D Saletti

P Forquin

A comparison of DIC and grid measurements for processing spalling tests with the VFM and an 80-kpixel ultra-high speed camera

Keywords: full-field measurements, high strain rate, high speed imaging, spalling tests, grid method, DIC, virtual fields method

A comparison of DIC and grid measurements for processing spalling tests with the VFM and an 80-kpixel ultra-high speed camera

Dominique Saletti, Pascal Forquin

Introduction

The spalling technique is commonly used to investigate the dynamic tensile strength of brittle geomaterials (concrete, high strength concrete, rock) at strain rates ranging from a few tens of /s to about 200 /s. The experimental set-up consists in launching a short cylindrical projectile with a gas gun facility against a Hopkinson Pressure Bar, put in contact with the specimen. A dynamic tensile loading is created into the specimen by the reflection of a short compressive pulse at the free end of the specimen. Then, the tensile failure of the tested material can be analysed [2,3,4]. In the literature, spalling tests have been used to study the Dynamic Increase Factors (DIFs: ratio of dynamic strength to quasi-static strength) [4,5,6,7] of concrete in tension, revealing its sensitivity to the applied strain rate. This set-up was first used in its present form a century ago [START_REF] Landon | Proc. R. Soc[END_REF]. The post-processing of the test realised in 1923 was related to the velocity of ejection of the fragments linked to the distance they crossed, upon basic kinematic hypothesis. The technological improvement of measurement techniques during the last 30 years has increased the number of studies using this test method to analyse the mechanical properties of concrete-like materials. Among the techniques used to identify the maximal tensile strength of the specimen during a spalling test, the Novikov's method prevails [START_REF] Novikov | [END_REF]2,4]: it is based on the measurement of the velocity profile on the rear face of the sample.

However, it relies on the assumption of a linear-elastic behaviour of the tested material until the stress-peak and provides only its spall strength. No information on the softening behaviour that follows is available. Recently, Pierron and Forquin [1] introduced the use of a full-field measurement technique, the grid method, in the spalling tests of concrete. A Virtual Field Method (VFM) was associated to these measurements in order to get the stress field in the region of interest captured by an Ultra-High-Speed (UHS) camera. This was the first use of the full-field measurement in a spalling test. Digital Image Correlation (DIC) is an alternative technique to grid method to measure displacement fields at the surface of the specimen. This technique is widely used nowadays and is quite easy to be set by the application of a painted speckle.

However, it can be really challenging to use DIC in the spalling test conditions. The UHS cameras currently available at recording frequency of one million frames per second (Mfps) present low resolutions (around a hundred of kpixels) and DIC measurement is strongly dependent of this parameter. Nevertheless, as the improvement of UHS cameras is expected, the use of DIC in spalling tests has to be investigated as from now.

The aim of this study is to present a comparison between the performance of the grid method and the DIC technique in the evaluation of the stress, strain, acceleration and displacement in the specimen during a spalling test, after combining each full-field measurement to the Virtual Field Method. For this purpose, spalling tests were performed on an aluminium alloy. Two specimens were used: one with a grid glued on its surface and another with a painted speckle on its surface. The UHS camera Shimadzu HPV-1 (312 x 260 pixels 2 ) was used at a recording frequency of 500'000 and 1'000'000 frames per second. Performances and limitations of this camera have been first evaluated in previous works [10,11] by using the grid method. The HPV-1 camera being the first in-situ storage image sensor UHS camera (ISIS architecture: single CCD sensor with embedded memory storage) providing a resolution of about 80 kpixels at framerate up to 1Mfps, the present study aims to constitute a benchmark regarding the new cameras coming onto the market at this moment.

Experimental technique

Samples and spalling test technique

The material tested in this study is a high-strength aluminum, also used for the projectile and the Hopkinson bar of the spalling testing set-up and is characterized by a 1D wave speed C of 5090 m/s, a density of 2810 kg/m 3 and a Young's modulus equal to 72.8 GPa [4]. The samples are cylindrical, 45 mm in diameter and 140 mm in length for the one with a grid and 100 mm for the one with a painted speckle. These dimensions are summarized in the Figure 1. This difference in length has no influence on the results of the study: there is no influence on the level of uniaxial stress in the specimen as the sample is expected to have an elastic behavior and the observation window used with the UHS camera, starting from the free end of the specimen, has the same size for both techniques. Both samples are instrumented with a 20 mm-long strain gauge placed at 50 mm from the rear face (the free end).

The spalling test set-up used in this study is composed of a 50 mm-long spherical-capended projectile and a Hopkinson bar both with a diameter of 45 mm. An illustration of the experimental set-up is given on Figure 2. A short incident compressive pulse is created and propagates through the Hopkinson bar. Then, the pulse is transmitted to the sample and reflects at the free-end of the specimen as a tensile pulse leading to a dynamic tensile loading within the sample. The particle velocity at the rear-face is recorded with a laser interferometer from Polytec, enabling velocity measurements up to 20 m/s with a 1.5 MHz bandwidth [4].

Optical measurement

A Shimadzu HPV-1 UHS camera was used in this study and described by Pierron and Forquin [1]. This device allows recording a sequence of 102 images up to one million frames per second (fps) with a constant resolution of 312 x 260 pixel². Two frame rates were employed: 1 Mfps and 500 kfps. For all the tests, the exposure time was set to 0.5 µs. The horizontal axis of the image corresponds to the longitudinal axis of the specimen and the left-hand side of the image corresponds to the free-end of the specimen (Figure 1). For the sake of comparison, the same image scale (about 0.2 mm per pixel) was set for both full-field measurement techniques. The length of the specimen capture by the camera is around 60 mm. Table 1 summarizes the different settings used in this paper.

Grid Method

For the grid method, the magnification was adjusted to get a 5-pixels grid spacing. The pitch of the grid being 1 mm, the image scale is 0.2 mm per pixel so the length of the specimen captured by the optical device is around 60 mm. This observation window with the grid can be seen on Figure 1(b), for a reference image. The displacement fields are computed in the same way as in Pierron and Forquin [1], thanks to a characterisation by phase modulation, considering the local intensity and the contrast produced by the grid on the image. As it was found in this study, a significant low-pass filtering should be used to extract the strain values. This is due to the fact that the amplitude of displacement is small (less than half a millimetre) leading to displacement maps with high noise content. Hence, a diffuse approximation is processed. This filtering procedure is a local fit of a second-degree polynomial using specific weighing function (more details can be found in [12]). As a full description of the grid method would overload the content of this paper, the authors also invite the reader, to complete the description, to refer to [START_REF] Surrel | Interferometry '94: Photomechanics[END_REF][START_REF] Avril | [END_REF]. More information on the metrological performance of the HPV1 ultra-high speed camera for full-field deformation measurements with the grid method are also given in [11].

Digital Image Correlation

The DIC (Digital Image Correlation) method has been widely used until now to investigate the mechanical response and damage behaviour of materials. In this study, the Correli Q4 code was used to measure the displacement and strain fields. The principle of this software is given by Besnard et al [15]. A Region of Interest (ROI) is defined on a reference image and a mesh grid is created with a user-defined element size. The elements of this mesh (with Q4-shape functions) are also called Zone of Interest (ZOI).

Based on a global approach, each element is dependent on the surrounding ones. The correlation computation consists of finding a displacement field u to link an image of the test sequence, the deformed image, g, to the reference image, f. The strain field is then computed on the surface of the specimen using the gradient of the displacement field.

Hence, black and white paints were applied at the surface of the specimen, creating a heterogeneous speckle, as it can be seen on Figure 1(a). The quality of the speckle and the settings of the camera were validated by an image analysis taking into account the histogram of the image. For this study, the image scale was set to 0.196 mm/px, close to the magnification set with the grid method. All the DIC computation results presented in this paper were obtained with a ZOI size of 8 px (around 1.5 times the pitch of the grid).

