Amal Mahboubi
email: amal.mahboubi@unicaen.fr

Luc Brun
email: luc.brun@ensicaen.fr

Donatello Conte
email: donatello.conte@univ-tours.fr

Pasquale Foggia
email: pfoggia@unisa.it

Mario Vento
email: mvento@unisa.it

Tracking System with Re-identification using a RGB String Kernel

Keywords: Re-identification, String kernel, Visual surveillance

People re-identification consists to identify a person which comes back in a scene where it has been previously detected. This key problem in visual surveillance applications may concern single or multi camera systems. Features encoding each person should be rich enough to provide an efficient re-identification while being sufficiently robust to remain significant through the different phenomena which may alter the appearance of a person in a video. We propose in this paper a method which encodes people's appearance through a string of salient points. The similarity between two such strings is encoded by a kernel. This last kernel is combined with a tracking algorithm in order to associate a set of strings to each person and to measure similarities between persons entering into the scene and persons who left it.

Introduction

The purpose of re-identification is to identify people coming back onto the field of view of a camera. Several types of features including interest point [START_REF] Hamdoun | Person re-identification in multi-camera system by signature based on interest point descriptors collected on short video sequences[END_REF][START_REF] Brun | People re-identification by graph kernels methods[END_REF], histograms [START_REF] Cong | People reidentification by spectral classification of silhouettes[END_REF][START_REF] Ijiri | Human re-identification through distance metric learning based on jensen-shannon kernel[END_REF][START_REF] Schwartz | Learning Discriminative Appearance-Based Models Using Partial Least Squares[END_REF][START_REF] Farenzena | Person reidentification by symmetry-driven accumulation of local features[END_REF], shape [START_REF] Doretto | Appearance-based person reidentification in camera networks: problem overview and current approaches[END_REF], graph based representation [START_REF] Wang | Shape and appearance context modeling[END_REF][START_REF] Iodice | Person re-identification based on enriched symmetry salient features and graph matching[END_REF][START_REF] Mahboubi | Tracking system with reidentification using a graph kernels approach[END_REF][START_REF] Brun | People re-identification by graph kernels methods[END_REF], have been proposed in the literature. However, some features like histograms do not encode any spatial information while some others like interest point and graph based representations may induce a matching step which requires important execution times. Moreover complex features like bags or graphs [START_REF] Mahboubi | Tracking system with reidentification using a graph kernels approach[END_REF] of interest points, RAG [START_REF] Brun | People re-identification by graph kernels methods[END_REF] may be sensitive to the evolution of the appearance of a person in a video due to his displacements or occlusions.

Independently of the type of features used to perform the re identification step, re-identification methods may be split into two categories: methods of the first group [START_REF] Hamdoun | Person re-identification in multi-camera system by signature based on interest point descriptors collected on short video sequences[END_REF] compute a unique signature for each object and perform the reidentification based on this single signature. Methods of the second group [START_REF] Cong | People reidentification by spectral classification of silhouettes[END_REF][START_REF] Zhao | Spatio-temporal tube data representation and kernel design for svm-based video object retrieval system[END_REF] delay the re-identification which is then performed on a set of signatures. This last approach imposes to base the comparison between two objects on a comparison of two sets of signatures rather than between two individual signatures. However such an approach can potentially better capture the variability of the appearance of a person over a video.

Our approach belongs to the second category and describes the appearance of a person by a set of RGB string descriptors (Section 2) computed over a sliding window. A kernel between two sets of strings (Section 3) is then applied in order to encode the similarity between two persons. The integration of this kernel into a tracking method is described in Section 4 while Section 5 reports several experiments which demonstrate the validity of our approach.

RGB String Descriptor Construction Scheme

One of the main challenges for people re-identification is to capture peoples' appearance properties. As mentioned in Section 1, several modelings have been developed. However, although complex models such as graph based representation offer the advantage of a precise modeling of the object, they usually require a complex matching step and important execution times. An alternative solution consists in using a string descriptor. Indeed, string allows an effective comparison while preserving useful information of the region of interest. Although a string usually encodes less information than a graph we expect a greater stability of this simpler structure over time.

The first step of our method consists in separating subjects from the background. To that end, we use binary object masks [START_REF] Brun | People re-identification by graph kernels methods[END_REF] defined by a foreground detection with shadow removals. Each moving person within a frame is thus associated to a mask that we characterize using a salient string. Each character of this string is defined by the couple of its coordinates (x,y) and its RGB value. The construction of a salient string is outlined in Figure 1. This construction consists of the following 3 steps: First, we apply a Deriche edge detector on each moving person according to its binary mask within a frame.

