Patrice Cacoub
email: patrice.cacoub@psl.aphp.fr

MD Cloe Comarmond

MD Fanny Domont

MD Léa Savey

MD David Saadoun

Smith Kline

Janssen

Prof Patrice Cacoub

Cryoglobulinemia Vasculitis

Keywords: cryoglobulins, cryoglobulinemia vasculitis, HCV, prognosis, treatment

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polyclonal IgG with or without monoclonal IgM with rheumatoid factor activity. Hepatitis C virus (HCV) infection represents the main cause of mixed CryoVas. The 10-year survival rates are 63%, 65% and 87% in HCV-positive mixed CryoVas, HCV-negative mixed CryoVas and type I CryoVas patients, respectively. In HCV-positive patients, baseline poor prognostic factors include the presence of severe liver fibrosis, and central nervous system, kidney, and heart involvement. Treatment with antivirals is associated with a good prognosis whereas use of immunosuppressant (including corticosteroids) is associated with a poor outcome. In HCV-negative patients, pulmonary and gastrointestinal involvement, renal insufficiency and age>65 years are independently associated with death. Increased risk of lymphoma should also be underlined. Treatment of type I CryoVas is that of the hemopathy; specific treatment also include plasma exchange, corticosteroids, rituximab and ilomedine. In HCV-CryoVas with mild to moderate disease, an optimal antiviral treatment should be given. For HCV-CryoVas with severe vasculitis (i.e. worsening of renal function, mononeuritis multiplex, extensive skin disease, intestinal ischemia…) control of disease with rituximab, with or without plasmapheresis, is required before initiation of antiviral therapy. Other immunosuppressants should be given only in case of refractory forms of CryoVas, frequently associated with underlying B-cell lymphoma.

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Cryoglobulins are immune complexes that may induce systemic vasculitis, a small vessel vasculitis involving mainly the skin, the joints, the peripheral nerve system and the kidneys.

During the last twenty five years, major progresses have been done after the discovery of the hepatitis C virus (HCV), which represents the main cause of cryoglobulins [START_REF] Terrier | Cryoglobulinemia vasculitis: an update[END_REF][START_REF] Cacoub | Extrahepatic manifestations of chronic hepatitis C. MULTIVIRC Group. Multidepartment Virus C[END_REF][START_REF] Ferri | Cryoglobulinemia and systemic manifestations of hepatitis C[END_REF][START_REF] Brouet | Biologic and clinical significance of cryoglobulins. A report of 86 cases[END_REF].

Cryoglobulinemia spectrum and diagnostic tests

Cryoglobulins are defined by the presence of circulating immunoglobulins that precipitate as serum is cooled below core body temperature and resolubilize when rewarmed.

Cryoglobulinemia is confirmed by the detection of protein that precipitates in the patient's serum maintained at 4°C during at least 7 days, and which dissolved when heated at 37°C.

In most expert center, patients are considered to have a significant cryoglobulin level when > 0.05 g/L on two determinations [START_REF] Brouet | Biologic and clinical significance of cryoglobulins. A report of 86 cases[END_REF][START_REF] Musset | Characterization of cryoglobulins by immunoblotting[END_REF][START_REF] Trejo | Cryoglobulinemia: study of etiologic factors and clinical and immunologic features in 443 patients from a single center[END_REF]. The benefit of the detection of cryoglobulinemia is the excellent diagnostic performance for cryoglobulinemic vasculitis in the context of clinical symptoms evocative of vasculitis, such as purpura, peripheral neuropathy or glomerulonephritis. After detection, cryoglobulinemia is categorized by immunochemical analysis into three types [START_REF] Brouet | Biologic and clinical significance of cryoglobulins. A report of 86 cases[END_REF]. Type I cryoglobulins are single monoclonal immunoglobulins always linked to a B-cell lymphoproliferative disorder [START_REF] Terrier | The spectrum of type I cryoglobulinemia vasculitis: new insights based on 64 cases[END_REF]. Type II cryoglobulins consist of polyclonal IgG with monoclonal IgM with rheumatoid factor activity. Types III cryoglobulins are comprised of polyclonal IgG and polyclonal IgM with rheumatoid factor activity. Type II and III are often referred to as mixed cryoglobulinemia. Some laboratories characterize cryoglobulinemia using immunofixation or immunoelectrophoresis, and quantify the cryoglobulin level by determining the cryocrit as the percentage of the total volume (by using appropriate tube). The use of immunoblotting for immunochemical characterization is a sensitive and specific method allowing a full identification in 98%, in comparison with immunofixation and immunoelectrophoresis in which identification is possible in only 54 and 28%, respectively. Limitations of testing methods are that each of the immunochemical assays previously described may be influenced by artifacts arising from ex vivo cryoprecipitation after blood drawing. In consequence, when a cryoglobulin is suspected, serum should be kept warm, and tests should be carried out at 37°C.

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Other laboratory surrogate markers, easier to detect than cryoglobulins, may provide indirect evidence of the presence of cryoglobulinemia such as low C4 serum complement fraction, decreased total hemolytic complement levels and/or presence of a monoclonal immunoglobulin or rheumatoid factor activity. Serum cryoglobulin may also interfere with a variety of laboratory tests and have been associated with spurious quantitation of plasma proteins and erythrocyte sedimentation rate, pseudo-leucocytosis, pseudo-thrombocytosis or pseudo-macrocytosis.

Main features of cryoglobulinemic vasculitis

The disease expression is variable, ranging from mild clinical symptoms (fatigue, purpura, arthralgia) to fulminant life-threatening complications (glomerulonephritis, widespread vasculitis)(1-3,6)(Table 1).

Fatigue is the main symptom, noted in 80-90% of patients. The main cutaneous sign is a palpable purpura which is reported in 70 to 90% of patients, but cutaneous ulcers may occur.

It always begins at the lower limbs and may extend to abdominal area, less frequently to the trunk and upper limbs. It persists 3 to 10 days with a residual brownish pigmentation.

Raynaud's syndrome and acrocyanosis, which may evolve to digital ulcerations, can occur.

Arthralgia is reported in 40-60% of patients. Joint pains are bilateral and symmetric, nondeforming and involved mainly knees and hands, more seldom elbows and ankles. Frank arthritis is reported in less than 10% of patients. Neurologic manifestations range from pure sensory axonopathy to mononeuritis multiplex (60-70%). The most frequently described form is a distal sensory or sensory-motor polyneuropathy. Polyneuropathy usually presents with painful, asymmetric paresthesia which later become symmetric. Motor deficit is inconstant and mainly affects the lower limbs, appearing a few months to a few years after sensory symptoms. Involvement of the central nervous system (<10%) may manifest as stroke, epilepsy or cognitive impairment. Renal manifestations are reported in 20 to 35% of patients.

The most frequent clinical and pathological picture is that of acute or chronic type-I membranoproliferative glomerulonephritis with sub-endothelial deposits. It represents more than 80% of cryoglobulinemic renal diseases. It is strongly associated with the presence of

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type II cryoglobulinemia with IgMκ rheumatoid factor. The most frequent presentation (55%) is proteinuria with microscopic hematuria and a variable degree of renal insufficiency. A sicca syndrome has been reported in 20-40% of patients. However, those meeting definite Sjögren's syndrome are rarely encountered. Other manifestations are rare (<5%). Abdominal pains and gastrointestinal bleeding secondary to mesenteric vasculitis has been described. Cardiac involvement include mitral valvular damage, coronary vasculitis complicated by myocardial infarction, pericarditis or congestive cardiac failure. Lungs can be involved usually without clinical symptoms but some patients may present moderate exercise dyspnoea, dry cough, interstitial lung fibrosis, pleural effusions, or haemoptysis, which can be the consequence of pulmonary intra-alveolar haemorrhages.

Prognosis of cryoglobulinemia vasculitis

Cryoglobulinemia vasculitis is associated with significant morbidity and mortality. Some studies before the HCV era underlined the bad prognosis factor of renal involvement [START_REF] Tarantino | Long-term predictors of survival in essential mixed cryoglobulinemic glomerulonephritis[END_REF].

More recent studies described the prognosis of patients with HCV-positive and HCV-negative mixed cryoglobulinemia vasculitis and identified prognostic factors of survival [START_REF] Ferri | Mixed cryoglobulinemia: demographic, clinical, and serologic features and survival in 231 patients[END_REF][START_REF] Rossa | Mortality rate and outcome factors in mixed cryoglobulinaemia: the impact of hepatitis C virus[END_REF][START_REF] Terrier | Prognostic factors in patients with hepatitis C virus infection and systemic vasculitis[END_REF]. Survival according to the type of cryoglobulinemia and HCV status is represented in Figure 1.

In HCV-positive patients with mixed cryoglobulinemia vasculitis, the 1-year, 3-year, 5-year, and 10-year survival rates were 96%, 86%, 75%, and 63%, respectively. Deaths were mainly related to serious infections and end-stage liver disease [START_REF] Terrier | Prognostic factors in patients with hepatitis C virus infection and systemic vasculitis[END_REF]. Baseline factors associated with a poor prognosis were the presence of severe liver fibrosis [Metavir fibrosis score ≥ 3](HR 5.31), central nervous system involvement (HR 2.74), kidney involvement (HR 1.91), and heart involvement (HR 4.2). The Five-Factors Score (FFS) [START_REF] Guillevin | The Five-Factor Score revisited: assessment of prognoses of systemic necrotizing vasculitides based on the French Vasculitis Study Group (FVSG) cohort[END_REF], a vasculitis scoring system based on five clinical items (proteinuria > 1 gr/day, serum creatinine >140 µmol/L, cardiomyopathy, severe gastrointestinal involvement and central nervous system involvement) with the presence of each being accorded 1 point, was significantly associated with outcome. In multivariate analysis, severe fibrosis (HR 10.8) and the FFS (HR 2.49) were significantly associated with a poor prognosis. Among patients without severe fibrosis, the FFS was a good predictor of outcome, while among those with severe fibrosis, the severity of

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vasculitis had no prognostic value. Treatment with the combination of Pegylated interferon plus ribavirin was associated with a good prognosis (HR 0.34), whereas treatment with immunosuppressive agents (including corticosteroids) was associated with a poor outcome, even after adjustment for the severity of vasculitis (HR 4.05) [START_REF] Terrier | Prognostic factors in patients with hepatitis C virus infection and systemic vasculitis[END_REF].