The Virtual Field Method (VFM)

The Virtual Field Method is based on the principle of the virtual work. It was successfully used for processing the experimental data of a spalling test in association with the grid method [1]. One advantage of this technique is that it can be used with any full-field measurement technique that measures kinematic fields.

Before using this method, the first step lies on the double differentiation of the displacement fields. A temporal fitting is applied on this result with a second-order polynomial function over a sliding of five images for measurements obtained with DIC and seven images for measurements obtained with the grid method. This results in an acceleration map required for the computation of the stress along the specimen with the Virtual Field Method.

As described in Pierron and Forquin [1], by defining in this case a rigid body-like virtual field, the mean stress in any cross-section Sx of coordinate x along the length of the sample filmed by the camera can be calculated according to Eq. 1:

𝜎 !! (𝑥, 𝑡) = -𝜌𝑏(𝑥)𝑎 ! (𝑥, 𝑡) (1)
Where t corresponds to the current time, 𝜎 !! denotes the mean axial stress in the cross section Sx of coordinate x, 𝜌 is the mass per unit volume of the sample, b(x) corresponds to the length between the cross-section Sx and the free-end, and 𝑎 ! (𝑥, 𝑡) corresponds to the mean acceleration between the cross-section Sx and the free-end.

Finally, the stress-strain curves in cross section Sx can be obtained by combining the axial stress measurements with the axial strain 𝜀 !! 𝑥, 𝑡 , measured with DIC or grid method.

Measurement results and discussion

In order to have a comparison as relevant as possible, the authors tried to perform all the spalling tests with the same kinetic input energy. The amplitude of input loading can be evaluated by comparing the velocities measured with the laser interferometer at the free-end of the specimen and reported on Figure 3. The maximum rear face velocity varies between 9.7 m/s and 12.5 m/s. The black lines refer to the experiments performed with the grid method and the grey lines correspond to the tests conducted with the DIC method. The two different time periods of the curves are related to the different lengths of specimen.

In the next sections, the results provided by both full-field measurement techniques (grid and DIC) are compared to the results obtained from independent measurement systems. In a first part, the kinematic fields are compared to the laser interferometer measurements. In a second part, the strain field measurements and the stress values along the specimen obtained with the VFM are compared to measurements from the strain gauges glued on the samples.

Comparison with the laser interferometer measurement

Displacement

The displacement on the free-end is obtained from the laser measurement by single time-integration of the particle velocity. On Figure 4, a comparison is made with the displacement given by the full-field measurements.

In the case of the grid method, the displacement of the free end of the specimen corresponds to the mean axial displacement along the first transversal line of the grid.

In the case of DIC computations, the displacement is not directly measured at the free end of the specimen. This is due to the fact that, once the ROI is selected for the computation, the software creates a mesh inside this ROI with margins. So, the displacement is evaluated at 2.5 mm from the free-end (ZOI size of 8 px). Nevertheless, this distance to the free-end is supposed to be small enough to have no influence on the evaluation of the displacement at the free end. As for the grid method, the displacement is averaged along the first transversal line of the mesh.

Figure 4 presents the displacement as function of time measured in each test. Despite the fact that the displacement measurement is not evaluated exactly at the free-end of the specimen, the DIC measurements appear to be very close to the interferometer ones.

Both measurements performed with the grid and DIC methods seem to be in good agreement with those obtained from the laser interferometer. However, for the GRID-02 test, the measurement presents a noise perceptibly higher than in the three other tests, resulting in a displacement measurement significantly different from the standard laser one. A summary of the deviation of measurement is presented in the Table 2.

Comparisons have been done for two values of displacement: 0.1 mm and 0.2 mm. This range of value is consistent with the displacement measurement usually found for brittle such as concrete in spalling test. An evaluation has also been made for interval of displacement of 0.2 mm (0.05 mm to 0.25 mm), in order to analysis the variation of the difference between the laser interferometer values and the one with digital image methods. A mean value (in %) is presented for each test and the standard deviation is also given. The DIC technique seems to give better results than the grid method regarding displacement. The deviations from the laser measurements can be partially explained by the noisy content of the image, due to the UHS camera. However, in the case of GRID-02 test, the important gap reported in Table 2 can be also related to the sensitivity of the grid method. Indeed, if 5-pixels grid spacing is not correctly set for the image, a slight difference may lead to an important deviation of the measurement. This is not the case of DIC, which explain why the difference between DIC-01 and DIC-02 are not as important as in the grid method case.

Acceleration

As the acceleration maps are used to evaluate the stress in the specimen with the virtual field method (Eq. 1), it is important to assess the quality of the acceleration measurements with both full-field measurement methods (Grid and DIC). Acceleration is first calculated by time-deriving the particle velocity measurement of the laser interferometer. Regarding the optical measurement, accelerations are computed as described in the previous section, by temporal fitting of a second-order polynomial function over a number of images depending on the full-field measurement technique:

five images are used for the DIC and seven for the grid method. The acceleration is evaluated for each image by spatial-averaging the acceleration values on each node along the closest transversal edge to the free-end. As for displacement, accelerations with the DIC method are not really evaluated at the free-end of the specimen but at 2.5 mm from the free-end.

The results are presented in the Figure 5. First, the magnitude and shape of the acceleration in all tests (DIC-01, DIC-02, GRID-01 and GRID-02) are quite consistent with the interferometer measurements. The discrepancy observed for GRID-02 can be linked to the noise observed in the displacement measurement. It is observed that the results provided by the grid method seem to be noisier than the ones obtained from the DIC method. As for displacement, a comparison between the laser interferometer and the optical measurements have been done and presented in the Table 3.

Apart from the fact that the light level might have slightly changed between DIC-01 and DIC-02 tests, the frame rate used for the two tests seems to have an influence on the results. Inter-frame time between two images was set to 1 µs for DIC-01 and 2 µs for DIC-02 with the same time exposure (0.5 µs). This effect can also be observed between GRID-01 and GRID-02, in a less significant way. With the DIC method the sensitivity to the variation of light at 1µs (due to the technology of the sensor of HPV1 camera) seems to have more influence on the results. Finally, regarding the level of noise in acceleration measurement (Figure 5), one may ask whether the acceleration map and the virtual field method can be employed for measuring the stress in the sample (Eq. 1). In fact, the spatial-averaging of the acceleration over the length b according to the Equation (1) reduces the noise observed here.

Comparison with strain gauge measurements

Strain gauges provide a measurement of the strain in a local area of the specimen. For both specimens, a strain gauge is located at 50 mm from the free-end and delivers a measurement of the longitudinal strain that is assumed to be homogeneous over the cross-section of the specimen. By making the assumption of an elastic behaviour of the specimen during the test, the stress at this location can also be evaluated.

In the next section, a comparison of experimental results is proposed over a period of time about 80 µs corresponding to the time interval between the beginning of the test to the beginning of the second compressive phase.

Strain measurement

As with strain gauge measurements, the strain values obtained from DIC and grid techniques were averaged along the transverse direction of the specimen and over a zone of length 22 mm for DIC and 20 mm for the grid method corresponding to the position of the gauge.

The results are presented in the Figure 6. As for acceleration, the change of strain measured by DIC and grid methods is similar to the data obtained from the strain gauges. Regarding the maximum value of strain in compression, overestimations of 34 % for GRID-01 and 42 % for DIC-01 are reported. In the tensile stage, which is of greater interest in the spalling tests, a difference of 17 % for GRID-01, 18 % for GRID-02, 14 % for DIC-02 is reported compared to the strain gauges results. Considering visually the results on the whole process, the grid method may produce noisier measurement than the DIC method, especially in the case of low contrast or wrong spatial scaling adjustment. For instance in GRID-02 test, a part of the noise is supposed to comes from a weaker grey-level dynamic of images that increases the displacement deviation (Figure 4d). Otherwise, if GRID-02 experiment is not considered, according to the values reported in Table 4, the errors made in the measurement of strain by the two techniques are of the same magnitude.