The second stage consists in building a discriminating curve of the object. Contour points provided by the Deriche detector are used to build this curve. Let us consider the bounding box of an object obj a . Thanks to the Deriche filter obj a should be delineated by two main contours (Figure 1-step-1). For each height value y, the mean on the bounding box of the x coordinates weighted by the squared mean of the gradient should thus provide a central point inside obj a (a character of the string). This average coordinate is described by the equation

x(y) = n i=1 |∇I(x i , y)| 2 .x i n i=1 |∇I(x i , y)| 2 (1)
where (x i , y) are the coordinates of the considered point and |∇I(x i , y)| is the amplitude of its gradient. The symbol n denotes the height of the bounding box.

The last and third step, enforce the quality of the resulting curve. Indeed, the resulting curve (Figure 1-step-2) is sensible to small perturbations of the gradient on each mask and contains important discontinuities. This last point may alter the similarity of two curves of a same person taken on two different frames. We thus propose to regularize this curve through an energy minimization framework. Our energy function (equation 2) combines two terms: the first one encodes the attachment to the initial curve (x y ). The second term is a regularization term which enforces the continuity of the curve.

We hence assume that, the energy functional is described as follows:

(x) = n y=1 (x y -x y ) 2 + λ(x y -x y-1 ) 2 (2)
where λ is a tuning parameter. The average coordinate xy is given by equation 1 and x y is the corresponding final coordinate. The symbol n denotes the height of the bounding box.

Minimization of equation 2 leads to search for the zeros of its gradient:

∂ ∂x y = 2(1 + 2λ)x y -2λ(x y-1 + x y+1 ) -2x y = 0 (3)
Equation 3 corresponds to the formulation of a tridiagonal system which can be solved in O(n). This last minimization step obtained using equation 3 provides the final curve, where each point is associated to its RGB value (Figure 1-step-3).

People description

Curves encoding people's appearance may be altered by the addition of erroneous extremities encoding for example a part of the floor or a difference of sampling due to the variations of the distance between a person and the camera. In order to cope with such variations we consider each curve as a string and encode the similarity between two strings thanks to the global alignment kernel defined by [START_REF] Cuturi | Fast global alignment kernels[END_REF]:

K GA (s 1 , s 2 ) = π∈A(n,m) e -Ds 1 ,s 2 (π) (4)
where n and m, denote the length of the first string s 1 and the second string s 2 respectively. An alignment is noted π and A(n, m) represents the set of all alignments between s 1 and s 2 . The symbol D denotes the Dynamic Time Warping distance. It measures the discrepancy between two strings s 1 and s 2 according to an alignment π. Function D is defined [START_REF] Cuturi | Fast global alignment kernels[END_REF] as:

D s1,s2 (π) = |π| i=1 ϕ(x π1(i) , y π2(i) ) (5)
where s 1 = (x i ) i∈{1,..,n} , s 2 = (y i ) i∈{1,...m} and function ϕ corresponds to a distance function defined [START_REF] Cuturi | Fast global alignment kernels[END_REF] as follows:

ϕ(x, y) = 1 2σ 2 x -y 2 + log(2 -e -x-y 2 2σ 2 ) (6)
where x and y denote the RGB values of the first object and the second object respectively. Symbol σ denotes a tuning parameter. The log term is added to the squared Euclidean distance xy 2 in order to ensure the definite positiveness of K GA (equation 4) [START_REF] Cuturi | Fast global alignment kernels[END_REF].

People's Kernel

As the appearance of a person evolves in a scene, due to slight changes of the pose, the use of a single string is inappropriate to identify a person. Assuming that, the appearance of a person is established on a set of successive frames.

The global appearance of a person over a video is described by a set of salient strings. The temporal window over which this set is built is called the history tracking window (HTW). Each person in the video is hence not defined by a single string but by a set of strings (on HTW). This set may include outlier strings, due to slight changes of the pose or occlusion. The construction of a representative string based on a simple average of all the strings of a set (in the Hilbert space defined by the kernel) may be sensible to such outliers. We thus suggest to enforce the robustness of our representative string through the use of an one class SVM classifier in order to remove outliers.