Baseline factors associated with prognosis in patients with non-infectious mixed cryoglobulinemia vasculitis have been recently reported in a large study [START_REF] Terrier | Management of non infectious mixed cryoglobulinemia vasculitis: data from 242 cases included in the CryoVas survey[END_REF][START_REF] Terrier | Prognostic factors of survival in patients with non-infectious mixed cryoglobulinaemia vasculitis: data from 242 cases included in the CryoVas survey[END_REF]. One-year, 2-year, 5-year and 10-year overall survival rates were 91%, 89%, 79% and 65%, respectively. Deaths were related to serious infections in half of cases and to vasculitis flare in 20%. Pulmonary and gastrointestinal involvement, glomerular filtration rate < 60 ml/min and age >65 years were independently associated with death. A prognostic score including these 4 variables, the CryoVas Score (CVS), for the prediction of survival at 5 years was devised. One point score was assigned to each prognostic variable. At 5 years the death rates were 2.6%, 13.1%, 29.6% and 38.5% for a CVS of 0, 1, 2 and ≥3, respectively. At 1 year the death rates were 0%, 3.2%, 18.5% and 30.8% for a CVS of 0, 1, 2 and ≥3, respectively. The area under the curve for the CVS was higher compared with the FFS, indicating a better performance of the CVS [START_REF] Terrier | Prognostic factors of survival in patients with non-infectious mixed cryoglobulinaemia vasculitis: data from 242 cases included in the CryoVas survey[END_REF]. Increased risk of lymphoma in the follow up of such patients should also be underlined [START_REF] Saadoun | Increased risks of lymphoma and death among patients with non-hepatitis C virus-related mixed cryoglobulinemia[END_REF]. Data on the prognosis of type I cryoglobulinemia vasculitis has been recently reported on a series of 64 patients [START_REF] Terrier | The spectrum of type I cryoglobulinemia vasculitis: new insights based on 64 cases[END_REF]. The 1-year, 3-year, 5-year and 10-year survival rates were 97%, 94%, 94% and 87%, respectively. Type I cryoglobulinemia vasculitis related to hematologic malignancy tended to be associated with a poorer prognosis compared to monoclonal gammopathy of unknown significance. Severe infections accounted for half of the deaths.

Management

The production of cryoglobulins is most often the consequence of an underlying disorder that needs an etiological check-up. It depends, at least in part, according to the immunochemical determination (Figure 2). Main causes are summarized in Table 2.

In type I cryoglobulinemia vasculitis, it is mandatory to look for the presence of an underlying B-cell lymphoproliferative disorder, mainly Waldenström macroglobulinemia, multiple

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myeloma or monoclonal gammopathy of unknown significance. Type I cryoglobulinemic vasculitis are life-threatening because of the severity of cutaneous and visceral involvement and the underlying hematological disorder [START_REF] Terrier | The spectrum of type I cryoglobulinemia vasculitis: new insights based on 64 cases[END_REF]. Treatment of cryoglobulinemic vasculitis is that of the B-cell lymphoproliferative disorder. Specific treatment may also be indicated, including plasma exchange, corticosteroids, rituximab or ilomedine [START_REF] Terrier | The spectrum of type I cryoglobulinemia vasculitis: new insights based on 64 cases[END_REF][START_REF] Terrier | Safety and efficacy of rituximab in nonviral cryoglobulinemia vasculitis: data from the French Autoimmunity and Rituximab registry[END_REF].

In type II and III cryoglobulinemia (mixed cryoglobulinemia), the main etiological agent is by far HCV infection (70-90%). HCV-induced mixed cryoglobulinemic vasculitis manifestations respond to clearance of HCV, i.e. sustained virologic response (SVR). During the decade 2002-2012, using a combination antiviral therapy with Pegylated interferon (PegIFN) plus ribavirin for twelve months permitted to achieve a SVR in 50-60% of patients [START_REF] Cacoub | Hepatitis C virus-induced vasculitis: therapeutic options[END_REF][START_REF] Saadoun | Antiviral therapy for hepatitis C virus-associated mixed cryoglobulinemia vasculitis: a long-term follow up study[END_REF].

Patients who relapsed for HCV infection after responding to antiviral therapy usually relapsed for the vasculitis with the return of viremia [START_REF] Terrier | Efficacy and tolerability of rituximab with or without PEGylated interferon alfa-2b plus ribavirin in severe hepatitis C virus-related vasculitis: a long-term followup study of thirty-two patients[END_REF]. In case of persistent mixed cryoglobulin, relapse of vasculitis might also occur in a few patients despite achieving a SVR. In such patients, a different underlying condition should be considered, especially B-cell lymphoma [START_REF] Landau | Relapse of hepatitis C virus-associated mixed cryoglobulinemia vasculitis in patients with sustained viral response[END_REF]. Recent use of triple HCV therapy with PegIFN/ribavirin and a specifically-targeted antiviral agent (NS3/4A protease inhibitor, i.e. boceprevir or telaprevir) led to improved SVR rates (65-70%) in HCV genotype 1 infection [START_REF] Saadoun | Peg-IFNαRibavirin/Protease inhibitor combination in severe hepatitis C virus associated mixed cryoglobulinemia vasculitis[END_REF][START_REF] Gragnani | Triple antiviral therapy in hepatitis C virus infection with or without mixed cryoglobulinaemia: A prospective, controlled pilot study[END_REF]. However, such combination should be given for 48 weeks and serious adverse events occurred in up to 47% of patients [START_REF] Saadoun | Peg-IFNαRibavirin/Protease inhibitor combination in severe hepatitis C virus associated mixed cryoglobulinemia vasculitis[END_REF]. Other direct-acting antivirals are now becoming available. The NS3/4A inhibitor simeprevir and NS5B inhibitor sofosbuvir have recently been licensed. These agents facilitate the use of shortened courses of combination IFN-free therapy, which are associated with high (>95%) SVR rates and relatively few toxicities. International guidelines (i.e. EASL 2014) [START_REF] Association | EASL Clinical Practice Guidelines: management of hepatitis C virus infection[END_REF] state that treatment should be scheduled, not deferred, for patients with significant liver fibrosis and those with significant extra-hepatic manifestations, such as symptomatic cryoglobulinemia. As far as SVR has been previously associated to mixed cryoglobulinemia vasculitis remission in most patients, no doubt that new HCV treatments should add a major benefit. Rituximab is an interesting therapy in mixed cryoglobulinemia vasculitis, as it targets B-cells, which are responsible for cryoglobulin production and finally vasculitis lesions [START_REF] Cacoub | Anti-CD20 monoclonal antibody (rituximab) treatment for cryoglobulinemic vasculitis: where do we stand?[END_REF]. A

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9 randomized controlled trial in 57 patients with HCV-mixed cryoglobulinemia vasculitis showed that rituximab has a better efficacy than conventional treatment (i.e. corticosteroids, azathioprine, cyclophosphamide, or plasmapheresis) [START_REF] Vita | A randomized controlled trial of rituximab for the treatment of severe cryoglobulinemic vasculitis[END_REF]. Similar results have been reported in a placebo controlled trial [START_REF] Sneller | A randomized controlled trial of rituximab following failure of antiviral therapy for hepatitis C virus-associated cryoglobulinemic vasculitis[END_REF]. Two controlled clinical trials showed that rituximab plus PegIFN/ribavirin compared to PegIFN/ribavirin led to a shorter time to clinical remission, better renal response rate, and higher rates of cryoglobulin clearance [START_REF] Dammacco | Pegylated interferon-alpha, ribavirin, and rituximab combined therapy of hepatitis C virus-related mixed cryoglobulinemia: a long-term study[END_REF][START_REF] Saadoun | Rituximab plus Peg-interferon-alpha/ribavirin compared with Peg-interferon-alpha/ribavirin in hepatitis C-related mixed cryoglobulinemia[END_REF]. The use of rituximab was shown to be safe in HCV infected patients, in contrast with what was observed in hepatitis B virus infected patients.

To summarize, the management must be individualized according to the underlying disorder and the severity of disease. In HCV-mixed cryoglobulinemia vasculitis with mild to moderate disease, an optimal antiviral treatment should be given (Figure 3). For patients with severe vasculitis (i.e. worsening of renal function, mononeuritis multiplex, extensive skin disease, intestinal ischemia…) control of disease with rituximab, with or without plasmapheresis, is usually required before initiation of antiviral therapy. Room for other treatment strategies is very limited. Low-dose corticosteroids may help to control minor intermittent inflammatory signs such arthralgia but do not succeed in case of major organ involvement. Other immunosuppressant should be given only in case of refractory forms of HCV-mixed cryoglobulinemia vasculitis, frequently associated with underlying B-cell lymphoma [START_REF] Saadoun | Using rituximab plus fludarabine and cyclophosphamide as a treatment for refractory mixed cryoglobulinemia associated with lymphoma[END_REF].

Follow up

During immunosuppressive and/or antiviral treatment (for HCV-related cryoglobulinemia vasculitis), signs and symptoms gradually improve, varying from weeks (i.e. purpura, glomerulonephritis, arthralgia) to months (peripheral neuropathy). With treatment, most patients can achieve a partial or complete remission. In HCV-related cryoglobulinemia vasculitis, the clinical and immunological response is closely related to the viral response.

During treatment, biological improvement can be assessed by the quantification of cryoglobulinemia and other surrogate markers (C4, CH50, rheumatoid factor). The time course of HCV viral load also represents a major predictive factor of long term outcome.

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Long-term outcome is dependent on the occurrence of complications. Patients with non-HCV-related cryoglobulinemia vasculitis have an increased risk of death, primarily due to sepsis, and a 4-fold increased risk of developing B-cell non-Hodgkin lymphoma [START_REF] Terrier | Management of non infectious mixed cryoglobulinemia vasculitis: data from 242 cases included in the CryoVas survey[END_REF]. In HCVrelated cryoglobulinemia vasculitis, the overall risk of B-cell non-Hodgkin lymphoma is about 35 times higher than in the general population [START_REF] Monti | Incidence and characteristics of non-Hodgkin lymphomas in a multicenter case file of patients with hepatitis C virus-related symptomatic mixed cryoglobulinemias[END_REF]. These patients are also exposed to HCV chronic infection-induced liver disease, i.e. liver fibrosis, cirrhosis and hepatocellular carcinoma.