Stress measurement

For a uniaxial stress-state in the sample and considering an elastic behaviour of the sample the stress can be evaluated in the cross-section at the strain gauge location by:

𝜎 !! (𝑥, 𝑡) = 𝐸𝜀 !! (𝑥, 𝑡) (2)
Where 𝜎 !! is the uniaxial stress along the x-axis and 𝜀 !! the uniaxial strain along the xaxis and measured by the strain gauge.

As described in the previous section, the stress in the same cross-section can be evaluated with the full-field measurement technique (Eq. 1). By applying the Virtual Field Method to the kinematic fields, the stress can be evaluated for each cross-section of the specimen included in the observation window visualised with the camera. To make the comparison with the strain gauge measurement as relevant as possible, the stress is calculated by averaging the local stress in a zone of length of 22 mm for DIC and 20 mm for the grid method. Figure 7 reveals the same conclusion than for the strain: the shapes of the curves are consistent with the strain-gauges measurements.

Regarding the maximum stress values in the compression stage, the difference between the strain gauge and the optical measurements are: 18.4 % for GRID-01, 28 % for GRID-02, 44 % for DIC-01, 13.2 % for DIC-02. For the tensile stage, the deviation between the strain gauge and optical measurements are: 25.8 % for GRID-01, 30.4 % for GRID-02, 5.5 % for DIC-01 and 20 % for DIC-02. These values are obtained by analysing the maximal values obtained in each phase (compression and tension), and constitute a first estimate of the error that could be made by evaluating the spall strength of materials with this experimental processing. The corresponding stress deviations (mean value and standard deviation) are reported for each phase (compression and tension) in the Table 5. As it was expected, the stress curves present less noise than in the case of the "spot measurement" of acceleration (Figure 5) as the spatial-averaging of the acceleration to evaluate the stress (Eq. 1) constitutes a filter of the data. According to the values of deviation in the tensile phase, (of greater interest for testing the tensile strength of geomaterials), one can see that the differences obtained with grid method and DIC are quite similar if GRID-02 is not considered (12.3 Mpa for GRID-01 compared to 16.8 MPa and 13.0 MPa for DIC).

Stress-strain curves

The last point of comparison available with the measurements conducted in this study is the production of a stress-strain curve. Figure 8 presents for each test the curves obtained with the VFM applied to the kinematic measurements. The plots of the strain gauge data are straight lines, due to the linear assumption of an elastic behaviour (Eq.

2)

.

GRID-02 is clearly different from the expected shape. This is mostly due to the poor quality of displacement and strain measurements presented in Figure 6d and Figure 6d.

For GRID-01, DIC-01 and DIC-02, the gap observed from the expected linear behaviour can be both explained by the error in the measurement of the stress and of the strain with the grid and DIC methods. This effect is emphasised for DIC-01 test. In order to appreciate theses results, Young modulus has been evaluated from these curves with ordinary least-squares (OLS) estimation and the results are presented in the Table 6.

The difference with the standard Young Modulus value of 72.8 GPa is established. If GRID-02 is not considered, an error between 10 % and 15 % is obtained.

Conclusion

In this study, the authors attempt to make a comparison between the use of the grid method and the digital image correlation method in the Virtual Fields Method to postprocess a spalling test. The results are compared to reference values, which are obtained with a laser interferometer regarding displacement and acceleration, and obtained with a strain gauge glued on the sample regarding strain and stress. This approach was used to minimize the bias due the fact that it was not possible to apply the grid method and the DIC method for a same test on a same specimen. So, these techniques were assumed to be a standard for this study and quantitative comparison has been proposed. The level of quality of the full-field measurements produced in this study is partly linked to the quality of the CCD sensor of the Shimadzu-HPV1 UHS camera. Nevertheless, at the time of the study, only few cameras can reach the same level of performance and the fact that the same camera with the same settings was used for all the tests reduces a potential bias from this point of view.

By considering all the comparisons made in this study, the advantages and the drawbacks of each method can be listed. First, the grid method is a technique that is dependent from the adjustment of the spatial scaling of the image to an odd number of pixels per grid pitch. Consequently, the grid method may be sensitive to a bad adjustment of the pixel spacing of the grid. On the other hand, the results obtain with the DIC are more stable from a test to another one. Moreover the setting time is considerably decreased with the DIC method and it provides flexibility for the choice of the window size. On the other hand, solving contrast and spatial scaling problems, noise obtained with the DIC and grid methods seems to be similar as for the measurement of strain and displacement than for the local measurement of acceleration (Table 2).

Nevertheless, the DIC method is sensitive to the resolution of the image and the size of the zone of interest has a great influence on the quality of the results. In this study, a ZOI of 8-by-8 pixels 2 has been applied in order to be in accordance with 5-pixel grid spacing of the grid method. The results may be improved by increasing the size of the ZOI but the low definition of the image obtained by the 80-kpixels-UHS camera limited this possibility in the present study. The grid method appears, in that case, to have a much better spatial resolution. Another point is that to perform the DIC processing, a mesh is created on this image. In Correli Q4 , the margin employed to create this mesh leads to a loss of information (as an example, the displacement at the free-end of the sample was impossible to obtain). This is not the case for the grid method for which the grid is directly printed on the surface of the specimen.

Regarding the accuracy in the measurement of the stress (Table 5), which is of a great interest for the spalling test, the performances of the DIC and the grid method are quite similar and it cannot be concluded there is an interest into choosing a technique instead of another in the case of the measurement of small strain gradients. In the future, the increase of the spatial resolution of ultra-high speed imaging at frame-rates up to few Mfps could more favour the DIC technique over the grid method.

Table captions

Table 1. Summary of the test campaign (DIC: Digital Image Correlation).

Table 2. Differences (%) in the measurement of the displacement between the laser interferometer and DIC and grid techniques. (STD: standard deviation).

Table 3. Differences (%) in the measurement of the acceleration between the laser interferometer and DIC and grid techniques. (STD: standard deviation).

Table 4. Differences (%) in the measurement of the strain at 50 mm from the free-end of the specimen between the gauge and DIC and grid techniques. (STD: standard deviation).

Table 5. Difference (MPa) between the measurement of the stress at 50 mm from the free-end of the specimen between the gauge and DIC and grid techniques. (STD: standard deviation). Table 6. Young modulus values identified with an ordinary least-squares evaluation.

Figure 1 .

 1 Figure 1. Description of the two specimens used for the study. (a) Reference image used

Figure 2 .

 2 Figure 2. Experimental device for spalling tests. (The ultra-high-speed camera is not

Figure 3 .

 3 Figure 3. Velocity measured at the free-end of the specimen for the four tests.

Figure 4 .

 4 Figure 4. Displacement measurement with laser interferometer and the DIC (a, b) or the

Figure 5 .

 5 Figure 5. Acceleration measurement with laser interferometer and the DIC (a, b) or the

Figure 6 .

 6 Figure 6. Strain measurement at 50 mm from the free-end of the specimen. Comparison

Figure 7 .

 7 Figure 7. Stress measurement at 50 mm from the free-end of the specimen. Comparison

Figure 8 .

 8 Figure 8. Strain-stress curves at 50 mm from the free-end of the specimen. Comparison

Figure 1 :

 1 Figure 1: Description of the two specimens used for the study. (a) Reference image used for DIC computations with a painted speckle pattern. (b) Reference image used for the grid method computations. (c) Dimensions of the specimen. Dimensions are given in mm.

Figure 2 :

 2 Figure 2: Experimental device for spalling tests. (The ultra-high-speed camera is not represented).

Figure 3 :

 3 Figure 3: Velocity measured at the free-end of the specimen for the four tests.

Figure 4 :

 4 Figure 4: Displacement measurement with laser interferometer and the DIC (a, b) or the grid method (c, d).

Figure 5 :

 5 Figure 5: Acceleration measurement with laser interferometer and the DIC (a, b) or the grid method (c, d).

Figure 6 :

 6 Figure 6: Strain measurement at 50 mm from the free-end of the specimen. Comparison between values from strain gauges and the DIC (a, b) or the grid methods (c, d).