Let H denotes the Hilbert space defined by K GA (equation 4). In order to get a robust model encoding the mean appearance of a person, we first use K GA to project the mapping of all strings onto the unit-sphere of H. This operation is performed by normalizing our kernel [START_REF] Desobry | An online kernel change detection algorithm[END_REF]. Following [START_REF] Desobry | An online kernel change detection algorithm[END_REF], we then apply a one class ν-SVM on each set of strings describing a person. From a geometrical point of view, this operation is equivalent to model the set of projected strings by a spherical cap defined by a weight vector w and an offset ρ both provided by the ν-SVM algorithm. These two parameters define the hyper plane whose intersection with the unit sphere defines the spherical cap. Strings whose projection on the unit sphere lies outside the spherical cap are considered as outliers. Each person is thus encoded by a triplet (w, ρ, S) where S corresponds to the set of strings and (w, ρ) are defined from a one class ν-SVM. Figure 2 gives the geometric interpretation of (w, ρ); The parameter w indicates the center of the spherical cap and may be intuitively understood as the vector encoding the mean appearance of a person over its HTW window. The parameter ρ influence the radius of the spherical cap and may be understood as the extend of the set of representative strings in S.

Let P A = (w A , ρ A , S A ) and P B = (w B , ρ B , S B ) denote two triplets encoding two persons A and B. The distance between A and B is defined from the angle between vectors w A and w B defined as follows [START_REF] Desobry | An online kernel change detection algorithm[END_REF]:

d sphere (w A , w B ) = arccos w T A K A,B w B w A w B (7)
where w A and w B denote the norms of w A and w B in H and K A,B is a

|S A | × |S B | matrix defined by K A,B = (K norm (t, t ′ )) (t,t ′ )∈SA×SB
, where K norm denotes our normalized kernel. Based on d sphere , the kernel between A and B is defined as the following product of RBF kernels:

K change (P A , P B ) = e
Where σ moy and σ origin are tuning variables.

Re-identification

Our tracking algorithm is based on a previous work [START_REF] Mahboubi | Tracking system with reidentification using a graph kernels approach[END_REF]. The tracking algorithm uses four labels 'new', 'get-out', 'unknown' and 'get-back' with the following meaning: 'new ' refers to an object classified as new, 'get-out' represents an object leaving the scene, 'unknown' describes a query object (an object recently appeared, not yet classified) and 'get-back ' refers to an object classified as an old one after a re-identification step. Re-identification is achieved using the similarity (equation 8) between each unknown person and all the get-out persons. All masks detected in the first frame of a video are regarded as new persons. Then a mask detected in frame t + 1 is regarded as matched if a large overlap exists between its bounding box and a bounding box defined in frame t. In this case, the mask is assigned to the same person than in frame t.

If one mask at frame t does not have any successor in frame t + 1, the associated person is marked as get-out. Its curve at frame t is added to the sliding HTW window containing the last strings of this person. Its triplet P = (w, ρ, S) (Section 3) computed over the last |HT W | frames is stored in an output object data base noted DB o .

In the case of a person (at frame t) referring to an unmatched mask in frame t -1, the unmatched person is initially labeled as 'get-in'. When a 'getin' person is found, if there is no 'get-out' persons (DB o is empty) we label this 'get-in' person as new. This 'get-in' person is then tracked along the video using the previously described protocol. Furthermore, if there is at least one 'get-out' person we should postpone the identification of this 'get-in' person by labeling it as 'unknown'. This 'unknown' person is then tracked on |HT W | frames in order to have its description by a triplet (w, ρ, S). Using this description we calculate the value of kernel K change (equation 8) between this unknown person and all get-out persons present in our database. Similarities between the unknown person and get-out persons are sorted in decreasing order so that the first get-out person of this list corresponds to the best candidate for a reidentification. Our criterion to map an unknown person to 'get-out', and thus to label it as get-back is based on a threshold on the first two maximal similarity values max ker and max 2 of the list of similarities (max 2 ≤ max Ker ). This criterion called, SC is defined as max ker > th 1 and max2 maxKer < th 2 , where th 1 and th 2 are experimentally fixed thresholds. Notice that, SC is reduced to a fixed threshold on max ker when the set of get-out persons is reduced to one or two elements. An unknown person whose SC criterion is false is labeled as a new person. Both new and get-back persons are tracked between frames until they get out from the video and reach the get-out state.

Classically, any tracking algorithm has to cope with many phenomena such as occlusions. In this paper we limit the study to overlapping bounding boxes. When an overlap greater than an experimentally fixed threshold occurs between two bounding boxes, an occlusion is found. We assume two kinds of occlusions: partial occlusion where the occluded object remains visible and severe occlusion where the occluded object is completely hidden. If two or more objects (detected at time t) merge together (at time t + 1) to form one new object, this object is deemed to be a group rather than an occlusion. Group cases are not considered in this work.

Experiments

The proposed algorithm has been tested on v01 and v05 video sequences of the PETS'09 S2L1 dataset 1 . Each sequence contains multiple persons and occlusions cases.