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Clinical significance

• In HCV-negative patients with cryoglobulinemic vasculitis (CryoVas), pulmonary, gastrointestinal and renal involvement, and age>65 years are associated with death.

• In HCV-positive patients with CryoVas, antivirals are associated with a good prognosis whereas use of immunosuppressant is associated with a poor outcome.

• Increased risk of lymphoma exists in both forms.

• For HCV patients with severe vasculitis, rituximab, with or without plasmapheresis, is required before initiation of antiviral therapy.

1 Figure 1 : 2 Figure 2 . 3 Figure 3 .

 112233 Figure 1: Survival rates (Kaplan Meier) in cryoglobulinemia vasculitis according to the type of cryoglobulin (I, II or III) and hepatitis C virus (HCV) status (from ref 1).

Table 1 .

 1 Main demographic and clinical features of patients with cryoglobulinemia vasculitis according to hepatitis C virus (HCV) status and immunochemical type of the cryoglobulin (from ref 1).

	HCV status	HCV negative	HCV positive
	• Type of the cryoglobulin	Monoclonal	Mixed	Mixed
	• Number of patients	64	242	165
	• Age (years)	65	63	60
	• Female (%)	56	69	54
	Clinical features
	• Skin (%)	86	83	76
	• Purpura (%)	69	75	71
	• Necrosis (%)	28	16	1
	• Ulcers (%)	27	14	4
	• Livedo (%)	13	2	4

Table 2 .

 2 Etiologic factors in patients with cryoglobulinemia

	Etiologic factors	Trejo et al. (6)	Saadoun et al. (15)
	Number of patients	443	1434
	Infection	75%	92%
	Hepatitis C virus	73%	91%
	Hepatitis B virus	3%	0.5%
	HIV	19%	0.5%
	Auto-immune disorders	24%	3%
	Primary Sjögren syndrome	9%	-
	Systemic lupus erythematosus	7%	-
	Rheumatoid artritis	0.5%	-
	Hematologic disorders	7%	2.5%
	Non-Hodgkin lymphoma	4%	-
	Chronic lymphocytic leukemia	1%	-
	Multiple myeloma	1%	-
	Hodgkin lymphoma	0.5%	-
	Essential cryoglobulinemia	11%	2.5%

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Zui Tao
email: zui.tao@hds.utc.fr

Philippe Bonnifait
email: philippe.bonnifait@hds.utc.fr

MODELING L1-GPS ERRORS FOR AN ENHANCED DATA FUSION WITH LANE MARKING MAPS FOR ROAD AUTOMATED VEHICLES

This paper describes a method which models the time correlation errors of a standalone L1-GPS receiver by integrating front-view camera measurements map-matched with a lane marking map. An identification method of the parameters of the shaping model is presented and evaluated with real data. The observability of the augmented state vector is demonstrated according to an algebraic definition. A positioning solver based on extended Kalman filtering with measured input is developed in the local ENU (East-North-Up) frame. This formulation allows including efficiently speed sensors in a dead-reckoned way. Outdoor experiments results carried out with a ground truth system are used to illustrate the performance of the proposed method.

1

INTRODUCTION

Estimating the pose in real-time is a primary function for road automated vehicles. Recently, highly accurate digital maps have become key components for autonomous vehicle navigation and can enhance the positioning performance [START_REF] Laneurit | Accurate vehicle positioning on a numerical map[END_REF][2] [START_REF] Jo | GPS-bias correction for precise localization of autonomous vehicles[END_REF]. In this paper, we propose to use a lane marking map of the navigation area with centimetre-level precision. The map consists of two-lane roadways with dashed lane markings in the centre of the road and solid lane markings on the both sides of the road. Lane marking is expressed by polylines in a local frame near the navigation area. In order to exploit this lane marking map, we have integrated a camera from the Lane Departing Warning Systems of the experimental vehicle. The camera's lane marking detection module is able to measure the lateral distance between the detected lane marking and the vehicle in the camera frame. The camera can also identify the type of the detected lane markings (solid, dashed and road edge). Since the camera gives relative measurements, the next step is to relate the measures with the vehicle's state. For this, we have proposed a refined camera observation model which express camera measurement by a function of the state vector and the parameters of the detected lane marking [START_REF] Tao | Mapping and localization using GPS, lane markings and proprioceptive sensors[END_REF]. So a data association process is necessary to associate a camera measurement with a certain lane marking segment in the map database. It is similar to a map matching process. The difference is that the map matching process can introduce a non-zero mean errors by simply projecting the vehicle position onto a segment which usually represents the road centreline. However, the camera has limitations. For example, there is no lane markings in some parts of the navigation area and the camera often fails to detect lane marking at cross-roads. If the uncertainty domain grows too quickly during these times, it can be very challenging to distinguish different lanes when the camera retrieves measurements. Therefore Dead-Reckoning (DR) sensors are integrated to increase the performance particularly in terms of availability. We demonstrate the observability of the gyro bias thanks to the camera observation. It is important to note that the camera observation can only improve the positioning in lateral direction for a given moment, although the longitudinal accuracy is also improved if the road changes direction. GPS is very useful to compensate DR's long-term drift and it is mandatory for a cold start initialization of the localization system. However the L1-GPS positioning errors are not white and can be affected by strong biases, which are mainly due to atmosphere propagation delays, multi-path and real-time orbit errors, particularly in urban area.

In this paper, we study GPS biases shaping models that are used in a filter by augmenting the state vector. The GPS errors are studied thanks to the use of a high-end localization system with centimetre-level accuracy. Autocorrelations of different sequences are analysed to find repeatable behaviour supposing that the bias is stationary (GPS measures with abrupt bias changing according to multi-path is supposed to be rejected by the localization solver). The bias is modeled by an autoregressive model. Parameters identification methods are discussed for integrating the shaping filter into the localization solver. The observability of GPS biases being not obvious, one of our contribution is the demonstration of the observability of the augmented state vector, which contains the pose of the vehicle, a gyro bias and GPS errors, according to an algebraic definition.

The remainder is organized as follows. Section 2 introduces the GPS error modeling. Section 3 describes the system modeling and demonstrates the observability of the state vector. Outdoor experimental results are reported in Section 4. Section 5 concludes the paper.

GPS ERROR MODELS FOR LOOSELY COUPLING DATA FUSION

GPS is mandatory for a cold start initialization of the system. Moreover, GPS information has to be used as much as possible as long as it is consistent with the pose estimate.

Indeed, when there is no lane marking in a navigation area or when the camera fails to detect lane markings at crossroads for instance, GPS is useful to improve the accuracy of the pose information and compensate Dead-Reckoning errors. Moreover, since the camera observations provide only lateral correction, if the vehicle travels in a long straight road, the longitudinal drift of a map-aided dead-reckoned estimate can become significant. The GPS information can again be used to correct the longitudinal drift.

In order to do the data fusion of GPS fixes, we propose to estimate their positioning errors by augmenting the state vector. In this section, the errors on GPS fixes are described and modelled with shaping filters.

Typical GPS errors

As well known, loosely coupling L1-GPS with other sensors is a challenging task since GPS positioning errors are not white and can be affected by strong biases (due to atmosphere propagation delays) and multipath, particularly in urban areas. Fig. 1 illustrates these issues on a real test with a ground truth system: positioning errors can reach several meters, they are strongly correlated and can have jumps during short times. The solution that we propose is to model the correlation to compensate the biases and to reject fixes that are due essentially to multipath. Therefore, each L1-GPS error can be modelled by a zero-mean white noise passing through a shaping filter to yield an output statistically similar to the error under consideration. Let [εx εy] T denotes the vector of GPS errors. The problem is to find a structure for the filter and then to estimate its parameters and the variance of the driving noise. Moreover, GPS errors are quite non-stationary (even if they have a correlation from day to day at a given place since the repetition of the satellites geometry is approximately 24 hours). So, the error model has to be quite robust with respect to this nonstationarity.

Autoregressive (AR) process for modelling GPS random errors

An AR model is a representation of a type of random process. The name autoregressive comes from the fact that each signal sample is regressed on the previous values of itself. The AR process can be described using a pole-zero transfer system (𝐻(𝑧)) as follows:

𝐻(𝑧) = 𝑂(𝑧) 𝐼(𝑧) = 𝛽 0 1+∑ 𝑎 𝑛 𝑧 -𝑛 𝑝 𝑛=1 (1)
where 𝐼(𝑧) is the z-transform of the input 𝐼 𝑘 , 𝑂(𝑧) is the z-transform of the output 𝑂 𝑘 . 𝛽 0 2 represents the estimated variance of the white noise input to the AR model; 𝑝 is the AR order.

Applying the inverse z-transform to (1), the AR sequential process in the time domain is given by:

𝑂 𝑘 = -∑ 𝑎 𝑛 𝑂 𝑘-𝑛 + 𝛽 0 𝐼 𝑘 𝑝 𝑛=1 (2)
In [START_REF] Tao | Mapping and localization using GPS, lane markings and proprioceptive sensors[END_REF], the AR processes are used to model the randomness of inertial sensor measurements. The residual random error component is modelled as a zero-mean white noise passing through a shaping filter to yield an output with an adequate time-correlation. Here, we suggest using the same AR structure to model GPS random errors. So, in our case, (2) becomes:

{ 𝜀 𝑥,𝑘 = -∑ 𝑎 𝑥,𝑛 𝜀 𝑥,𝑘-𝑛 + 𝜔 𝑥,𝑘 𝑝 𝑛=1 𝜀 𝑦,𝑘 = -∑ 𝑎 𝑦,𝑛 𝜀 𝑦,𝑘-𝑛 + 𝜔 𝑦,𝑘 𝑝 𝑛=1 (3)
where 𝜀 𝑥 and 𝜀 𝑦 are the non-white errors on GPS position fixes; 𝜔 𝑥 and 𝜔 𝑦 are the input white noises. The following section discusses the determination of the AR model coefficients (𝑎 𝑥,𝑛 and 𝑎 𝑦,𝑛 ), the input white noises and the AR order 𝑝.