Figure 7 :

 7 Figure 7: Stress measurement at 50 mm from the free-end of the specimen. Comparison between the strain gauge measurements and the one obtained with VFM associated to the DIC (a, b) or the grid method (c, d).

Figure 8 :

 8 Figure 8: Strain-stress curves at 50 mm from the free-end of the specimen. Comparison between strain gauge measurements and the one obtained with VFM associated to DIC (a, b) or grid method (c, d).

Table 1 : Summary of the test campaign (DIC: Digital Image Correlation).

 1

Acknowledgements

This work has been partially supported by the LabEx Tec 21 (Investissements d'Avenirgrant agreement n°ANR-11-LABX-0030)


MD Adrien Bouglé
email: adrien.bougle@aphp.fr

MD Arthur Le Gall

MD Florence Dumas

PhD ; Guillaume Geri

MD, PhD Isabelle Malissin

MD Sebastian Voicu

MD Bruno Mégarbane

MD, PhD Alain Cariou

MD, PhD Nicolas Deye

Extra Corporeal Life Support for Cardiac ARrest patients with post-cardiac arrest syndrome: the ECCAR study

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Despite many improvements in Cardiac Arrest (CA) management, survival rate ranges from 11 to 17% [START_REF] Atwood | Incidence of EMS-treated out-of-hospital cardiac arrest in Europe[END_REF][START_REF] Dumas | Long-Term Prognosis Following Resuscitation From Out of Hospital Cardiac Arrest[END_REF]. Among CA patients who survived initial resuscitation, less than 30% survived to hospital discharge [START_REF] Laver | Mode of death after admission to an intensive care unit following cardiac arrest[END_REF][START_REF] Nolan | Outcome following admission to UK intensive care units after cardiac arrest: a secondary analysis of the ICNARC Case Mix Programme Database*: ICNARC Case Mix Programme Database[END_REF][START_REF] Lemiale | Intensive care unit mortality after cardiac arrest: the relative contribution of shock and brain injury in a large cohort[END_REF]. Post Cardiac Arrest shock (PCAS), defined as the association of a myocardial dysfunction and vasoplegia occurring after return on spontaneous circulation (ROSC) [START_REF] Mongardon | Postcardiac arrest syndrome: from immediate resuscitation to long-term outcome[END_REF], is globally responsible of one-third of deaths [START_REF] Lemiale | Intensive care unit mortality after cardiac arrest: the relative contribution of shock and brain injury in a large cohort[END_REF]. While persistence of myocardial dysfunction at 24h may be associated with early death [START_REF] Laurent | Reversible myocardial dysfunction in survivors of out-of-hospital cardiac arrest[END_REF], no differences in neurological outcomes have been shown between post-CA patients with PCAS and those without PCAS [START_REF] Lemiale | Intensive care unit mortality after cardiac arrest: the relative contribution of shock and brain injury in a large cohort[END_REF][START_REF] Laurent | Reversible myocardial dysfunction in survivors of out-of-hospital cardiac arrest[END_REF].

Recently, two studies have described the use of Extracorporeal Life Support (ECLS) in successfully resuscitated CA patients experiencing severe PCAS [START_REF] De Chambrun | Venoarterial extracorporeal membrane oxygenation for refractory cardiogenic shock postcardiac arrest[END_REF][START_REF] Bougouin | Post-cardiac arrest shock treated with veno-arterial extracorporeal membrane oxygenation[END_REF]. Although survival benefit was not demonstrated, ECLS-assisted patients had acceptable neurological prognosis. A solid understanding of key governing factors that lead those patients to die are thus requested to better select the patients the most likely to benefit for this strategy.

Our objectives were 1/ to describe a cohort of PCAS patients treated with ECLS and 2/ to identify factors that lead physicians to indicate initiation of ECLS in post-CA patients.

Material and Methods

Population and Data collection:

This retrospective observational study was conducted in two tertiary university centers in Paris. We included consecutive patients admitted to intensive care unit (ICU) for CA and PCAS (defined as the need for continuous norepinephrine or epinephrine infusion to maintain mean arterial pressure above 60 mmHg for more than 6 hours following restoration of ROSC despite adequate fluid loading [START_REF] Lemiale | Intensive care unit mortality after cardiac arrest: the relative contribution of shock and brain injury in a large cohort[END_REF]), and for whom an ECLS was initiated. Patients with refractory CA and in-hospital CA (except those that occurred in the cath-lab and the emergency ward) were not included.

ECLS-treated patients' data were collected retrospectively. Prospective database implemented in Cochin Hospital was used to identify control group of patients experiencing PCAS without ECLS [START_REF] Dumas | Long-Term Prognosis Following Resuscitation From Out of Hospital Cardiac Arrest[END_REF].

Our local ethics committees approved the data collection and study protocol (CE SRLF N° 12-384).

Treatment protocol

Patients admitted for CA were treated according to international guidelines, and similar procedures have been described elsewhere [START_REF] Dumas | Long-Term Prognosis Following Resuscitation From Out of Hospital Cardiac Arrest[END_REF][START_REF] Chelly | Benefit of an early and systematic imaging procedure after cardiac arrest: Insights from the PROCAT (Parisian Region Out of Hospital Cardiac Arrest) registry[END_REF]. ECLS implantation and patient's management during ECLS support, including anticoagulant treatment or weaning procedure followed ELSO guidelines [START_REF]Extracorporeal Life Support Organization (ELSO)[END_REF] and were previously described [START_REF] Mégarbane | Emergency feasibility in medical intensive care unit of extracorporeal life support for refractory cardiac arrest[END_REF].

Neurological outcome was daily assessed by ICU physicians, until death or ICU discharge.

According to guidelines [START_REF] Morley | Part 3: Evidence Evaluation Process: 2010 International Consensus on Cardiopulmonary Resuscitation and Emergency Cardiovascular Care Science With Treatment Recommendations[END_REF][START_REF] Peberdy | Part 9: Post-Cardiac Arrest Care: 2010 American Heart Association Guidelines for Cardiopulmonary Resuscitation and Emergency Cardiovascular Care[END_REF][START_REF] Wijdicks | Practice Parameter: Prediction of outcome in comatose survivors after cardiopulmonary resuscitation (an evidence-based review): Report of the Quality Standards Subcommittee of the American Academy of Neurology[END_REF][START_REF] Booth | Is this patient dead, vegetative, or severely neurologically impaired?: assessing outcome for comatose survivors of cardiac arrest[END_REF], neuroprognostication was performed daily using a multimodal approach, and life-sustaining therapies withdrawal decision was taken during a collegial consultation.

Outcomes

The primary outcome was the neurological evolution at one year, assessed by the Cerebral Performance Category [START_REF] Phelps | Cerebral Performance Category and Long-Term Prognosis Following Out-of-Hospital Cardiac Arrest[END_REF] (Favorable Outcome : CPC score = I -II ; Poor Outcome: CPC score = III -V) [START_REF] Adrie | Predicting survival with good neurological recovery at hospital admission after successful resuscitation of out-of-hospital cardiac arrest: the OHCA score[END_REF] at 1 year.

Analysis

We performed a description of factors associated with unfavorable neurologic outcomes at one year in the population of PCAS patients treated with ECLS. A logistic regression was performed to assess the association between the selected variables and the neurological outcome. ECLS group was compared with control group, using two-sided t test, or chi 2 test when necessary. Finally, we performed a univariate and multivariate analysis, using a stepwise logistic regression, to identify factors associated with the ECLS implantation.

Results are expressed as median (interquartiles 25-75) or number (percentage). The R project software (The R Foundation for Statistical Computing, Vienna, Austria) was used for statistical analysis.

Results

From January 2005 to December 2014, 46 PCAS patients treated by ECLS were included.

