Tarek Manasfi
email: tarek.manasfi@univ-amu.fr

Brice Temime-Roussel
email: brice.temime-roussel@univ-amu.fr

Bruno Coulomb
email: bruno.coulomb@univ-amu.fr

Laurent Vassalo
email: laurent.vassalo@univ-amu.fr

Jean-Luc Boudenne
email: jean-luc.boudenne@univ-amu.fr

Occurrence of brominated disinfection byproducts in the air and water of chlorinated seawater swimming pools

Keywords: Disinfection byproducts, seawater swimming pools, brominated compounds, chlorination, total organic halide

An undesirable consequence of disinfection is the formation of chemical contaminants known as disinfection byproducts (DBPs). Chronic exposure to DBPs has been linked to adverse health effects. The occurrence of DBPs in chlorinated pools filled with seawater (such as thalassotherapy pools and pools in spas) has received little attention so far. The present study evaluated the speciation and levels of disinfection byproducts in indoor swimming pools filled with seawater and treated with chlorine. Water and air samples were collected from three indoor swimming pools located in Southern France. Several classes of DBPs including trihalomethanes, haloacetic acids, haloacetonitriles, and trihaloacetaldehydes were analyzed in water. Halogenated volatile organic compounds were analyzed in air. Extractable organic halide (EOX) contents were determined using combustion micro-coulometry system. The speciation of DBPs identified in the three pools was predominantly brominated. The mean (arithmetic) concentration of bromoform, dibromoacetic acid, tribromoacetic acid, dibromoacetonitrile and bromal hydrate in the three pools were 79.2, 72.9, 59.9, 26.9 and 10.0 µg/L, respectively. By weight, HAAs represented the most abundant chemical class followed by THMs. In air, bromoform was the most abundant THM occurring at a mean concentration of 133.2 µg/m 3 in the three pools. The mean EOX level was 706 µgCl -/L for the three pools. In average, the quantified DBPs accounted for only 14% of EOX, thus 86% of EOX remained unknown. Further research is warranted to identify the unknown DBPs.