AR coefficients and noises estimation

There are different methods to estimate the parameters by fitting an AR model to the input data. In [START_REF] Nassar | Improving the inertial navigation system (INS) error model for INS and INS/DGPS Applications[END_REF], three different methods for the estimation of AR model parameters are investigated: the Yule-Walker method, the covariance method and the Burg's method. The Yule-Walker method determines first the sample autocorrelation sequence of the input signal (GPS residual errors in our case). Then the AR model parameters are optimally computed by solving a set of linear normal equations in a least-square sense. However, the Yule-walker method performs adequately only for very long data records [START_REF] Jackson | Digital Filters and Signal Processing[END_REF] and it may introduce a large bias in the estimated AR coefficients, since it does not guarantee a stable solution. The covariance method is similar to the Yule-Walker method in minimizing the prediction error in the least-squares sense. Burg's method was introduced to overcome most of the drawbacks of the other modelling techniques by providing both stable and high resolution, especially for short data records [START_REF] Burg | Maximum entropy spectral analysis[END_REF]. Burg's method tries to make the maximum use of the data by defining both a forward and a backward prediction error terms. For these reasons, the Burg's method is adopted here to estimate the AR coefficients and the variance of the input white noises of the shaping filter.

Discussion on the AR order

In this section, the choice of the order of the AR model is discussed. Considering the complexity and time efficiency of integrating the AR model into a shaping filter, the study is limited up to order 2.

Eight tests have been made to collect the GPS data for a vehicle driving in normal conditions. The GPS errors are calculated in comparison to a ground truth system with centimetre-level accuracy. The AR parameters are calculated with Burg's method.

Fig. 3 shows the variation of the AR1 and AR2 coefficients respectively. One can notice that the biggest variation of the AR1 coefficients is not more than 0.05%. However, the variation of AR2 coefficients reaches nearly 40%. Even if the sequences, which we have used to identify the parameters, are probably too short to estimate the AR2 parameters adequately, it is clear that the stability of an AR1 model is better. Our strategy is so to use a lower order filter but more robust to the non-stationarity, which means in other words an AR process of order 1.

(a) AR1 coefficients variation (b) AR2 coefficients variation Fig. 3. AR coefficients estimation variation (Burg's method)

In order to validate the shaping filter, we reverse it in offline processing by using the following discrete time difference system:

{ 𝜔 𝑥,𝑘 = 𝜀 𝑥,𝑘 + 𝑎 𝑥 𝜀 𝑥,𝑘-1 𝜔 𝑦,𝑘 = 𝜀 𝑦,𝑘 + 𝑎 𝑦 𝜀 𝑦,𝑘-1 (4)
The autocorrelations of 𝜔 𝑥,𝑘 and 𝜔 𝑦,𝑘 are given in Fig. 4 (red ones), which approximate quite well a Delta-Dirac. Thus, we can conclude that these signals are white noise sequences, and the AR1 model defined by ( 4) is a good shaping filter.

SYSTEM MODELING AND STRUCTURAL PROPERTIES ANALYSIS

In section 2, the GPS positioning errors have been modelled by a first order autoregressive model. A classical way to handle this kind of modelling is to augment the state vector with a shaping filter [START_REF] Bar-Shalom | Estimation with Applications to Tracking and Navigation[END_REF]. The state vector becomes:

𝑋 = [𝑥, 𝑦, 𝜓, 𝜀 𝜔 , 𝜀 𝑥 , 𝜀 𝑦 ] 𝑇 (5)
The state evolution model is:

where (𝑥, 𝑦, 𝜓) is the vehicle 2D pose; 𝜀 𝜔 is the bias of gyro measurements; 𝜏 𝑥 and 𝜏 𝑦 are the time constants of the shaping filter.

Since GPS component errors are additive, their observability is not obvious. In this section, we prove the observability of the state vector.

Theorem: (cf. [START_REF] Sert | Localizability of unicycle mobiles robots: An algebraic point of view[END_REF]) A state element is observable with respect to 𝑍 = {𝑌, 𝑈}, if and only if it can be expressed by an algebraic function of component of 𝑍 and a finite number of their derivatives. 𝑌 is the measurement vector and 𝑈 is the input vector.

In [START_REF] Sert | Localizability of unicycle mobiles robots: An algebraic point of view[END_REF], this algebraic definition of observability is used to prove that angular measurements provided by a camera are enough to perform localization in challenging conditions. For nonlinear systems, this definition of observability is more powerful than geometrical concepts based on Lie derivatives [START_REF] Hermann | Nonlinear controllability and observability[END_REF] since it provides necessary and sufficient conditions [START_REF] Wijesoma | On the observability of path constrained vehicle localization[END_REF].

In [START_REF] Tao | Mapping and localization using GPS, lane markings and proprioceptive sensors[END_REF], we compared three different GPS error models, and the observability was proved in a simplified case: frameto-frame transformation is done by choosing the origin point of working frame on the lane marking with its x-axis parallel with the lane marking. The longitudinal errors are observable as soon as the vehicle trajectory presents changes of direction. However, if the vehicle travels along a long straight road and the GPS longitudinal error property changes with time, the observability is not guaranteed. Here, we demonstrate the observability in a fixed frame in which GPS errors on 𝑥 and 𝑦 are modelled as autoregressive processes.

Fig. 5. Simplified camera observation model

In order to prove the observability of GPS measurement errors, let us simplify the state-space model by supposing that camera and the GPS antenna are coinciding with point 𝑀 (Fig. 5). As in [START_REF] Tao | Mapping and localization using GPS, lane markings and proprioceptive sensors[END_REF], a frame-to-frame transformation is performed to simplify the camera observation model (cf. [START_REF] Tao | Tightly coupling GPS with lane markings for autonomous vehicle navigation[END_REF]) by choosing the origin of the working frame as point 𝐴 of the detected lane marking with its x-axis parallel to the lane marking. Consequently, camera and GPS observation model are simplified to:

𝐶 0 = 𝑦/cos𝜓 (7)
and

{ 𝑥 𝐺𝑃𝑆 = 𝑥 + 𝜀 𝑥 𝑦 𝐺𝑃𝑆 = 𝑦 + 𝜀 𝑦 (8)
We have 𝑌 = [𝑥 𝐺𝑃𝑆 , 𝑦 𝐺𝑃𝑆 , 𝐶 0 ] and 𝑈 = [𝑣, 𝜔] to analyze the observability of the state vector in the algebraic framework.

Observability of the vehicle heading 𝝍 and gyro bias 𝜺 𝝎

By taking the derivative of (7), we have:

𝑦̇= 𝐶 0 ̇• cos𝜓 -𝐶 0 • 𝜓 ̇• sin𝜓 (9) x y A B
By plugging 𝑦̇= 𝑣 • sin𝜓 and 𝜓 ̇= 𝜔 -𝜀 𝜔 into (9):

𝑣 • sin𝜓 = 𝐶 0 ̇• cos𝜓 -𝐶 0 (𝜔 -𝜀 𝜔 )sin𝜓 (10)
By taking the derivative of (10), we have:

[𝑣̇+ 2𝐶 0 ̇(𝜔 -𝜀 𝜔 ) + 𝜔̇• 𝐶 0 ]sin𝜓 = [𝐶 0 ̈-𝐶 0 (𝜔 -𝜀 𝜔 ) 2 -𝑣(𝜔 -𝜀 𝜔 )]cos𝜓 (11)
If 𝜓 is identically null (the vehicle is travelling parallel to the lane marking) then 𝜓 ̇= 0 and we have 𝜀 𝜔 = 𝜔, the gyro bias is then observable. Moreover, in this case, we have 𝐶 0 ̇ is identically null so that one can observe that 𝜓 is identically null. Now, suppose that 𝜓 is non null. By [START_REF] Hermann | Nonlinear controllability and observability[END_REF], we can work out:

𝜀 𝜔 = 𝑣•sin𝜓-𝐶 0 ̇•cos𝜓 𝐶 0 •sin𝜓 + 𝜔 ( 12
)
𝐶 0 is physically non null because the lane markings are on the sides of the lane. By plugging ( 12) into [START_REF] Wijesoma | On the observability of path constrained vehicle localization[END_REF], one gets a non-singular expression when the vehicle linear or rotational speeds are not null or when the vehicle accelerates or decelerates:

(𝑣̇• 𝐶 0 -3𝑣 • 𝐶 0 ̇+ 𝜔̇• 𝐶 0 2 )sin 3 𝜓 -(3𝐶 0 ̇2 -𝐶 0 ̈• 𝐶 0 ) cos 3 𝜓 -(2𝐶 0 ̇2 -𝐶 0 ̈• 𝐶 0 ) cos𝜓 + 𝑣 • 𝐶 0 ̇• sin𝜓 = 0 (13)
From ( 13), there exists an implicit function 𝛷 𝜓 of 𝐶 0 , 𝐶 0 ̇, 𝐶 0 ̈, 𝑣, 𝑣, 𝜔 and 𝜔̇ such that:

𝜓 = 𝛷 𝜓 (𝐶 0 , 𝐶 0 ̇, 𝐶 0 ̈, 𝑣, 𝑣̇, 𝜔, 𝜔̇) (14)
𝜓 is therefore observable. By using ( 14) in ( 12), a function 𝛷 𝜀 𝜔 can give 𝜀 𝜔 :

𝜀 𝜔 = 𝛷 𝜀 𝜔 (𝐶 0 , 𝐶 0 ̇, 𝐶 0 ̈, 𝑣, 𝑣, 𝜔, 𝜔̇)

𝜀 𝜔 is therefore observable.

3.2

Observability of the vehicle position (𝒙, 𝒚) and GPS errors (𝜺 𝒙 , 𝜺 𝒚 )

By taking the derivative of (8), we have:

𝑥̇𝐺 𝑃𝑆 = 𝑣 • cos𝜓 -𝜀 𝑥 /𝜏 𝑥 (16) So we can get:

𝜀 𝑥 = 𝜏 𝑥 (𝑣 • cos𝜓 -𝑥̇𝐺 𝑃𝑆 ) (17)
Since 𝜓 is observable, 𝜀 𝑥 is observable. So 𝑥 = 𝑥 𝐺𝑃𝑆 -𝜀 𝑥 is observable.