Three patients were non-included because of in-Hospital CA. Among the 3 patients nonincluded, one was admitted for septic shock consecutive to a pulmonary infection, the CA occured 8 days after the admission, and the patient deceased. One patient was a severely burned patient with ARDS. He deceased 17 days after his admission while on ECLS for CA consecutive to pulmonary embolism occurring 14 days after his admission. The last nonincluded patient was admitted for intoxication with beta-blockers, the ECLS being inserted 5 days after his admission, for extreme hemodynamic instability, he died while on ECLS.

Finally, 43 patients fulfilled the inclusion criteria. We also include a control population composed by 878 PCAS patients. ECLS population was predominantly young males, with a previous history of coronary events (Table 1). Sixty percent of them presented an initial shockable rhythm, with No-Flow of 2 [0-10] min and a Low-Flow of 28 min.

Hemodynamic parameters are described in table 2.

Nine patients survived (21%) at ICU discharge: myocardial recovery was observed for 7 patients (78%), one benefited from a heart transplantation, and one patient died at one year from end stage cancer. A favorable neurological outcome at one year was observed for 8 (19%) of the ECLS cohort (89% of survivors).

Death rate during the ICU stay (79%) was mainly related to multiple organ failure (MOF) (63%). Forty-five percent of death by MOF occurred in the first three days after ICU admission (Figure 1). ECLS inefficacy, defined as the inability to maintain cardiac output and arterial pressure despite maximal therapeutic investment, was observed in 11 of deceased patients (31%). Life-sustaining therapy withdrawal was initiated for 9 of them (26%), and cerebral brain death was pronounced for 2 patients (6%).

No statistical difference was found between centers except for the percentage of bystander CPR and Low-Flow duration (Table S1).

ECLS-treated patients who survived without severe neurological disability were younger than those with severe neurological impairment (Table 1). CPR characteristics and severity scores were not different between the favorable and the poor neurological outcome group, despite OHCA score showed a trend toward higher values in poor neurological group. By contrast, blood lactate level at ECLS implantation discriminated the two groups (Table 2 and figure S1). Coronary etiology of CA was associated with unfavorable outcome at one year, whereas the arrhythmia was associated with a better prognosis (Table 1).

ECLS-treated patients were younger, with a longer time to ROSC and a higher proportion of non-public location of CA and bystanded CPR, as compared to control group (Table 3). ECLS-treated patients had higher blood lactate and creatinine levels than the control.

In multivariate analysis (Figure 2), factors independently associated with ECLS implantation were as follows: age < 62 years old, serum creatinine > 109 µmol/l, administration of adrenaline < 2 mg, and public location of CA.

When considering the whole PCAS population, non-survivors at ICU discharge were older and experienced higher blood lactate and serum creatinine levels (Table 4). Time to ROSC were longer when comparing non-survivors to survivors. The etiology for CA in survivors was predominantly cardiac, with higher rates of coronary angioplasty. The proportion of ECLStreated patients was not different in survivors versus non-survivors.

Conclusions Discussion

Emphasizing on functional neurological outcomes, this observational study offers interesting findings.

The present retrospective study aimed at reporting the ten-year experience of two Parisian intensive care units in the application of ECLS for PCAS patients. Even though the death rate was high, the survivors of ECLS-treated PCAS population exerted no or minor neurological disabilities. Furthermore, the death rate in the ECLS-treated population is of a magnitude of the death rate of the PCAS population, although the severity was higher in the first population as compared to the second. The latter observation might raise the question of the potential benefit of ECLS in such a severe population. It also highlights the need for better identification of patients who could benefit of such investment. Therefore, we have identified blood lactates level at ECLS implantation and reversible cause of OHCA as potential factors associated with better outcomes.

In the survivors of ECLS-treated PCAS population, the potential for recovery of neurological function was high (89% of surviving patients were alive without severe neurological impairment). These data are consistent with previously published data [START_REF] Lemiale | Intensive care unit mortality after cardiac arrest: the relative contribution of shock and brain injury in a large cohort[END_REF][START_REF] Laurent | Reversible myocardial dysfunction in survivors of out-of-hospital cardiac arrest[END_REF], although ECLS wasn't used in those latter studies. Faster time to implantation could be a particular endpoint to achieve, as suggested by available data in the setting of refractory cardiogenic shock [START_REF] Rihal | SCAI/ACC/HFSA/STS Clinical Expert Consensus Statement on the Use of Percutaneous Mechanical Circulatory Support Devices in Cardiovascular Care (Endorsed by the American Heart Association, the Cardiological Society of India, and Sociedad Latino Americana de Cardiologia Intervencion; Affirmation of Value by the Canadian Association of Interventional Cardiology-Association Canadienne de Cardiologie d'intervention) *[END_REF].

Well-designed studies are lacking to support this hypothesis in the setting of PCAS. On the contrary, selecting patients the most likely to benefit for such a therapy could improve functional outcomes. Indeed, despite we observed that the mortality was not significantly different in the ECLS-treated population as compared to the control, blood lactate level, as well as the etiology of CA, was associated with neurological outcomes. Initiating ECLS on patients with low blood lactate level, and suffering for PCAS consecutive to reversible cause, could improve survival rates. Indeed, even though Bougouin et al. [START_REF] Bougouin | Post-cardiac arrest shock treated with veno-arterial extracorporeal membrane oxygenation[END_REF] showed no association between ECLS implantation and survival, our study suggests that the coronary etiology could be a potential confounding factor. Reversible causes of myocardial dysfunction could then have a better prognosis in terms of myocardial recovery [START_REF] Shavadia | Infarct Size, Shock, and Heart Failure: Does Reperfusion Strategy Matter in Early Presenting Patients With ST-Segment Elevation Myocardial Infarction?[END_REF]. By contrast, in case of constituted myocardial infarct, the potential for recovery could be altered [START_REF] Sakamoto | Extracorporeal Life Support for Cardiogenic Shock or Cardiac Arrest Due to Acute Coronary Syndrome[END_REF][START_REF] Chen | Analysis of the outcome for patients experiencing myocardial infarction and cardiopulmonary resuscitation refractory to conventional therapies necessitating extracorporeal life support rescue[END_REF][START_REF] Chen | Experience and result of extracorporeal membrane oxygenation in treating fulminant myocarditis with shock: what mechanical support should be considered first?[END_REF]. In fact, mortality observed in patients treated with ECLS for PCAS secondary to acute coronary syndrome, was higher than mortality observed in patients treated with ECLS for reversible causes. The mortality rates observed in our study remained high, but were comparable to those reported in the two previously published studies, respectively 72 [START_REF] De Chambrun | Venoarterial extracorporeal membrane oxygenation for refractory cardiogenic shock postcardiac arrest[END_REF] and 73% [START_REF] Bougouin | Post-cardiac arrest shock treated with veno-arterial extracorporeal membrane oxygenation[END_REF].

Complications occurred frequently, but were close to those reported in a meta-analysis of 20 studies evaluating ECLS usage [START_REF] Cheng | Complications of Extracorporeal Membrane Oxygenation for Treatment of Cardiogenic Shock and Cardiac Arrest: A Meta-Analysis of 1,866 Adult Patients[END_REF]. The most frequent complication in our study was acute kidney injury requesting renal replacement therapy (50%), being probably more a marker of the severity of the shock rather than a specific complication of ECLS. On the contrary, the high rates of specific complications of ECLS observed in our cohort, as the rate of lower limb ischemia (28% versus 17% in Cheng's study [START_REF] Cheng | Complications of Extracorporeal Membrane Oxygenation for Treatment of Cardiogenic Shock and Cardiac Arrest: A Meta-Analysis of 1,866 Adult Patients[END_REF]), could worsened the prognosis of some patients. However, ECLS implantation was performed by physicians trained to percutaneous cannulation with previously published good results [START_REF] Mégarbane | Emergency feasibility in medical intensive care unit of extracorporeal life support for refractory cardiac arrest[END_REF].

The retrospective design of the study limits the strength of the findings. We focused on a specific subpopulation of PCAS patients, and we retrieved data from 10 years' experience of two tertiary care centers. No randomized study could have been achievable in a reasonable time-frame. A matched analysis designed to identify the variables associated with survival would have been useful, but the low sample size of the ECLS cohort, as well as the particular severity of these patients have prevented us to conduct such a matching. Moreover, we were unable to collect information regarding severity at admission in the control population.