Introduction

Disinfection is a critical process in which pathogenic microorganisms are eliminated from water. During this process, undesirable byproducts known as disinfection byproducts (DBPs) are formed because of reactions between disinfectants and organic compounds present in water. Swimming pool water constitutes a medium in which complex loads of organic compounds are brought into water by swimmers [START_REF] Lakind | The good, the bad, and the volatile: Can we have both healthy pools and healthy people?[END_REF]. Discharges of saliva, sweat, hair particles, or personal care products are sources of organic compounds that react with disinfectants and ultimately lead to the formation of DBPs (Chowdhury et al., 2014b;Hansen et al., 2012;[START_REF] Kim | Formation of disinfection by-products in chlorinated swimming pool water[END_REF][START_REF] Teo | Chemical contaminants in swimming pools: Occurrence, implications and control[END_REF]. The occurrence of DBPs in swimming pools constitutes a health concern since exposure to these compounds has been linked to a range of adverse health effects [START_REF] Hrudey | Chlorination disinfection by-products, public health risk tradeoffs and me[END_REF][START_REF] Villanueva | Overview of Disinfection By-products and Associated Health Effects[END_REF]. Chronic exposure to DBPs has been associated with an increased risk of bladder cancer [START_REF] Villanueva | Disinfection byproducts and bladder cancer: a pooled analysis[END_REF]. Some epidemiological studies have suggested an increased risk of asthma among professional swimmers and child swimmers [START_REF] Font-Ribera | Short-term changes in respiratory biomarkers after swimming in a chlorinated pool[END_REF][START_REF] Weisel | Childhood Asthma and Environmental Exposures at Swimming Pools: State of the Science and Research Recommendations[END_REF]. Some studies have demonstrated that DBPs could induce adverse reproductive health outcomes [START_REF] Klinefelter | Preliminary screening for the potential of drinking water disinfection byproducts to alter male reproduction[END_REF][START_REF] Nieuwenhuijsen | Chlorination disinfection byproducts in water and their association with adverse reproductive outcomes: a review[END_REF]. Furthermore, extensive evidence exists about the genotoxicity and carcinogenicity of several DBPs [START_REF] Richardson | Occurrence, genotoxicity, and carcinogenicity of regulated and emerging disinfection by-products in drinking water: A review and roadmap for research[END_REF]. Exposure to DBPs in swimming pools may take place via dermal absorption, inhalation, and ingestion (Zwiener et al., 2007a). Inhalation and dermal exposure have been considered to be the main routes of human exposure to DBPs in swimming pools, while ingestion from accidental water swallowing has been classified as a minor route [START_REF] Xu | Dermal uptake of chloroform and haloketones during bathing[END_REF]Zwiener et al., 2007a). The occurrence of DBPs in swimming pools has been investigated in numerous studies (Chowdhury et al., 2014b). Among DBPs, trihalomethanes (THMs) and haloacetic acids (HAAs) have been studied extensively in swimming pools around the world [START_REF] Aggazzotti | Survey of volatile halogenated organics (VHO) in Italy. Levels of VHO in drinking waters, surface waters and swimming pools[END_REF][START_REF] Aggazzotti | Plasma Chloroform Concentrations in Swimmers Using Indoor Swimming Pools[END_REF][START_REF] Chu | Distribution and determinants of trihalomethane concentrations in indoor swimming pools[END_REF][START_REF] Daiber | Progressive Increase in Disinfection Byproducts and Mutagenicity from Source to Tap to Swimming Pool and Spa Water: Impact of Human Inputs[END_REF][START_REF] Dyck | Trihalomethane exposures in indoor swimming pools: A level III fugacity model[END_REF][START_REF] Judd | Disinfection by-product formation in swimming pool waters: A simple mass balance[END_REF][START_REF] Kim | Formation of disinfection by-products in chlorinated swimming pool water[END_REF][START_REF] Manasfi | Identification of disinfection by-products in freshwater and seawater swimming pools and evaluation of genotoxicity[END_REF][START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF][START_REF] Simard | Variability of chlorination by-product occurrence in water of indoor and outdoor swimming pools[END_REF]. [START_REF] Richardson | What's in the Pool? A Comprehensive Identification of Disinfection By-products and Assessment of Mutagenicity of Chlorinated and Brominated Swimming Pool Water[END_REF] identified more than 100 DBPs and measured the concentrations of chloramines and THMs in chlorinated and brominated swimming pools. Recently, [START_REF] Daiber | Progressive Increase in Disinfection Byproducts and Mutagenicity from Source to Tap to Swimming Pool and Spa Water: Impact of Human Inputs[END_REF] evaluated the occurrence of DBPs and the associated mutagenicity of water in swimming pools and spas. However, the overwhelming majority of these studies investigated the levels and speciation of DBPs in chlorinated swimming pools filled with municipal (tap) water. Very little data has been documented regarding the speciation and levels of DBPs in chlorinated pools filled with seawater. In the latter, the high salt content particularly in bromide and the slightly basic pH (~8) could affect the formation reactions of DBPs leading to DBP profiles and distributions distinct from those typically found in tap water pools (Hansen et al., 2012;[START_REF] Hua | Effect of Bromide and Iodide Ions on the Formation and Speciation of Disinfection Byproducts during Chlorination[END_REF][START_REF] Le Roux | Formation of NDMA and halogenated DBPs by chloramination of tertiary amines: The influence of bromide ion[END_REF]. Since the early 1900s, the use of seawater in swimming pools has been widely practiced in thalassotherapy centers in Europe for presumed health benefits [START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF]. Furthermore, seawater pools can now be found in water parks around the Mediterranean and on cruise ships and ferries (World Health Organization, 2006). Seawater pools are also found in hotels and spas over the world, especially those offering wellness programs [START_REF] Smith | Health and Wellness Tourism[END_REF]. In France, there are around fifty thalassotherapy centers distributed along the coasts [START_REF] Charlier | The healing Sea: a Sustainable coastal Ocean resource: thalassotherapy[END_REF]. According to some estimates, French thalassotherapy centers welcome more than one million users annually (Schwartz, 2005). For adverse health outcome considerations, the formation of DBPs in seawater is an issue of concern since the few studies conducted in seawater pool setting showed a predominance of brominated DBPs. Several studies have provided evidence regarding the far higher toxicities of brominated DBPs compared to their chlorinated analogues [START_REF] Jeong | Occurrence and Comparative Toxicity of Haloacetaldehyde Disinfection Byproducts in Drinking Water[END_REF][START_REF] Manasfi | Assessing the genotoxicity of two commonly occurring byproducts of water disinfection : Chloral hydrate and bromal hydrate[END_REF][START_REF] Plewa | Mammalian cell cytotoxicity and genotoxicity of the haloacetic acids, a major class of drinking water disinfection byproducts[END_REF]Richardson et al., 2007;[START_REF] Yang | Toxic Impact of Bromide and Iodide on Drinking Water Disinfected with Chlorine or Chloramines[END_REF]. In previous investigations, [START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF] studied the levels of two chemical classes of DBPs namely trihalomethanes (THMs) and haloacetic acids (HAAs) in chlorinated seawater pools. In a recent study, [START_REF] Manasfi | Identification of disinfection by-products in freshwater and seawater swimming pools and evaluation of genotoxicity[END_REF] reported the levels of several classes of DBPs including THMs, HAAs, haloacetonitriles (HANs), and trihaloacetaldehydes (THAs) in seawater pools in Southeastern France. However, no data has been provided so far regarding the occurrence of DBPs in the air of seawater pools and the organic halide contents of water in these pools. The present study was conducted in order to investigate the speciation and levels of DBPs in the air and water of indoor seawater pools in Southern France. The study also aimed at determining the extractable organic halide (EOX) contents of these pools and evaluating the contribution of the traditionally measured and some emerging DBP chemical classes to the EOX concentrations. Determining the occurrence of DBPs in air and water of seawater pools will help document data that is necessary for risk assessment studies.