With 𝑦 = 𝐶 0 • cos𝜓 and (14), 𝑦 is observable. With 𝜀 𝑦 = 𝑦 𝐺𝑃𝑆 -𝐶 0 • cos𝜓 , 𝜀 𝑦 is observable. So far, we have proved that every element in the state vector 𝑋 can be expressed as an algebraic function of the components of [𝑌, 𝑈] and a finite number of their derivatives. We can consequently conclude that the state vector with its associated state space is observable as long as the vehicle moves.

A positioning solver based on extended Kalman filtering with measured input has been developed and implemented in the local ENU frame. The location of the camera in the body frame is taken into account to get an accurate correction, please refer to [START_REF] Tao | Tightly coupling GPS with lane markings for autonomous vehicle navigation[END_REF] for more details about the EKF filter with measured input, the map matching method and the complete camera observation model. Outdoor experimental results are given in section 4.

RESULTS

Experimental set-up

Outdoor experiments have been carried out near Paris France in May 2013. Three tests were performed. Every test went on about 5 minutes, and the travelling distance was 3 km with a typical speed of 30 km/h in the straight road. The vehicle passed through a strong urban canyon with 300 meters' length. The experimental vehicle was equipped with an IMU Oxford RT3000 which provides ground truth data at 100Hz rate. A CAN-bus gateway was used to access to the wheel speed sensors and the yaw rate gyro. A Mobileye camera was used to detect the lane markings at 10Hz. A low-cost Ublox 6T GPS receiver with a patch antenna provided position measurements at 5Hz.

Localization results

The localization performance is studied by using a data replay processing implemented in C++ (identical to the software used in real-time) on different sequences than the ones used for AR parameters identification. Fig. 6a 1 gives the global performance of three tests by stand-alone U-blox and Map-aided positioning. By using mapaided positioning, 95% lateral positioning errors (PE) are less than 0.68m and 95% and the longitudinal ones are less than 0.88m. Fig. 7 compares the cumulative distributions of the absolute positioning errors. The localization accuracy is highly improved by map-aided positioning on both lateral and longitudinal directions.

CONCLUSIONS

In this paper, we have first proposed an identification method of autoregressive parameters of shaping models of GPS errors. As shown, the GPS errors are well modeled by first order AR processes. This modelling keeps a complete observability of the augmented state vector when the vehicle is moving, which has been demonstrated according to an algebraic definition. A localization solver has been implemented in a local ENU frame to validate the proposed method with real outdoor data. The positioning accuracy is highly improved compared to stand-alone GPS. It is interesting to point out that 𝜀 𝑦 is directly observable if the road is East oriented, which means that it is possible to use a more refined model to estimate 𝜀 𝑦 . A perspective of this research is so to study if an implementation of the localization solver can be done in a road frame changing from one road to another in a sequential way.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Errors of L1-GPS solutions in the local navigation frame

Fig. 4 .

 4 Fig. 4. Autocorrelation of experimental signal and the inverse of the shaping filter

  𝜓 ̇= 𝜔 -𝜀 𝜔 𝜀 𝜔 ̇= 0 𝜀 𝑥 ̇= -𝜀 𝑥 /𝜏 𝑥 𝜀 𝑦 ̇= -𝜀 𝑦 /𝜏 𝑦

Fig. 7 .

 7 Fig. 7. Cumulative distribution function of the positioning errors

  shows the test scene in the local ENU frame. The grey bounds represent buildings which are from OpenStreetMap to illustrate the urban condition of the test scene. The black lines represent the lane marking map expressed by polylines. The test scene mainly consists of two-lane roadways with dashed lane marking in the centre of the road and solid ones on both sides of the road. The map reaches a few-centimetres-level accuracy with often a better accuracy. The red line stands for the ground truth of the test trajectory of test 1. Fig.6bshows changes of lateral and longitudinal positioning errors over time with ±3𝜎 bounds of test 1 estimated by the extended Kalman filter. One can notice that the uncertainty on lateral position increases greatly when lane marking measurements are not detected (in practice it remains often acceptable for autonomous navigation since this occurs mainly at roads intersections). The filter yields a better consistence on lateral positioning.

	(a) Test scene			(b) Map-aided positioning errors
	Fig. 6. Test scene and Map-aided lateral and longitudinal positioning errors
		Lateral PE (m) Longitudinal PE (m)
		I	II	I	II
	mean	1.30	0.07	1.55	-0.32
	Std. dev.	1.12	0.29	1.18	0.32
	median	0.96	0.10	1.31	0.30
	95 th percentile	3.20	0.68	3.88	0.88
	max	6.78	1.83	4.69	1.50
	Table 1. Positioning error statistics. (I: Stand-alone U-blox; II: Map-aided positioning)
	Table

Acknowledgements

The authors would like to thank Vincent Frémont, Stéphane Bonnet and Javier-Ibañez Guzman for their support in the experiments.


Guang Yang
email: guangyang@shu.edu.cn

Hongfei Chen

Catherine Boussard-Plédel

Jean-Christophe Sangleboeuf
email: jean-christophe.sangleboeuf@univ-rennes1.fr

Bruno Bureau

Effect of physical aging on fracture behavior of Te 2 As 3 Se 5 glass fibers

Keywords: Fracture, shape factor, glass fiber, chalcogenide glass

Fracture surface characteristics of Te 2 As 3 Se 5 (TAS) glass fibers aged in light and in dark have been investigated respectively for understanding physical aging effect on their fracture behavior.

The properties including tensile strength (ı), surface flaw depth (Į), and mirror radii (r m ) were measured by DY30 Adamel Lomarghy and SEM respectively. Shape factor extracted by fitting of ı vs Į confirms that fractures of fibers aged in dark for 4 months originate from their surface flaw, but it does not work for fibers aged in light for 4 months. However, mirror constants (=ır m 1/2 ) of fracture surface for the TAS glass fibers aged in dark are in a good agreement with those aged in light. One possible reason is that the photoinduced effect changes the structure of glass surface during the physical aging.

Introduction

Chalcogenide glasses possess large transparency in the infrared (IR) range, covering two atmosphere windows (2-12 ȝm), as well as their good thermo-mechanical properties which make the glass easy to be drawn into fibers [START_REF] Zakery | Optical properties and applications of chalcogenide glasses: a review[END_REF][START_REF] Eggleton | Chalcogenide photonics[END_REF][START_REF] Gao | Mid-infrared supercontinuum generation in a suspended-core As2S3 chalcogenide microstructured optical fiber[END_REF]. The glass with TAS composition shows a large domain of transmission in the mid-IR from 800-4000 cm -1 with a minimum for the attenuation of 1dB/m and an excellent resistance to devitrification during fiber drawing process [START_REF] Keirsse | Chalcogenide glass fibers used as biosensors[END_REF][START_REF] Pouvreau | Mechanical properties of a TAS fiber: a preliminary study[END_REF][START_REF] Shiryaev | Recent progress in preparation of chalcogenide As-Se-Te glasses with low impurity content[END_REF][START_REF] Delaizir | Influence of ageing conditions on the mechanical properties of Te-As-Se fibres[END_REF]. Therefore TAS fibers have been used as bio-sensor for medical and environmental detections [START_REF] Keirsse | Chalcogenide glass fibers used as biosensors[END_REF][START_REF] Lucas | Advances in chalcogenide fiber evanescent wave biochemical sensing[END_REF][START_REF] Anne | Chalcogenide Glass Optical Waveguides for Infrared Biosensing[END_REF].

Structure of TAS glasses are based on a two dimensional glass network where atomic As is bridged by chalcogen chain fragments, and introduction of tellurium in TAS glasses induces breaking of chalcogen chain and formation of AsSe 3-x Te x pyramidal units [START_REF] Ma | Covalent bond connectivity, medium range order, and physical properties in TeX and TeXAs glasses[END_REF][START_REF] Delaizir | Structural characterizations of As-Se-Te glasses[END_REF][START_REF] Alekberov | Raman scattering in As-Se-S and As-Se-Te Chalcogenide vitreous semiconductors[END_REF]. Our previous researches have reported that the surface quality of TAS fibers, physical aging conditions, such as light, load and air, and glass structural relaxation, have effect on the ı [START_REF] Pouvreau | Mechanical properties of a TAS fiber: a preliminary study[END_REF][START_REF] Delaizir | Influence of ageing conditions on the mechanical properties of Te-As-Se fibres[END_REF][START_REF] Yang | Effect of Physical Aging Conditions on the Mechanical Properties of Te2As3Se5 (TAS) Glass Fibers[END_REF]. However, so far for TAS glass fibers there is little report about correlation between the ı and Į or r m under different aging conditions. In this work, we carried out a detail research on the correlation between the ı and Į or r m for TAS fibers aged in light and in dark respectively.

Experiments

TAS fibers were drawn from glass pre-forms synthesized in vacuum from high purity raw materials. Elementary substances, selenium and arsenic, were further purified to eliminate the remaining oxygen and hydrogen with the volatilization technique by heating at 240 and 290 o C respectively under vacuum for several hours. The required amounts of Te, As and Se were sealed in a special silica tube under vacuum and sublimated (at 800 o C), to remove carbon and compounds with higher boiling points. The mixture was maintained at 750 o C for 12 h in a rocking furnace to ensure a good homogenization of the liquid. Then the ampoule was quenched in water and annealed at 120 o C, near the glass transition temperature for 2 hours. The obtained samples had a 1.0 cm large diameter and were 10.0 cm long. The glassy nature of the obtained glassy preform rod was confirmed by X-ray dispersion analysis (Philips PW3230, Philips, Almedo, Netherlands). The infrared optical homogeneity of the preform rod and the quality, including the absence of some obvious crystals and bubbles, were verified with a thermal-imaging camera (FLIR PM 390 ThermaCAM, FLIR Inframetrics, Portland, OR).