We limited the inclusion to the patients admitted for OHCA on purpose, even though the outcomes of the 3 patients non-included could have influenced the overall results of this study. Indeed, OHCA is a sudden and life-threatening pathology for whom the delay for initiation of the treatments is a key aspect of the prognosis. In-Hospital CA is a more heterogeneous entity, where pre-existing life-threatening pathology leads to CA. The prognosis of the CA should be the combination of the pre-existing condition and the CA by itself. It would have been difficult to conclude on the ECLS intervention, because of this heterogeneity.

Conclusion

Despite high rate of death in the ECLS-treated population, the neurological outcomes of the survivors suggest a potential beneficial effect of ECLS on neurological recovery and justify its implantation for extremely severe population, as a salvage therapy. While ECLS initiation, reported in this present work, does not impact mortality, neurologic outcomes of survivors suggest a potential beneficial effect on neurological recovery. The neurological evolution could be more likely related to the initial brain injury, rather than the PCAS by itself. Furthermore, Reversible etiologies of cardiac arrest were associated with better outcomes, emphasizing on selection of patients who could benefit of such a therapy. Considering the assistance only for patients for whom the myocardial depression has the potential to recover could be an interesting option to improve outcomes. Then, considering ECLS for a carefully selected population of PCAS patients could be promising.

Figure 1 :

 1 Figure 1: Mode and timing of death during ICU length of stay in the ECLS treated

Figure 2 :

 2 Figure 2: Multivariate analysis of factors associated with ECLS initiation in the PCAS

Acknowledgment

We would like to thank intensive care departments in Lariboisière and Cochin hospitals, for having helping us to gather data.

No external funding has been hired for this study. No conflicts of interest to declare.


Baptiste Magnier
email: baptiste.magnier@mines-ales.fr

Philippe Montesinos
email: philippe.montesinos@mines-ales.fr

Daniel Diep
email: daniel.diep@mines-ales.fr

Texture Removal Preserving Edges by Diffusion

Keywords:

This article is devoted to a new method for removing texture in images through an image region classification technique using a smoothing rotating filter followed by a diffusion process designed to preserve object contours. This approach lies in associating a descriptor, capable of classifying each pixel as a texture pixel, a homogenous region pixel or an edge pixel, with an anisotropic edge detector serving to define two directions of the edges introduced into an anisotropic diffusion algorithm. Due to the presence of the image region descriptor, the anisotropic diffusion is able to accurately control diffusion near the edges and corner points and moreover remove textured regions. Our results and evaluations based on image segmentation and classical edge detection, which correctly extract objects within the image, compared with anisotropic diffusion methods and nonlinear filters, enable validating our approach.

Introduction

Texture removal is fundamental for image segmentation [1] [START_REF] Deriche | Recursively implementing the gaussian and its derivatives[END_REF] [3] [START_REF] Monga | An optimal region growing algorithm for image segmentation[END_REF] or cartoon generation [START_REF] Buades | Fast cartoon+ texture image filters[END_REF]. Filtering techniques cannot be adapted in the presence of strong texture [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF]. Though efficient for removing impulse noise in images, the median filter, the α-trimmed means filter [START_REF] Bednar | Alpha-trimmed means and their relationship to median filters[END_REF], the Kuwahara filter [START_REF] Kuwahara | Processing of RIangiocardiographic images[END_REF] and all their generalizations are still unable to remove heavy texture while preserving edges in the image and moreover wind up eroding corners (Fig. 1).

In [START_REF] Buades | Fast cartoon+ texture image filters[END_REF], the authors have developed an approach for both removing textures and preserving edges. The algorithm is able to determine whether a pixel belongs to a textured region via a local total variation of the image around this point. If the pixel belongs to a textured region, then the local total variation is strong. This approach depends on the scale parameter, namely the standard deviation of the Gaussian σ convolved with the original image, which proves to be efficient at removing thin textures in images. However, a low value of parameter σ will maintain a strong texture, whereas a high parameter value will remove small objects and blur edges.

In image restoration, the Partial Differential Equation (PDE) is often used to regularize images in instances where image boundaries control a diffusion process [START_REF] Kornprobst | Mathematical problems in image processing: partial differential equations and the calculus of variations[END_REF] [START_REF] Magnier | Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels[END_REF]. Over homogenous regions, the diffusion is isotropic; at edge points on the other hand, diffusion is either altered by the gradient magnitude in the contour direction or else inhibited [START_REF] Alvarez | Image selective smoothing and edge detection by nonlinear diffusion[END_REF]. For the diffusion scheme developed by Perona-Malik [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF], control is performed with finite differences, making it possible to preserve many contours of small objects or small structures. The Mean Curvature Motion (M CM ) method consists of solely diffusing in the contour direction [START_REF] Catté | A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets[END_REF], even within homogeneous regions. According to some diffusion approaches, Gaussian filtering is used for gradient estimation, thus improving the robustness of diffusion control over noise [START_REF] Alvarez | Image selective smoothing and edge detection by nonlinear diffusion[END_REF] [14] [15] [16]. Nevertheless, these methods are often introduced to enhance small structures but not necessarily to restore images containing considerable noise, therefore resulting in greater texture yet without the ability to remove texture while preserving the accuracy of edges.

In this paper, we have combined two techniques stemming from our previous work [3] [17]. We will begin by describing the rotating filter and its texture detection capabilities before presenting an anisotropic edge detector that defines two contour directions for an edge crossing a pixel. As a final step, we will introduce an anisotropic diffusion method to accurately control diffusion near the edges and corner points while proceeding with an isotropic diffusion inside the textured regions. More specifically, our detector yields two distinct directions on edges or corners, with this information enabling anisotropic diffusion in the detected directions.

Texture detection

In order to detect whether a pixel belongs to a textured region, a homogeneous region or an edge, we apply a smoothing rotating filter and then analyze the resulting signal. For each pixel of the original image, a rotating half smoothing filter produces a signal s, which is a function of both a rotation angle θ and the underlying signal. Smoothing with rotating filters ensures that the image is smoothed with a bank of rotated anisotropic half Gaussian kernels:

G (µ,λ) (x, y, θ) = C • I θ * H (-y) • e - x 2 2λ 2 + y 2 2µ 2 (1)
where I θ corresponds to a rotated image of orientation θ (the image is oriented instead of the filter so as to decrease algorithmic complexity and to allow use of a recursive Gaussian filter [START_REF] Montesinos | A new perceptual edge detector in color images[END_REF]), C is a normalization coefficient [START_REF] Deriche | Recursively implementing the gaussian and its derivatives[END_REF], (x, y) are pixel coordinates, and (µ, λ) are the standard deviations of the Gaussian filter (as illustrated in Fig. 2). Since only the causal part of the filter is actually needed, we simply "cut" the smoothing kernel in half; this operation corresponds to the Heaviside function H, and its implementation is rather straightforward. Like in [START_REF] Montesinos | A new perceptual edge detector in color images[END_REF], the image is oriented instead of the filter due to concern over increased algorithmic complexity while allowing for use of a recursive Gaussian filter [START_REF] Deriche | Recursively implementing the gaussian and its derivatives[END_REF]. Application of the rotating half-filter at a single point of a gray level image in a 360 scan provides each pixel with a characterizing signal s(θ), which is a single function of the orientation angle θ. From these pixel signals, we are now able to extract the descriptors that will discriminate edges and regions [START_REF] Magnier | Texture removal by pixel classification using a rotating filter[END_REF]. For all pixels lying in a homogeneous region, s(θ) will remain constant. On the contrary, in a textured region, s(θ) will be stochastic. If a pixel lies at the border between several different homogenous regions, s(θ) will contain several flat areas. If the pixel lies between a homogenous region and a textured region, s(θ) will contain only one flat area. However, if the textured region is not too accentuated, s(θ) will only consist of a flat signal as a result of the smoothing filter, and moreover the region will be considered as a homogenous region. This protocol enables classifying pixels located between two textured regions.