In our first experiment we have evaluated how different values of the length of HTW may affect the re-identification accuracy. Figure 4 shows the effects for HTW changes on the true positive measurement for each view. The obtained results show that, v01 performs at peak efficiency for HTW=30. Video v05 attains its optimum at HTW=20. These curves also show that the length of HTW is not a crucial parameter of our method.

In a second experiment we show the improvement of the proposed kernel with respect to an histogram based approach. Similarly to [START_REF] Satta | A multiple component matching framework for person re-identification[END_REF] where histograms are defined from the already extracted blob (segmented parts), we propose the following histograms construction scheme: color histograms are computed on HTW frames for both the query object and each get-out persons contained in DB o . Then, we try to map the query object with one of the get-out objects already stored in DB o using EMD distance [START_REF] Rubner | The earth moverś distance as a metric for image retrieval[END_REF] between histograms. If a map is found, the query object gets the label of the mapped get-out object, and we update DB o . Otherwise, we create a new label for the query object. The map criterion used here is similar to the above SC criterion (Section 4), nevertheless the best candidate corresponds to the minimum since we use distances. Table 1 reports the comparison results between histogram-based and kernel-based approaches. As it can be seen from Table 1 the results of the proposed kernel give slightly higher values than the histogram approach regarding v05, while the results are clearly better for v01. We attribute this to the high detection accuracy in v01. Furthermore, v05 contains a lot of severe occlusions which are not specifically addressed in the proposed method. Indeed on such severe occlusions a large part of a person is usually hidden by an other person.

To validate our method of re-identification we used the Cumulative Matching Characteristic (CMC) curves. The CMC curve represents the percentage of times the correct identity match is found in the first n matches. Figure 5 shows the CMC curves for the two views. We can see that the performance of v01 is much better than that of v05. This last result being due to the large number of occlusions occurring in v05. We also used the exhaustive comparison of 13 methods defined in [START_REF] Ellis | Pets2009 and winter-pets 2009 results: a combined evaluation[END_REF] in order to compare our results to the state of the art. The study [START_REF] Ellis | Pets2009 and winter-pets 2009 results: a combined evaluation[END_REF] did a quantitative evaluation of the results submitted by contributing authors of the two PETS workshops in 2009 on PETS'09 S2.L1 dataset. We noticed that the submitted results of [START_REF] Berclaz | Evaluation of probabilistic occupancy map people detection for surveillance systems[END_REF] outmatch all other methods using the MODA, MOTA, MODP, MOTP SODA and SFDA metrics described in [START_REF] Kasturi | Framework for performance evaluation of face, text, and vehicle detection and tracking in video: Data, metrics, and protocol[END_REF]. Therefore, we only compare our results to this last method. Table 2 depicts the following: the left column shows the best results [START_REF] Berclaz | Evaluation of probabilistic occupancy map people detection for surveillance systems[END_REF] obtained by methods described in [START_REF] Ellis | Pets2009 and winter-pets 2009 results: a combined evaluation[END_REF] on each video. The second columns of Table 2 shows that our method obtains a lower MODA index than [START_REF] Berclaz | Evaluation of probabilistic occupancy map people detection for surveillance systems[END_REF] on v05 but clearly outperform this last method on v01. These results may again be explained by the high number of occlusions in v05 which are overcome by [START_REF] Berclaz | Evaluation of probabilistic occupancy map people detection for surveillance systems[END_REF] using multiple views of each person while the present method is restricted to a single view. These results indicate thus the relevance of the proposed re-identification method when objects are not severely occluded.

Conclusion

In this work, we addressed the people re-identification problem by proposing a new approach based on RGB string kernels. Our re-identification system is based on a simple matching criterion to follow a person along a video. Person's description and kernel between these descriptions is used to remove ambiguities when a person reappears in the video. A benchmark public dataset was used to validate our method. Our experiments results show that the proposed approach outperformed state-of-the art methods when few severe occlusions occur.

Our future research will focus on the investigation of occlusion scene and group problems still using a single camera. To handle these phenomena, we should for each object severely occluded or entering into a group, suspend the update of its curves during the frames where it is hidden. Indeed in such cases no reliable feature may be extracted to characterize hidden persons.

Fig. 1 .

 1 Fig. 1. RGB string construction steps

Fig. 2 .

 2 Fig. 2. Geometrical interpretation of equation 7

Fig. 3 .

 3 Fig. 3. The block diagram of the proposed method

Fig. 4 .

 4 Fig. 4. HTW effects Fig. 5. CMC curves

Table 1 .

 1 Kernel vs. histogram

	view01	view05
	Hist Ker Hist Ker
	True P 2514 4885 1360 1706
	False P 2371 0 1365 1019
	Missed 124 124 84 84

Table 2 .