Optical fiber was drawn from a home-made drawing tower with a protection gas flow (He, 2.5 L/min) as shown in Figure 1. The fiber velocity, diameter, tension, and helium flow velocity, as well as the average furnace temperature, were continuously monitored (data recording frequency of 1 Hz) [START_REF] Yang | Viscosity of As 2 Se 3 Glass During the Fiber Drawing Process[END_REF]. The fiber diameter was measured using a laser interferometer. Glass cylinders are heated up to the softening temperature at 290 o C, and flowed to the appropriate diameter by tuning both the temperature (and thus the viscosity) and the drawing speed. The diameters of the fiber had been made about 400 µm. The fiber was fixed into a special drum, which was separated into many parts with some rungs and each part of which was with a length of 13 cm to keep fiber without any touch with the drum. After the fiber was synthesized, they were immediately stored individually in three conditions: in dark, and in light (fluorescent tubes on one side of fibers), for 0.5, 1.5, 3, 4 and 5 months respectively at room temperature and under atmosphere. Thus, some surface abrasion could induce fracture-initiating flaws during fiber drawing process, but no more surface abrasion occurs after fiber drawing and during fiber storage.

They were tested in tension after physical aging for different periods of time at room temperature and in air.

Tensile tests were carried out on a DY30 Adamel Lomarghy testing machine (DY 30 Adamel Lhomargy, MTS Systems, Ivy sur Seine, France). Fibers were end-tabbed to prevent against sliding and/or indentation. Alignment was optimized on a set of fibers prior to testing.

Displacement controlled experiments were conducted on specimens with 7.0 cm long gauges, using a 100 N load cell (precision of 0.1 N), a cross head speed of 1.0 mm/min (apparent deformation rate 2.4×10 -4 s -1 ). After tensile tests, the TAS fiber's surface and fracture surface were characterized using SEM (JSM6301F, JEOL, Tokyo, Japan). From these SEM images, all parameters in Figure 2 (Į and r m ) of fracture surface were measured by a Quartz PCI Lite/Satellite Image Acquisition software (Quartz PCI, Quartz Imaging Corporation, Vancouver, Canada).

Results and discussion

Initial defects

Figure 2 shows the typical fracture surface with general appearance of fracture mirror and other related features on silicate fibers. It has been demonstrated that the failure begins from an initial and small surface flaw with depth Į on surface of silicate fibers, then the crack promptly propagates through the fiber, giving birth to three distinct regions of fracture features named as the mirror, mist and hackle [START_REF] Feih | Tensile strength and fracture surface characterisation of sized and unsized glass fibers[END_REF][START_REF] Koiter | Rectangular Tensile Sheet With Symmetric Edge Cracks[END_REF][START_REF] Krohn | Relation of Flaw Size to Mirror in the Fracture of Glass[END_REF].

For a sharp flaw on fiber's surface, where the flaw size is considered small compared with the radius of the glass fiber, the strength σ and flaw depth Į can be related as [START_REF] Feih | Tensile strength and fracture surface characterisation of sized and unsized glass fibers[END_REF]:

IC K Y = σ πα (1)
where Y is shape factor depending on initial crack geometry (the initial flaw depth Į) and its size in relation to the fiber radius r, and K IC is toughness of bulk glass. There are two simplified cases of Y, including a semi-circular flaw in an infinite body with a constant value of Y=0.64 and a straight surface cracks in an infinite body with Y=1.126 [START_REF] Feih | Tensile strength and fracture surface characterisation of sized and unsized glass fibers[END_REF][START_REF] Koiter | Rectangular Tensile Sheet With Symmetric Edge Cracks[END_REF][START_REF] Krohn | Relation of Flaw Size to Mirror in the Fracture of Glass[END_REF]. Figure 3 shows the tensile strength vs the initial flaw depth. First of all, due to the similar failure behavior, we fitted both conditions, viz. in dark and in light, in one way which can be expressed as:

But we observed an invalid adjusted coefficient of determination, R 2 § -0.23. The mathematically invalid fitting could be caused by mixture of points with different aging conditions. Thus, we have fitted the tensile stress vs the initial flaw depth of TAS fibers for samples aged in light and in dark respectively, as shown in Figure 3. With our experimental K IC (0.18 ± 0.05MPa.m 1/2 ) of bulk TAS glass, the Y are obtained as 0.83 in dark condition and 1.34 in light condition respectively. The Y equaling to 0.83 for dark condition lies well within the region of (0.668, 1.126), which means the fracture originates from initial flaw on sample's surface. But the Y (1.34) for fibers aged in light is obviously beyond the region. However, from the SEM images of fibers aged in light, those aged in dark and even those of fresh fibers, most their fracture surfaces are similar as in Figure 2. On one side, this excludes an important effect from glass structure relaxation with physical aging in light or in dark conditions for all fibers. On the other side, this could be correlated to photoinduced effect on the surface of TAS fibers with a depth about several microns, which is covering the initial flaws [START_REF] Owen | Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors[END_REF][START_REF] Shimakawa | Photoinduced effects and metastability in amorphous semiconductors and insulators[END_REF][START_REF] Yang | A photo-stable chalcogenide glass[END_REF][START_REF] Gueguen | Photoinduced fluidity in chalcogenide glasses at low and high intensities: A model accounting for photon efficiency[END_REF]. It could be explained as that the photoinduced effect changes local glass structure (within fiber's surface) during the physical aging, as mentioned by many previous researches on chalcogenide glasses [START_REF] Owen | Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors[END_REF][START_REF] Shimakawa | Photoinduced effects and metastability in amorphous semiconductors and insulators[END_REF][START_REF] Yang | A photo-stable chalcogenide glass[END_REF][START_REF] Gueguen | Photoinduced fluidity in chalcogenide glasses at low and high intensities: A model accounting for photon efficiency[END_REF]. The variation of the local structure could induce decaying of K IC in light condition . For example, if we suppose that fracture behavior of fibers aged in light and in dark have a same Y (0.83), then the K IC could decay from 0.18 ± 0.05MPa.m 1/2 to 0.13 ± 0.05MPa.m 1/2 . And the adjust R 2 are 0.78 and 0.70, which are mathematically valid and much better than -0.23 of the blue solid fitting in Figure 3. Furthermore details about variation about the ı during physical aging in the two conditions can be found in our previous paper [START_REF] Yang | Effect of Physical Aging Conditions on the Mechanical Properties of Te2As3Se5 (TAS) Glass Fibers[END_REF].

Additionally, new defects (the maximum size is about 100 nm in Figure 4), which may result from a reaction between fiber and water or O 2 during physical aging, is much smaller than the dimension, 2b, of initial flaw within the range from 2 to 10 ȝm as shown in Figure 5(b). This confirms that the fracture does not originate from the new defects appearing after physically aged in two conditions.

Mirror region

Most fracture surfaces have similar mirror regions with semi-circular shapes. It has been extensively demonstrated the product of fiber strength ı and the square root of the mirror radius r M (inner mirror radius) or the mist radius r H (outer mirror radius) is constant in silicate glasses [START_REF] Feih | Tensile strength and fracture surface characterisation of sized and unsized glass fibers[END_REF][START_REF] Mecholsky | Prediction of Fracture Energy and Flaw Size in Glasses from Measurements of Mirror Size[END_REF][START_REF] Shand | Breaking Stress of Glass Determined from Dimensions of Fracture Mirrors[END_REF]:

1/ 2 M 1 (r ) A σ = (3) 1/ 2 H 2 (r ) A σ = (4)
where A 1 and A 2 are the so-called mirror constants. From the above equations, the size of the mirror region relates to strength of fiber, viz., higher strength fiber has smaller fracture mirror region.

Figure 6 shows the plots of tensile stress vs inner and outer mirror size for fibers aged 4 months in light and in dark respectively. The mirror constants of TAS fibers (inner 0.33 ± 0.01MPa m 1/2 and outer 0.39 ± 0.01 MPa m 1/2 for dark condition, and inner 0. and outter 2.42 MPa m 1/2 ) with enhanced strength [START_REF] Mecholsky | Prediction of Fracture Energy and Flaw Size in Glasses from Measurements of Mirror Size[END_REF]. The minima mirror constants of TAS fibers are due to the weakest bond energy among above four compositions. The bond energy of Te-Se, As-Se, As-S, Ge-Se, and Si-O are 170, 177, 198, 215, and 369 kJ/mol respectively, which are well in consistent with above result [START_REF] Pauling | The Nature of the Chemical Bond[END_REF]. Both of mirror constants determined from experiments show good R 2 ( § 0.91 and 0.81 of inner mirror constants, while 0.92 and 0.83 of outer mirror for fibers aged in dark and in light conditions respectively). Figure 6 exhibits that the fitting results of fibers aged in dark condition for inner and outer mirror constant are in a good agreement with those of fiber aged in light. Even we could do fitting of the two conditions in one curve, because the photoinudced effect only influences on a few micron of fiber's surface [START_REF] Owen | Photo-induced structural and physico-chemical changes in amorphous chalcogenide semiconductors[END_REF][START_REF] Shimakawa | Photoinduced effects and metastability in amorphous semiconductors and insulators[END_REF][START_REF] Yang | A photo-stable chalcogenide glass[END_REF]. Here we just exhibits the data of fibers aged for 4 months, because we do not have enough data for other aged times and they will be researched in future.

The present work shows that the fracture surface pattern of TAS fibers (aged in dark or light) can be divided into three types of failure pattern. First type of failure of the fracture surface is major feature as shown in Figure 5(a) ((b) is enlargement of the mirror region), which is similar to that of silicate glassy fibers in Figure 2. Figure 5(b) also exhibits that the initial flaw could be a particle or a tiny crack on the surface of fiber samples, which may be due to defects on preform-rod formed when polishing with alumina powder or contacting with pulley during drawing process [START_REF] Pouvreau | Mechanical properties of a TAS fiber: a preliminary study[END_REF]. Usually the sample with first type failure indicates higher stress with smaller size of mirror and even with a wave-like pattern (Figure 5 is the least appearance of the failure type with a whole circular inside fiber, but fracture seems to originate from insider in fiber instead of an initial surface flaw.

Conclusions

The experimental shape factor confirms that the fracture of fibers aged in dark originates from the initial flaw on fiber's surface for fibers aged in light rather than the new defects generated during physical aging, but it is not same in light condition due to the photoinduced effect on the change of fiber's surface structure. However, mirror constants of fibers aged in two conditions determined from experiments are similar, because the photoinudced effect only influences on a few micron of fiber's surface. The fracture surfaces of fibers are divided into three types of failure pattern: with mirror region on the edge of fiber's fracture surface, with mirror region inside of fiber's fracture surface, and no mirror region. Further research on K IC and the mirror constants will be carried out by longer time (1 year or more) physical aging.

