates for all For all these images, we first determine the most discriminant segmentations.
We apply the All segmentation methods give quite good results according algorithm described in Section II and detailed in , and to the mean classification error rates. MMP and variational we keep only the feature set such that the cumulative sum approaches are more efficient than the ML-based segmentation of weights exceeds 0. Only a small number of features are because they take into account the spatial dependence between retained.
For our implementations, the accuracy in the localization of the boundaries of the seabed convergence time of a variational image typically corresponds regions because texture features extracted for pixels close to to one iteration of the MMP algorithm. The variational region-based approach does not need the with respect to incidence angles, additional segmentation re- choice of an analysis window and operates globally on region sults are reported for image I2 and I3 for which the seafloor composed of pixels belonging imenf the same class.
It resorts texture variability is clearer. It can be mean error rate for different window sizes. This method can however be appropriate when the aim of the VI. We proposed two segmentation algorithms for sonar-image The gateau approach is also interesting because it is segmentation: Being deterministic, region-based variational algorithm, both based on a novel sim- the variational approach can be very fast particularly if we use ilarity measure between seafloor-type images according to the appropriate initialization such as an initial segmentation based statistics of their responses to a large set of filters.
Imen similar- gatewux the ML criterion. Mean segmentation error rate for several window sizes. I2 region-based segmentation with and without angular weighting. The resulting weighting factors are exploited on the one hand for filter selection and, imeme the other hand, for taking into account the incidence angular dependence of seafloor tex- tures.
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The gaateaux is the cooccurrence matrices outperform the other features for our sonar images. The results show that the performance of the Bayesian approach depends on the size of the analysis window. I3 MMP-based segmentation with and without angular weighting. Le Chenadec and J. Active contour mod-  A. Sethian, Level Set Methods. Calculus of variations or shape gradients? Augustin, angular response of acoustic backscatter: Tunisia, in imebe, the D.
She is currently a Postdoctor with Telecom Conf. Her research interests include texture analysis and segmentation with  M. From  P. Sincehe  Q.