 2 Evaluation results

	View	work of [1] MODA MODA MOTA SFDA current work
	v01	0.67	0.97	0.97 0.91
	v05	0.72	0.60	0.60 0.81

Available at http://www.cvg.rdg.ac.uk/PETS2009/a.html


Oussama Hadjerci

Adel Hafiane

Pascal Makris

Donatello Conte

Pierre Vieyres

Alain Delbos

Nerve detection in ultrasound images using median Gabor binary pattern

Keywords: image segmentation, feature extraction, image texture analysis, supervised learning, nerve detection, regional anesthesia

Ultrasound in regional anesthesia (RA) has increased in popularity over the last years. The nerve localization presents a key step for RA practice, it is therefore valuable to develop a tool able to facilitate this practice. The nerve detection in the ultrasound images is a challenging task, since the noise and other artifacts corrupt the visual properties of such kind of tissue. In this paper we propose a new method to address this problem. The proposed technique operates in two steps. As the median nerve belongs to a hyperechoic region, the first step consists in the segmentation of this type of region using the k-means algorithm. The second step is more critical; it deals with nerve structure detection in noisy data. For that purpose, a new descriptor is developed. It combines tow methods median binary pattern (MBP) and Gabor filter to obtain the median Gabor binary pattern (MGBP). The method was tested on 173 ultrasound images of the median nerve obtained from three patients. The results showed that the proposed approach achieves better accuracy than the original MBP, Gabor descriptor and other popular descriptors.

Introduction

Regional anesthesia (RA) is performed by injecting the anesthetic close to a nerve block to immobilize a part of human body. Ultrasound imaging is an essential way in the practice of RA, it allows the visualization of the anatomical tissues, and it facilitates the needle control [START_REF] Woodworth | Efficacy of computer-based video and simulation in ultrasound-guided regional anesthesia training[END_REF]. However, RA is a complex technique that requires a long learning process and years of experience [START_REF] Woodworth | Efficacy of computer-based video and simulation in ultrasound-guided regional anesthesia training[END_REF][START_REF] Marhofer | Ultrasound-guided regional anesthesia: Current concepts and future trends[END_REF]. Hence, it is important to provide anesthetists with a tool based on ultrasound images to improve the RA practice.

Segmentation and detection in ultrasound (US) images have been applied to several applications such as abdomen, breast, liver, kidney, etc [START_REF] Stoitsis | Texture characterization of carotid atherosclerotic plaque from b-mode ultrasound using gabor filters[END_REF][START_REF] Nikolaos | Comparison of multiresolution features for texture classification of carotid atherosclerosis from b-mode ultrasound[END_REF][START_REF] Khanna | Us image segmentation based on expectation maximization and gabor filter[END_REF][START_REF] Ghose | Prostate segmentation with local binary patterns guided active appearance models[END_REF]. Very few works have studied the automatic nerve detection in the US images [START_REF] Thouin | Nerve region segmentation for ultrasound guided local regional anaesthesia (lra)[END_REF]. The nerve region is not a salient structure in the ultrasound images, due to the poor quality of the US imaging modality that generates many effects such as speckle noise, signal degradation, artifacts, etc [START_REF] Noble | Ultrasound image segmentation: A survey[END_REF]. Indeed, the segmentation and recognition in the US images are among the most challenging problems in the field of image processing and analysis. Numerous segmentation approaches, such as classification, active contour and graph cuts, have been used to tackle this issue [START_REF] Noble | Ultrasound image segmentation: A survey[END_REF]. According to the type of application, these methods require choosing relevant features to detect the regions of interest. Texture information is an important cue for many applications including the nerve blocks detection. However, texture analysis in US images is not an easy task. Nevertheless, several works have shown useful properties using texture to segment different tissues in US images. Features based on gray level correlation matrix (GLCM) [START_REF] Haralick | Textural features for image classification[END_REF], have been used for the detection of cardiac images [START_REF] Boukerroui | A multiparametric and multiresolution segmentation algorithm of 3-d ultrasonic data(hrlk)[END_REF], and the placenta [START_REF] Malathi | Histogram based classification of ultrasound images of placenta[END_REF]. In another work, GLCM has been utilized to guide the evolution of active contour for detecting the Thyroid Gland [START_REF] Tesar | Genetic algorithms for thyroid gland ultrasound image feature reduction(haralick)[END_REF]. Recently the wavelet approach has been used with support vector machine (SVM) classifier to detect the prostate region [START_REF] Zaim | Feature based classification of prostate us images using multiwavelet and kernel svm[END_REF], and also thresholding based wavelet has been used to remove the noise to detect the prostate [START_REF] Knoll | Outlining of the prostate using snakes with shape restrictions based on the wavelet transform (doctoral thesis: Dissertation)[END_REF]. In [START_REF] Shen | Segmentation of prostate boundaries from ultrasound images using statistical shape model[END_REF] Gabor filter bank has been combined with active contours for the prostate detection. Gabor filter is also utilized with expectation and maximization algorithm to detect liver and cystic kidney [START_REF] Khanna | Us image segmentation based on expectation maximization and gabor filter[END_REF]. The local binary pattern (LBP) has been also utilized in the purpose of the prostate segmentation [START_REF] Ghose | Prostate segmentation with local binary patterns guided active appearance models[END_REF]. The performance of texture-based methods depends on the type of the tissue in the US images. Most of the state-of-the-art techniques have been applied to either hyperechoic or hypoechoic regions. The textural aspect of these regions is different each other, which requires different approaches. The nerve region presents a particular pattern that can be hypoechoic or hyperechoic structure, depending on the size of the nerve, the probe frequency and the angle of the ultrasound beam [START_REF] Marhofer | Ultrasound-guided regional anesthesia: Current concepts and future trends[END_REF]. In this work, we address the problem of "median nerve" detection that presents a hyperechoic structure with a particular textural information. Due to the poor quality of the US images the nerve region is not easy to distinguish among others anatomical structures. The traditional texture features are not be sufficient to handle such a situation. In this paper, we propose a new method for detecting the median nerve. This method consists in two phases. The first one separates the foreground regions (hyperechoic tissues). The second phase extracts the nerve area in the foreground using support vector machine (SVM) and a new type of features that is a combination between Gabor filter and median binary patterns (MBP) [START_REF] Hafiane | Rotationally invariant hashing of median binary patterns for texture classification[END_REF]. Fig. 1 shows the flowchart of the proposed technique.