  33 ± 0.01MPa m 1/2 and outer 0.40 ± 0.01 MPa m 1/2 for light condition) are close to those of As 2 S 3 fibers (inner 0.56 MPa m 1/2 , and outer 0.65 MPa m 1/2 ) or those of Ge 33 As 12 Se 55 fibers (inner 0.55 MPa m 1/2 , and outer 0.65 MPa m 1/2 ) with low strength, but less than those of SiO 2 fibers (inner 2.23 MPa m 1/2 ,

  (a)), while lower stress with larger size of mirror and without a wave-like pattern. Compared with fracture surface of fibers aged in dark, however, no evidence could be obtained from SEM images for photoinduced effect on initial flaw of fibers aged in light. The second type of failure (Figure 5(c)) reveals smooth fiber breakage without any indication of a surface fault. Unfortunately, it is not possible to confirm that we are indeed looking at the original fracture surface for these fibers with smooth fracture patterns because these fibers break into more than 2 parts during test. Therefore the fracture surfaces could well be a result of secondary breaks caused by bending of the fiber during fracture. The last type of failure (Figure 5(d))

Figure Captions:Fig. 1 .

 1 Figure Captions:

Fig. 2 .

 2 Fig. 2. A typical enlargement of the initial fracture part.

Fig. 3 .

 3 Fig. 3. Tensile strength vs initial flaw depth of TAS fibers aged in dark and in light for 4 months

Fig. 4 .

 4 Fig. 4. Surfaces of TAS fibers fresh (left), aged for 1.5 months in light (middle), and aged for 3

Fig. 5 .

 5 Fig. 5. Fracture surfaces of TAS fibers after physical aging. (a) is the first type failure aged for 1.5

Fig. 6 .

 6 Fig. 6. Tensile stress vs inner mirror radius (a) and outer mirror radius (b) of TAS fibers in dark

Acknowledgments

The authors wish to express their gratitude to Thierry Jouan, and Thierry Pain (Verres et Céramiques, UMR 6226, Université de Rennes 1).


Benjamin Perret
email: benjamin.perret@esiee.fr

Jean Cousty
email: jean.cousty@esiee.fr

Jean Carlo Rivera Ura

Silvio Jamil
email: sjamil@pucminas.br

F Guimarães

Evaluation of morphological hierarchies for supervised segmentation

Keywords: hierarchy, supervised segmentation, morphology

We propose a quantitative evaluation of morphological hierarchies (quasi-flat zones, constraint connectivity, watersheds, observation scale) in a novel framework based on the marked segmentation problem. We created a set of automatically generated markers for the one object image datasets of Grabcut and Weizmann. In order to evaluate the hierarchies, we applied the same segmentation strategy by combining several parameters and markers. Our results, which shows important differences among the considered hierarchies, give clues to understand the behaviour of each method in order to choose the best one for a given application. The code and the marker datasets are available online.

Introduction

We propose an application driven comparison of several partition hierarchies proposed in the mathematical morphology community: quasi-flat zones hierarchy [START_REF] Nagao | Region extraction and shape analysis in aerial photographs[END_REF][START_REF] Meyer | Morphological scale-space representation with levelings[END_REF], various watershed hierarchies [START_REF] Beucher | Watershed, hierarchical segmentation and waterfall algorithm[END_REF][START_REF] Najman | Geodesic saliency of watershed contours and hierarchical segmentation[END_REF][START_REF] Meyer | The dynamics of minima and contours[END_REF] (by altitude, area, volume, and dynamics), constrained connectivity hierarchy [START_REF] Soille | Constrained connectivity for hierarchical image partitioning and simplification[END_REF], hierarchical observation scale [START_REF] Guimarães | A hierarchical image segmentation algorithm based on an observation scale[END_REF]. Compared to the evaluation strategy proposed by Arbelaez et al. [START_REF] Arbelaez | Contour detection and hierarchical image segmentation[END_REF] which searches for the best segmentation compared to a ground truth segmentation without any prior on the number of regions, we propose to focus on the single object supervised segmentation relying on two marker images: the foreground marker indicates pixels that must be in the segmented object while the background marker gives a set of pixels that is not in the object. Thus, rather than searching if one can find a segmentation that resembles a human segmentation of the whole scene, we evaluate: 1) if a hierarchy contains a set of regions that matches a given object of the scene, and 2) how difficult it is to find this set.

The problem of the automated evaluation of supervised and interactive segmentation algorithms has recently received increasing attention [START_REF] Moschidis | A systematic performance evaluation of interactive image segmentation methods based on simulated user interaction[END_REF][START_REF] Mcguinness | Toward automated evaluation of interactive segmentation[END_REF][START_REF] Klava | A model for simulating user interaction in hierarchical segmentation[END_REF][START_REF] Zhao | A benchmark for interactive image segmentation algorithms[END_REF]. Following the idea of [START_REF] Zhao | A benchmark for interactive image segmentation algorithms[END_REF], and in order to perform an objective and quantitative evaluation, we have automatically generated markers from two publicly available one object image datasets: Grabcut [START_REF] Blake | Interactive image segmentation using an adaptive GMMRF model[END_REF] and Weizmann [START_REF] Alpert | Image segmentation by probabilistic bottom-up aggregation and cue integration[END_REF]. For each image of the databases, we created a set of several foreground and background markers from the ground truth segmentations. Those markers were designed in order to represent different difficulty levels and do not necessarily aim to reproduce possible user interactions. Then, we have selected a simple marked segmentation strategy which consists in searching for the largest regions of the hierarchy which intersect the foreground marker and does not touch the background marker. Our tests also evaluate the importance of several parameters as the adjacency relation and the dissimilarity measure between pixels.

The contributions of this paper are the following. We propose a novel evaluation framework for partition hierarchies relying on the marker based segmentation problem. The test images are taken from public datasets and the generated markers are available online at http://perso.esiee.fr/ ~perretb/markerdb/. This framework is applied to several morphological hierarchies and allows us to draw some conclusions on relevance of the evaluated hierarchies. A demonstration website where users can segment their own images using the evaluated hierarchies is also available at http://perso.esiee.fr/ ~perretb/ISeg/.

Hierarchies

We give a short description of the hierarchies that will be evaluated and the reader can refer to the cited articles in order to get formal definitions or additional information. A hierarchy of partitions is a sequence of partitions such that each partition is a refinement of the previous partition in the sequence. It is usually represented as a tree or a dendrogram and can be visualized as a saliency map, which is a contour map in which the grey level represents the strength of the contour: i.e., its level of disappearance in the hierarchy.

The links that exist among most of the presented hierarchies and efficient algorithms to construct them are described in [START_REF] Cousty | Constructive links between some morphological hierarchies on edge-weighted graphs[END_REF][START_REF] Najman | Playing with kruskal: Algorithms for morphological trees in edge-weighted graphs[END_REF].

The Quasi-Flat Zones (QFZ) hierarchy (Fig. 1(b)) is a classical structure that is constructed by considering the connected components of the level sets of the dissimilarity function [START_REF] Nagao | Region extraction and shape analysis in aerial photographs[END_REF][START_REF] Meyer | Morphological scale-space representation with levelings[END_REF]. More precisely, we say that two adjacent pixels of an image are λ-connected if there dissimilarity is lower than or equal to a value λ. For a given λ in R, the equivalence classes of the relation "is λ-connected" form the λ-partition of the image into its λ-connected components also called λ-flat zones. The set of all λ-partitions for every λ in R forms the QFZ hierarchy.

Constrained connectivity (CC) hierarchy (Fig. 1(c)) is a filtered version of the QFZ hierarchy [START_REF] Soille | Constrained connectivity for hierarchical image partitioning and simplification[END_REF]. It is constructed by adding additional constraints to the definition of the connectivity. In this work we consider only the global range constraint, which limit the maximal dissimilarity between two pixels of a same connected component. This idea was introduced in order to prevent the chaining effect that may appear in the QFZ hierarchy. Watershed (WS) hierarchies (Figs. 1(d), 1(e), 1(f ), and 1(g)) are constructed by considering the watershed segmentation of an image that is iteratively flooded under the control of an attribute [START_REF] Beucher | Watershed, hierarchical segmentation and waterfall algorithm[END_REF][START_REF] Najman | Geodesic saliency of watershed contours and hierarchical segmentation[END_REF][START_REF] Meyer | The dynamics of minima and contours[END_REF][START_REF] Cousty | Incremental algorithm for hierarchical minimum spanning forests and saliency of watershed cuts[END_REF]. For example, the watershed segmentations of the area closings of size k of an image for every positive integer k form the WS hierarchy by area of the image. In this article, we consider 4 possible attributes: altitude (WSAlt), dynamics (WSDyn), area (WSArea), and volume (WSVol).

Observation scale hierarchy (Fig. 1(h)) is a hierarchical version [START_REF] Guimarães | A hierarchical image segmentation algorithm based on an observation scale[END_REF] of Felzenswalb et al. segmentation algorithm [START_REF] Felzenszwalb | Efficient graph-based image segmentation[END_REF]. This approach relies on a predicate that measures the evidence for a boundary between two regions using scale and contrast information.

Supervised Segmentation algorithm

In this evaluation we have chosen to use the procedure described in [START_REF] Salembier | Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval[END_REF] that constructs a two classes segmentation from a hierarchy and two non-empty markers: one for the background and one for the object of interests. Its principle is to identify the object as the largest regions of the hierarchy that intersect the object marker but does not touch the background marker. This result can be computed efficiently in two passes on the hierarchy (real time interaction). In the first pass, we browse the hierarchy from the leaves to the root in order to determine for each node if it intersects each marker. The second pass, where the tree is browsed from the root to the leaves, determines the final class of each node following this rule:

if the node intersects the background then its final label is background ; else, if the node intersects the object marker then its final label is object; else the node has the same label as its parent.