The main purpose behind analyzing a 360 scan signal is to detect significant flat areas, which correspond to homogeneous regions of the image. After smoothing, i.e. s M (θ) = (s(θ-∆θ)+s(θ)+s(θ+∆θ))/3, the derivative s θ (θ) is calculated and flat areas are detected as intervals: s θ (θ) = s M (θ -∆θ) -s M (θ + ∆θ), so:

s θ (θ) = (s(θ -2 ∆θ) + s(θ -∆θ) + s(θ + ∆θ) + s(θ + 2 ∆θ))/3. (2)
A flat area is considered to be detected when the largest angular sector lies between 30 • and 360 • . The texture suppression method consists of both an anisotropic diffusion at edges, corner points and points between two textured regions, so as to preserve borders between regions, and an isotropic diffusion inside homogenous and textured regions. The black regions shown in Fig. 4(c) can be viewed as a rough edge detection and indicate regions where flat areas have been detected in Fig. 4(a). The original image will therefore be smoothed anisotropically in the black regions of Fig. 4(c) and isotropically in white regions; so it is interesting to apply a dilatation operator and then attenuate with of the black regions or remove some isolated black pixels. The curvatures of signal s(θ) (i.e. the second derivative of s(θ), similar to Eq. 2) serve to define two directions used for anisotropic diffusion in [START_REF] Magnier | Texture removal by pixel classification using a rotating filter[END_REF], though these diffusion directions are not accurate and may have a blurring effect on edges. We will use herein the diffusion directions computed from an anisotropic edge detector that has defined two directions, thus yielding a much more accurate diffusion.

Edge Detection Using Half Gaussian Kernels

Steerable filters [START_REF] Freeman | The design and use of steerable filters[END_REF] or anisotropic edge detectors [START_REF] Perona | Steerable-scalable kernels for edge detection and junction analysis[END_REF] perform well in detecting large linear structures. Near the corners however, the gradient magnitude decreases as edge information within the scope of the filter also decreases. Consequently, the robustness to noise relative to small objects declines substantially.

A simple solution to avoiding this effect is to consider paths that cross each pixel in several directions. The idea developed in [START_REF] Montesinos | A new perceptual edge detector in color images[END_REF] is to "cut" the derivative kernel (with smoothing) into two parts: the first part along an initial direction, and the second part along a second direction. At each pixel (x, y), a derivation filter is applied to obtain a derivative information Q(x, y, θ):

Q(x, y, θ) = I θ * C 1 • H (-y) • x • e - x 2 2λ 2 + y 2 2µ 2 (3)
where C 1 represents a normalization coefficient [START_REF] Deriche | Recursively implementing the gaussian and its derivatives[END_REF]. Q(x, y, θ) denotes the slope of a line derived from a pixel in the direction perpendicular to θ (as diagrammed in Fig. 3).

To obtain a gradient magnitude measure ∇I on each pixel P , we first compute the global extrema of the Q(x, y, θ) function with θ 1 and θ 2 (some examples are presented in Fig. 4(b)). Two of these extrema can then be combined to obtain ∇I :

         ∇I = max θ∈[0,360[ Q(x, y, θ) -min θ∈[0,360[ Q(x, y, θ) θ 1 = arg max θ∈[0,360[ (Q(x, y, θ)) θ 2 = arg min θ∈[0,360[ (Q(x, y, θ)) (4)
Once ∇I , θ 1 and θ 2 have been obtained, they are entered into our diffusion scheme. Due to the rotating filter lengths, this approach maintains its robustness to noise and computes two accurate diffusion orientations in the edge directions (illustrated in Fig. 3(b)). The authors in [START_REF] Magnier | Fast anisotropic edge detection using gamma correction in color images[END_REF], evaluated the edge detection used in this method as a function of noise level and in [START_REF] Magnier | Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels[END_REF] is shown how to restore images in function of ∇I and (θ 1 , θ 2 ) directions.

Anisotropic Diffusion in two edges directions

Unlike several diffusion schemes [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF] [11] [START_REF] Weickert | Anisotropic diffusion in image processing[END_REF] [15] [16], our control function does not depend on the image gradient but rather on a pre-established classification map of the initial image. As stated in Section 2, this classification lacks sharp distinction between region and edges. Tensor diffusion schemes preserve edges [START_REF] Weickert | Anisotropic diffusion in image processing[END_REF] [15] [16]; however, in order to remove texture while preserving contours, the standard deviation of the Gaussian σ must be high. Yet this solution will blur edges and over-smooth corners. Moreover, in [START_REF] Alvarez | Image selective smoothing and edge detection by nonlinear diffusion[END_REF] [14] [START_REF] Tschumperlé | Vector-valued image regularization with PDEs: A common framework for different applications[END_REF] [16], only one direction is considered at the edges. To minimize these effects, let's consider the two directions (θ 1 , θ 2 ) provided by Eq. 4 of the anisotropic edge detector only where flat areas have been detected (as illustrated in Fig. 4(c)).

The diffusion process can thus be described by the following newly equation:

∂I t ∂t = F A (I 0 ) • ∆I t + (1 -F A (I 0 )) • ∂ 2 I t ∂θ 1 ∂θ 2 , (5)
• t is the diffusion time,

• I 0 is the original image, • I t is the diffused image at time t,

• F A represents those regions where flat areas have been detected (illustrated in Fig. 5(a)):

→ F A = 0 in contour regions, thus: ∂It ∂t = ∂ 2 It ∂θ1∂θ2 → F A = 1

in textured or homogeneous regions, thus:

∂It ∂t = ∆I t , corresponding to the heat equation [START_REF] Koenderink | The structure of images[END_REF], an example can be seen in Fig. 4(d).

The authors in [START_REF] Magnier | Perceptual color image smoothing via a new region-based PDE scheme[END_REF] have developed a diffusion method based on the same pixel classification. Inside edge regions, a function of both the gradient magnitude derived by half Gaussian kernels (Eq. 4) and the angle between the two diffusion directions (θ 1 , θ 2 ) drives the diffusion process. This technique combines isotropic and anisotropic diffusion, while preserving the edges and corners of various objects in highly noisy images. Nonetheless, as shown in Fig. 8(h), textures are preserved inside contour regions given that they may contain a high gradient value, thereby inhibiting the diffusion process Eq. 4).

A of the diffusion process ∂It ∂t = ∂ 2 It ∂θ1∂θ2 leads to the difference between the derivative in the θ 1 direction and the derivative in the θ 2 direction, respectively, at the pixel level. As diagrammed in Fig. 5(b), at the time t, the diffused pixel results from interpolations in both the θ 1 and θ 2 orientations on a 3×3 mask.