Nerve Detection

The median nerve appears brighter in the US images since it is a hyperechoic structure. Therefore, the first step requires the segmentation of the hyperechoic foreground tissues to reduce the non useful information. In the next stage, the nerve is extracted from the foreground using texture features, called Median Gabor Binary Pattern (MGBP).

Hyperechoic tissues segmentation

To extract the hyperechoic tissues, we used Gaussian filtering processing to reduce the image noise, then k-means algorithm is applied to classify each pixel into background and foreground regions. Fig. 2 shows an example of the segmentation result, where we can distinguish the hyperechoic tissues from the other ones.

Feature extraction

As we are dealing with noisy data, it is important for the descriptor not to be sensitive to the noise. The Gabor descriptor can help to reduce the noise effect, since it is based on band-pass filtering process [START_REF] Daugman | Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters[END_REF]. However, frequency methods such as Gabor filter are not sufficient to characterize the nerve structure, it is more interesting to use additional information. The LBP based methods are among the best techniques for texture analysis and it can be combined with Gabor descriptors to achieve better performances as shown in [START_REF] Zhang | Local gabor binary pattern histogram sequence (lgbphs): A novel non-statistical model for face representation and recognition[END_REF]. This method called Local Gabor Binary Pattern (LGBP) has demonstrated some robustness with respect to the noise, while producing good performances for recognition task.

LGBP can be suitable for ultrasound images, however it may fail to characterize the nerve texture due to the importance of the noise. Median Binary Pattern (MPB) has more interesting properties when it deals with noisy textures. MBP incorporates the median filtering processing which helps to reduce the noise. We propose to combine MBP with Gabor Filters producing the Median Gabor Binary Pattern (MGBP) descriptor, as shown in Fig. 3. To compute the M GBP at the position (x, y) on a given image I, first, I is convolved with Gabor kernel, expressed by the following equation,

g(x, y) = exp[- 1 2 ( x ′2 σ 2 x + y ′2 σ 2 y )]cos(2πf x ′ ) (1)
where x ′ = xcosφ + ysinφ, y ′ = -xsinφ + ycosφ, φ is the filter direction, σ is the standard deviation of Gaussian envelope, and f is the frequency of cosine wave. We use the magnitude of the Gabor filter response, that is z(x, y) = |I(x, y) * g(x, y)|. The MGBP is determined by mapping from the response z(x, y) space to a localized binary pattern, thereby thresholding the neighborhood pixels against their median value. The MGBP at pixel (x, y) is defined as,