Finally, as this procedure tends to produce segmentations with a lot of holes in some hierarchies, we also consider a post-processing where the holes of the segmented object that do not contain a pixel of the background marker are filled.

Database and marker generation

We consider two publicly available datasets focused on the single object segmentation problem: Grabcut [START_REF] Blake | Interactive image segmentation using an adaptive GMMRF model[END_REF] and Weizmann [START_REF] Alpert | Image segmentation by probabilistic bottom-up aggregation and cue integration[END_REF]. Grabcut and Weizmann datasets are composed of 50 and of 100 colour images respectively. Each image contains at least one relatively large object which is identified in a ground-truth segmentation. In the Grabcut dataset, the ground truths are stored as tri-maps which identify the object, the background, and mixed pixels (which are excluded from the computation of the scores). In the Weizmann dataset, each image comes with 3 human 2 classes segmentations and the final ground truth is determined with a majority vote (a pixel is classified as object if at least two humans have classified it as object). In order to perform a fair and objective evaluation of the different hierarchies we propose several automatic strategies to generate object and background markers from the ground truth. Our main idea here is not to reproduce the interactive segmentation process experienced by a real user but rather to obtain markers representing either various difficulty levels using erosions of various sizes, or markers that resembles to human generated markers using skeletonization. The generated markers are the following (see Fig. 2):

-High Quality (HQ) marker: erosion by a ball of radius 7 pixels; -Medium Quality (MQ) marker: erosion by a ball of radius 30 pixels; -Low Quality (LQ) marker: erosion by a ball of radius 45 pixels; -Skeleton (Sk): morphological skeleton given by [START_REF] Chaussard | Robust skeletonization using the discrete lambda-medial axis[END_REF]; and -Frame (Fr): frame of the image minus the object ground truth if the object touches the frame (background only). Using the frame as the background marker is nearly equivalent to having no background marker in the sense that it does not depend of the ground truth or the image.

If a connected component is completely deleted by the erosion then a single point located in the ultimate erosion of this connected component is added to the marker.

In the following, the combination of the background marker MB and the foreground marker MF is denoted MB-MF (for example, HQ-MQ stands for the combination of a high quality marker for the background and a medium quality marker for the foreground). Among all the possible combinations of markers, we chose to concentrate on the following ones:

-HQ-HQ, MQ-MQ, LQ-LQ represent a sequence of increasing difficulty as the markers get smaller. Nevertheless, all those combinations are symmetric in the sense that the correct segmentation is roughly at equal distance from the foreground to the background marker; -Sk-Sk, MQ-Sk, Fr-Sk: here the foreground marker is always the skeleton of the ground-truth, while the background marker gets further and further from the ground-truth.

The performance of each segmentation result is evaluated with the F-measure

F = 2.Recall.P recision Recall + P recision (1)
with Recall = T P T P + F P , and P recision = T P T P + F N

where T P , F P , and F N stand respectively for the number of True Positives, False Positives, and False Negatives pixels.

Results and discussions

The overall results, combining the scores obtained with the 6 marker combinations on the two datasets (there are thus 6 × 150 = 900 measurements for each method), are presented in Fig. 3 using box-and-whisker plots. In these experiments, we considered a 4-adjacency relation with a Lab gradient (that is the Euclidean distance in the L*a*b* colour space) for the dissimilarity measure. We can see that the WSArea and WSVol globally achieve the best performance with very similar results. QFZ and CC are at the bottom of the ranking: while this result is not surprising for QFZ, which is the most basic method, it suggests that the global range constraint in CC, which is supposed to remove spurious regions from the hierarchy, has nearly no effect in this application. The theoretical similarity between QFZ and WSAlt [START_REF] Cousty | Constructive links between some morphological hierarchies on edge-weighted graphs[END_REF] is confirmed by the experiments which show similar results for the two methods. WSDyn provides a small improvement compared to QFZ. Surprisingly, WSVol which can been seen as a combination between WSArea and WSDyn does no seem to take advantage of the information given by the depth measure (similar to the dynamics) compared to WSArea. Finally, OS achieves slightly better results than QFZ, but it does not seem that the segmentation strategy is able to take advantage of the area regularization provided by the method as it remains far from WSArea and WSVol. The results per marker combination are presented in Fig. 5. The ranking remains the same in the symmetric cases (first row). Nevertheless, we can observe a large gap between the results obtained with low quality and medium quality markers (average increase of 0.1 on the median f-measure). In cases more similar to user interactions implying the skeleton as the foreground marker, we can see that all methods are relatively robust to the quality of the background marker. Nevertheless when the frame is used as the background marker, the combination is strongly asymmetric, and the results of WSVol and especially WSArea become less reliable (lower first quartile). This last effect is understandable as the area regularization used in WSArea tends to produce regions of homogeneous sizes which does not always reflect the content of the images. Fig. 4 shows the evolution of the segmentations with respect to the marker combination for the method WSVol on a sample image.

Concerning the influence of the adjacency relation, Fig. 6 presents the result obtained for two hierarchies QFZ and WSArea using a 4-or a 8-adjacency relation (with a Lab gradient and the 6 combinations of markers). We observe that there is nearly always a small gain when using a 8-adjacency instead of a 4-adjacency relation (see Fig. 6). Thus, due to the limited computational overhead, it seems a good idea to favour 8-adjacency over 4-adjacency relation in such segmentation applications.

The importance of the dissimilarity measure is illustrated in Fig. 7. We compare the results obtained with QFZ and WSArea with 3 different dissimilarity measures: 1) the absolute difference of the luminance (grey-scale image computed as the average of the RGB channels), 2) a city-block distance in the RGB space, and 3) an Euclidean distance in the Lab space. While the results are greatly improved by more complex dissimilarity measures for QFZ, the effect is mostly negligible for WSArea.

In Fig. 8, we measure the effect of filling the holes in detected object as a post processing of the segmentation process. As expected, the hierarchies that do not use a form of size regularization criterion are very sensitive to this postprocessing, meaning that there is a lot of small contrasted regions (noise, specular, or textures) that lies close to the root in such hierarchies: those regions are thus more probably assigned to the background. One can also note that there is an important difference of difficulty between Grabut and Weizmann datasets. In Fig. 9, which compiles the overall results (Fig. 3) per dataset (Lab gradient, and 4-adjacency relation), we can observe a significant difference in the median score and even a larger difference in the first quartile. Indeed a visual inspection of the results shows that Weizmann dataset, contrarily to Grabcut dataset, contains images of objects with either very low contrast or with very large scale textures that all the considered methods have difficulties to segment correctly.

Finally, Fig. 10 shows several examples of segmentations.

Conclusion

We performed a systematic and automatic comparison of several morphological hierarchies in the context of the supervised segmentation task. We have designed a framework in order to automatically generates markers from the ground-truth segmentations. The segmentation strategy, which extracts the object from the hierarchy and the markers, is voluntarily simple in order to keep the intelligence in the design of the hierarchy.

Our results suggest that the hierarchical watersheds based on area and volume attributes are generally the best choice among morphological hierarchies for such task. The only limiting case is when the information about the background marker is very weak: in this case, that is nearly the one marker segmentation problem with the adopted segmentation strategy, it is best suited to use a hierarchical watershed by dynamics.

It is of course difficult to say if these results can be generalized to other vision tasks. Nevertheless, we believe that our test framework is a good indicator to see if a given hierarchy is well suited to represent objects in natural scenes and how easy it is to extract such object from it. Moreover, as shown in [START_REF] Cousty | Constructive links between some morphological hierarchies on edge-weighted graphs[END_REF][START_REF] Najman | Playing with kruskal: Algorithms for morphological trees in edge-weighted graphs[END_REF], constructing a hierarchical watershed from the QFZ hierarchy is only a linear (with respect to the number of pixels) time post-processing and it may significantly improve results.

The marker datasets are available at http://perso.esiee.fr/ ~perretb/ markerdb/. We have also designed a web site http://perso.esiee.fr/ ~perretb/ ISeg/ that implements the segmentation strategy with an interactive interface and that enables to test the hierarchies on custom images. The site software is implemented in JavaScript and runs entirely in the client web browser: the code to construct the hierarchies and to perform the segmentation is available.

In future works, we plan to test if we obtain similar results in other evaluation frameworks as the one proposed by Arbelaez et al. [START_REF] Arbelaez | Contour detection and hierarchical image segmentation[END_REF] or more recently by Pont-Tuset et al. [START_REF] Pont-Tuset | Measures and meta-measures for the supervised evaluation of image segmentation[END_REF]. Another question we will have to investigate is also the comparison to non morphological hierarchies and state of the art supervised segmentation methods. Moreover, all those results show that none of the presented methods is perfect and the construction of better hierarchies is an open issue.

Fig. 1 .

 1 Fig. 1. Examples of saliency maps for each method.

Fig. 2 .

 2 Fig. 2. Different combinations of markers. The combination of markers is indicated in the caption of each sub-figure in the form Background Marker-Object Marker. In each figure the background and foreground marker are respectively depicted in red and blue.

Fig. 4 .

 4 Fig. 4. Segmentation examples using WSVol for the 6 marker combinations. In each figure the background and foreground marker are respectively depicted in red and blue while the contour of the segmentation result is in green.

Fig. 5 .

 5 Fig. 5. Results obtained with each hierarchy and each combination of markers. See description of Fig. 3.

Fig. 6 .Fig. 7 .Fig. 10 .

 6710 Fig. 6. Comparison between 4-and 8-adjacency relations. See description of Fig. 3.

  Results obtained with each hierarchy for all combinations of markers. For each method, we see: 1) the median F-measure (central bar), 2) the first and third quartile (extremities of the box), 3) the lowest datum still within 1.5 inter quartile range (difference between the third and first quartile) of the lower quartile, and the highest datum still within 1.5 inter quartile range of the upper quartile range (left and right extremities), and 4) the outliers (individual points).

	CC						.87
	OS						.88
	QFZ						.87
	WSAlt						.88
	WSArea							.92
	WSDyn						.89
	WSVol							.92
	.20	.30	.40	.50	.60	.70	.80	.90	1.00
	Fig. 3.

This work received funding from ANR (ANR-2010-BLAN-0205-03), CAPES/PVE under Grant 064965/2014-01, and CAPES/COFECUB under Grant 592/08.