Quantitative comparison of region detection

In order to carry out some quantitative results, we have conducted a number of tests of texture suppression using several approaches. The reference image contains only 5 known regions and these 5 regions are substituted by 5 different textures grey-level images, as illustrated in Fig. 6. As soon as the reference image is synthetic, it is straightforward to compare the processed images to ground truth. The original image being composed of 5 distinct regions, we compared each true region to the regions issued from a texture suppression method followed with a region segmentation algorithm [START_REF] Monga | An optimal region growing algorithm for image segmentation[END_REF]. This quantitative comparison is led with several approaches for the texture suppression: Perona-Malik [START_REF] Perona | Scale-space and edge detection using anisotropic diffusion[END_REF], Alvarez et al. [START_REF] Alvarez | Image selective smoothing and edge detection by nonlinear diffusion[END_REF], Bilateral filter [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF], texture filter of Buades et al. [START_REF] Buades | Fast cartoon+ texture image filters[END_REF], anisotropic diffusion scheme based on derivatives half Gaussian kernels of Magnier et al. [START_REF] Magnier | Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels[END_REF] and our proposed method. Note that in Fig. 7, we compare the region segmentation of the different texture suppression schemes with the region segmentation on the original image. As for our general applications, we used our texture detector with µ=5, λ=1.5 and ∆θ=5 • for flat area detection. The parameters used in an anisotropic edge detector to compute µ=5, λ=1.5 and ∆θ=2 • . λ represents the width the filter for the contour extraction (see Fig. 3), we use the same standard deviation parameter for each method using a Gaussian filter i.e. σ = 1 for [START_REF] Alvarez | Image selective smoothing and edge detection by nonlinear diffusion[END_REF], [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF], [START_REF] Buades | Fast cartoon+ texture image filters[END_REF], and [START_REF] Magnier | Evolution of image regularization with PDEs toward a new anisotropic smoothing based on half kernels[END_REF]. This pairwise comparison resulted into a 2×2 contingency table, or confusion matrix, which reports the number true positives, true negatives, false positives, and false negatives. False positive in this case means that the region segmentation scheme results in several regions for a considered known region on the 5 distinct regions and false negatives represent regions segmented growing outside a considered true region. Fig. 7 represents false positive/negative pixels on the region segmented images. Compared to other approaches, our method creates less false positive pixels and in general less false negatives (excepted for image 4, the segmentation region scheme creates two regions inside 3 distinct regions instead only one for each, thus creating pic in the graph). As illustrated in Fig. 6, note also that how our method is able to remove efficiency the high texture in images ( 6) and ( 7).

Experimental Results

In the image displayed in Fig. 8(a), the aim is to smooth the various textures present (wall, bushes) while preserving all objects (windows, panel, sidewalk). We introduced our detector with µ=5, λ=1.5 and ∆θ=5 • for flat area detection (Fig. 4(c)). The parameters used in an anisotropic edge detector to compute (θ 1 , θ 2 ) are µ=5, λ=1.5 and ∆θ=2 • (λ represents the width of the derivation filter, it must not be too thin in order to obtain robust edges directions in presence of strong textures). The result of our anisotropic diffusion is shown in Fig. 8(l) after 25 iterations. Note that a number of objects are perfectly visible and corners are sharp, whereas texture regions are smoothed and some have even merged, preserving edges between all of them.

We can now compare our results with several approaches, as well as with the well-known bilateral filters [START_REF] Tomasi | Bilateral filtering for gray and color images[END_REF] and image regularization approaches using PDEs. For most of these methods, the texture has not been completely removed from the wall (Fig. 8(b), (c), (d), (e), (f) and (g)). In the majority of cases, bush boundaries (Fig. 8(b), (c), (d), (e) and (f)) or panel corners (Fig. 8(e), (g) and (k)) have not been properly preserved. Tensorial approaches add a fiber effect to the texture provided the standard deviation of the Gaussian σ is small enough. Substitute σ leeds the diffusion to blur edges (e.g. σ = 4 in Fig. 8(j)).

To show the efficiency of our texture removal method (Fig. 9(d)), we compared edge detection [START_REF] Prewitt | Object enhancement and extraction[END_REF] on the original image and on the image obtained after diffusion. Edge detection on our diffused image (Fig. 8(p)) is less noisy than on the original. Moreover, edges of bushes, panels and windows appear clearly, whereas the contours of bushes and the wall have not been completely detected on the original image. Also, the method proposed in [START_REF] Magnier | Texture removal by pixel classification using a rotating filter[END_REF] fails to detect the top of the panel, and the approach in [16] blurs the edges of bushes (see bush on the left on Fig. 8(n) and(o)). We have also shown the efficiency of our texture removal approach using the region segmentation of Monga [START_REF] Monga | An optimal region growing algorithm for image segmentation[END_REF] as a post-processing step. Fig. 8(t) illustrates that our texture suppression allows a segmentation of bushes, the panel, the sidewalk and so on, contrary to Fig. 8(q), (r) and (s). Moreover, Fig. 9 indicates the efficiency of our method in depicting the image surface before and after our regularization scheme, during which regions become entirely flat so as to preserve sharp edges, close to the region segmentation of our result (Fig. 9 (c)).

In the second result presented in Fig. 10, the aim here is to remove the tshirt texture as the acquisition noise in the original image. The first step is to compute flat areas from each color channels of the colored image. To proceed, we apply the flat area detection technique to each channel [START_REF] Magnier | Texture removal in color images by anisotropic diffusion[END_REF]. For each pixel, if we detect at least one flat area for a given channel, then the diffusion will be anisotropic. Otherwise, if no flat area has been detected in any channel, then the diffusion will be isotropic. Thus, as shown in [START_REF] Magnier | Perceptual color image smoothing via a new region-based PDE scheme[END_REF], before synthesizing the regularized color image, we diffuse each image channel using the diffusion scheme presented in Eq. 4. We introduced our texture detector with µ=5, λ=1.5 and ∆θ=5 • for flat area detection. The parameters used in an anisotropic edge detector to compute (θ 1 , θ 2 ) are µ=5, λ=1.5 and ∆θ=2 • .

Our result presented in Fig. 10(f) was compared with several methods and evaluated with edge detection of Canny (σ=1) merged on the original image in order to move forward the contour preservation and the texture removal. Thereby, as shown here, the bilateral filter removes correctly the noise but preserves the t-shirt texture. Tensorial method [16] does not removes t-shirt stripes and blurs edges because the standard deviation of the Gaussian filter used for this method is too large (σ=3). The texture filter [START_REF] Buades | Fast cartoon+ texture image filters[END_REF] blurs edges and is not capable to remove the noise on the image top. Finally, we have compared our method with the Magnier et al. approach [START_REF] Magnier | Texture removal by pixel classification using a rotating filter[END_REF] extended in color [START_REF] Magnier | Texture removal in color images by anisotropic diffusion[END_REF] which suppress correctly the texture, but, as it is pointed with the edge detector, these technique blurs edges. On the contrary, our method eliminates both the texture of the t-shirt, the acquisition noise preserving sharped precise edges.

Conclusion

This paper is dedicated to defining a new method for removing texture in images by means of pixel classification using a smoothing rotating filter. Our classification method appears to be very promising since we have been able to correctly classify texture regions, homogenous regions and edge regions for various image types. Two-direction anisotropic diffusion provided by an edge detector using derivative half smoothing kernels maintains sharp edges and the corners of different objects. Comparing our results with existing algorithms and region segmentation on our results serves to validate our method. Next on our work program agenda is to enhance this method to treat medical images which are corrupted by a heavy noise.

Fig. 1 .

 1 Fig. 1. Nonlinear filters are not efficient for texture removal.

  Smoothing filter (b) Rotating filters (c) Discretized filter

Fig. 2 .

 2 Fig. 2. A half smoothing rotating filter.

  Half Anisotropic Gaussian kernels derivation filter at linear portions of contours and at corners.

Fig. 3 .

 3 Fig. 3. Oriented half kernel enables extracting two edge directions (θ 1 , θ 2 ).

Fig. 4 .

 4 Fig. 4. Points selection and associated Q(x, y, θ).

  An isotropic diffusion in homogeneous (b) Interpolations directions are estimated by regions and an anisotropic diffusion the derivatives half Gaussian kernels and the at level of edges. diffusion computed by interpolations is calculated in the two directions (θ1, θ2) on a 3×3 mask.

Fig. 5 .

 5 Fig. 5. Diagram of our diffusion scheme.

Fig. 6 .Fig. 7 .

 67 Fig. 6. Test textured images 200×200 composed of 5 distinct regions.

Fig. 8 .

 8 Fig.8. Texture diffusion using several methods then evaluation with edge detection (Prewitt kernels[START_REF] Prewitt | Object enhancement and extraction[END_REF]) and region segmentation.

Fig. 9 .

 9 Fig.9. Image surface of the original image, our result region segmentation of our result (see Fig.8) and texture suppressed with our method.

Fig. 10 .

 10 Fig. 10. Texture diffusion and evaluation with edge detection (Canny edge detector using the first derivative of the Gaussian filter with σ = 1).