M GBP P,R = P -1 p=0 δ(z p -z m )2 P δ = 1, x 0 0, x < 0 (2)
We adopted the same strategy as LBP and MBP [START_REF] Ojala | Multiresolution grayscale and rotation invariant texture classification with local binary patterns[END_REF][START_REF] Hafiane | Rotationally invariant hashing of median binary patterns for texture classification[END_REF] for the different parameters, where P is the number of neighbors and R is the radius of the circular neighborhood, z p is the pixel value in R and z m is the median value in this neighborhood. Rotational Invariance Uniform (RIU) is defined as,

M GBP riu2 P,R = P -1 p=0, δ(z p -z m ) if U (M GBP U P,R ) ≤ 2 P + 1 otherwise (3)
where

(M GBP U P,R ) = |δ(z p-1 -z m ) -δ(z 0 -z m )| + P -1 p=0 |δ(z p -z m ) -δ(z p-1 -z m )| (4)
After obtaining the local patterns in the processed image, we compute the MGBP hisotgram at each pixel within N × N centered patch. These histograms provide MGBP descriptors.

Nerve classification

In the classification process, each pixel of the segmented foreground is labeled as belonging, or not, to a nerve tissues. For that purpose we use the SVM algorithm to identify the nerve pixels. SVM classifier [START_REF] Vapnik | Statistical learning theory[END_REF] is based on intuitive geometric principles, aiming to define an optimal hyperplane in the training data so that minimum expected risk is achieved. SVM is widely used for image segmentation and classification showing very powerful discriminative properties. In this study, the linear kernel K(x, x ′ ) = (< x, x ′ >) n has shown the best performances compared to the non linear ones.

Experimentation

The experiments were conducted over 173 ultrasound images of the median nerve extracted from three US videos of patients. Data set was obtained in real conditions at Médipôle Garonne clinic (Toulouse, France). The ground truth was marked by regional anesthesia experts.

In the first stage the k-means segmentation was performed over all the images to segment the foreground (see section 2.1), then the classification process was applied over the foreground to extract the target region. For that purpose, the dataset were separated into three groups, each one containing a set of the US images of one patient; the images size is 633×418. We use one group for learning the model and the remaining ones for the tests. The cross validation procedure was used to generate the learning and testing sets (see Fig. 4). For each couple of learning/testing set, the SVM algorithm has been applied to classify the pixels. Specificity, sensitivity and accuracy were used to measure the performance of the tested methods,

Accuracy : Acc = Sn + Sp 2 , Sensitivity : Sn = tp tp + f n , Specif icity : Sp = tn tn + f p (5)
where tp, tn, f p, f n are respectively true positives, true negatives, false positives and false negatives. In order to illustrate the effectiveness of the proposed approach for the nerve detection, we have conducted comparative experiments with most of the popular methods of texture analysis in ultrasound images, such as the Gabor descriptor, LBP, MBP, Wavelet, GLCM and LGBP with different parameters. The Gabor filters have been generated using different combination of parameters for the orientation θ = (0, π/4, π/2, 3π/4) and the scale s = (1, 2, 3). The experiments of LBP and MBP have been generated using a several values for radius R and neighborhood P (i.e. R = (1, 2, 3) and P = (8, 16, 24)). Different Wavelet families have been applied to our data, in this experiment we kept the best parameters of each family. The GLCM descriptor was also tested with different orientations, whereas the distance of one pixel showed better results. Finally, it is also important to study the influence of the patch size, for our experiments the size 35 × 35 produced the best classification scores.

Evaluation of the texture methods

In this section we measure the performance of several state-of-the-art methods, by varying the parameters of each method as shown in Tables 1,2, 3, 4. From these tables, it can be seen that the best accuracy score for each method (bold type in the table) depends on the specific set of parameters. For the Gabor descriptor, scale=1, orientation (θ = π/2) and frequency (λ = 1) yielded the highest value (70.89%). For the LBP and MBP, the best parameters are LBP 3,24 riu and M BP 8,16,24 riu , respectively. For the Wavelet descriptor, the symlets wavelet, where the number of vanishing moments is five (sym5) [START_REF] Daubechies | Ten lectures on wavelets[END_REF] and level 3 produced 63.92%. GLCM yielded an accuracy of 62.45% for distance=1 and orientation=0. The best classification accuracy scores were obtained with Gabor and MBP descriptors produced the better accuracy (70.89% and 70.50%) compared to the traditional techniques. Best performance were obtained when these two methods were combined. Table 4 shows the MGBP and LGBP classification accuracies. It can be observed that MGBP achieves higher average accuracy (71.34%) than LGBP. The largest difference is about 8.79% when R = 1 and P = 8.

Params

Overall comparison

In this part, we compare the proposed method (MGBP) with the other techniques previously described, using only the best scores of each technique. Fig. 5 shows qualitative and quantitative experimental results. From this figure, we can see that MGBP reachs the highest correct classification rates (71.34%) among all the other approaches. The qualitative results demonstrate that MGBP provides better accuracy for nerve detection. In general, the combination of MBP and Gabor filter is more accurate than the original MBP or Gabor as a single feature. MGBP attains the best results and realizes a good tradeoff between the Sensitivity and Specificity, which enable an accurate nerve detection. However, the experimental results shows that the texture of nerve as hypoechoic tissues is hard to detect using mono model feature.

This demonstrates that MGBP is stable and robust for US images and proved to be a good descriptor for US images.

Conclusion

In this paper we have proposed a new technique for nerve detection in ultrasound images using two phases: the k-means clustering for foreground segmentation and the texture analysis to extract the nerve region amid the foreground hyperechoic tissues. The nerve identification presents the most critical part of this work. As the nerve presents some interesting textural properties, we focused on the texture analysis. A new method (MGBP) based on MBP and Gabor filter have been proposed as texture descriptor. The experimental evaluation on real data, showed that MGBP enables efficient detection of the nerve region compared to the tested state-of-the-art methods. This is due to the fact that MBP and Gabor enhance the texture profile in the noisy data, which increase the robustness of MGBP descriptor with respect to the speckle noise and other artifacts in the US images. In the future, we will explore the possibilities to extend the detection to others types of nerves.

Fig. 1 .

 1 Fig. 1. Flowchart of the nerve detection in the ultrasound images.

Fig. 2 .

 2 Fig. 2. Segmentation of hyperhecoic tissues using K-means.

Fig. 3 .

 3 Fig. 3. The stage of MGBP feature extraction method.

Fig. 4 .

 4 Fig. 4. Evaluation scheme.

Fig. 5 .

 5 Fig. 5. Comparison of classification results of the proposed method and the best method of analysis texture.

Table 1 :

 1 Classification results for different parameters of Gabor

		Scale=1	Params		Scale=2	Params	Scale=3
	θ	Acc	Sn	Sp	θ		Acc Sn	Sp	θ	Acc Sn	Sp
	0	66.13 52.36 79.90	0	65.37 50.58 80.15	0	63.91 46.96 80.86
	π/4	64.88 49.30 80.46	π/4 67.64 52.68 82.59	π/4 70.17 58.03 82.31
	π/2 70.89 58.47 83.32	π/2 68.04 53.97 82.10	π/2 66.22 45.32 87.12
	3π/4 70.48 51.19 89.77	3π/4 68.91 49.70 88.12	3π/4 60.36 38.35 82.37
			Params			LBP			MBP
		Type R	P	Acc	Sn	Sp	Acc	Sn	Sp
		u2	1	8	65.24 86.90 43.59 37.78 23.44 52.12
		ri	1	8	66.14 87.43 44.85 45.72 35.03 56.40
		ri	2	16	66.15 87.43 44.86 46.65 24.12 69.19
		riu2 1	8	66.14 87.43 44.85 58.77 47.11 70.42
		riu2 2	16	66.12 87.41 44.83 56.65 33.33 79.98
		riu2 3	24	64.91 86.39 43.42 53.59 32.61 74.57
		riu2 1,2,3 8,16,24 64.42 52.21 76.63 70.50 65.87 75.14

Table 2 :

 2 Classification results for different parameters of LBP and MBP

	Wavelet		Level=3		GLCM		Dist=1
	f amilies Acc	Sn	Sp	Orientation Acc	Sn	Sp
	bior3.3 63.74 60.29 67.19	0	62.45 79.04 45.86
	db6	63.82 60.74 66.90	π/4	59.58 79.61 39.56
	sym5 63.92 61.18 66.66	π/2	60.35 79.46 41.25
	coif 1 63.92 61.15 66.33	3π/4	60.06 79.58 40.54

Table 3 :

 3 Classification results for different Wavelet families and GLCM

	Params(riu2)		LGBP			MGBP
	R	P	Acc	Sn	Sp	Acc	Sn	Sp
	1	8	61,99 70.97 53.02 71.34 82.38 60.30
	2	16	62.55 44.42 80.68 57.01 50.29 63.73
	3	24	60.54 35.54 89.54 61,15 34.61 87.69
	1 2	8 16 61.14 68.97 53.31 68,20 77.39 59.01
	1 3	8 24 61.82 66.63 57.01 63,72 74.01 53.43
	2 3 16 24 60.12 46.63 74.17 60,42 40.39 80.45
	1 2 3 8 16 24 66.99 70.97 53.02 66.48 70.05 62.45

Table 4 :

 4 Classification results for different parameters of LGBP and MGBP