Materials and Methods

Study Site and Sample collection

Three indoor swimming pools located in Southern France were included in the study. All the pools were filled using seawater and treated with chlorine. A detailed description of the studied pools including type of activity, pool volume, pool area, water filtration type, and average daily frequentation is presented in Table S1. In all the pools, seawater was obtained from the Mediterranean and was sand filtered before filling the pools. The sampling campaign was conducted in spring 2016. Free residual chlorine and total chlorine were determined on-site during sampling. Other physicochemical parameters including temperature, pH, and conductivity were also determined on-site using specific electrodes (WTW Multiline P4 multimeter, Weilheim, Germany). Samples were collected in triplicates for laboratory analysis. To determine total organic carbon (TOC), total nitrogen (TN), and bromide (Br -) levels, samples were collected in amber glass bottles (1 L) with PTFE-lined screw caps. In addition, samples were collected in 65-mL vials with PTFE-lined screw caps for the analysis of DBPs and EOX in water. In these samples, ascorbic acid was added as a quenching agent in the vials before sampling, and the vials were filled without any remaining headspace to avoid any loss of volatile DBPs. All samples were transported at 4 °C and treated within 48 h. For the analysis of DBPs in air, canisters (Entech) of 6-liter capacity were used to sample air in the indoor pools. Sampling was performed by filling canisters from the air above the water level (1 m) in less than one minute. A blank canister was obtained by collecting air samples from the ambient air outside swimming pool facilities.

Chemicals

Analytical standards including THM calibration mix, halogenated volatile mix (containing HANs), HAA esters calibration mix, 2,3-dibromopropionic acid solution, and chloral hydrate solution were purchased from Supelco (USA). Tribromoacetaldehyde (97%) was purchased from Aldrich (United Kingdom) and was used to generate its hydrated form bromal hydrate (BH) in ultrapure water (Millipore, resistivity >18 MΩ cm). A standard stock solution of each compound was prepared in Methyl tert-butyl ether (MTBE, purity 99.8%) which was purchased from Merck (Germany). L-ascorbic acid, crystalline, reagent grade was purchased from Sigma (China). Sulfuric acid, analytical grade reagent, was purchased from Fisher Scientific (UK).

Water sample preparation

For the analysis of EOX, THMs, HANs, THAs sample aliquots (50 mL) were first adjusted to a pH value ranging between 4.5 and 5.5 by adding sulfuric acid. Samples were then extracted by liquid-liquid extraction (LLE) by adding MTBE (5 mL) and shaking manually during 2 min. Then, the organic phase was separated. For the analysis of HAAs, U.S.EPA method 552.3 (Domino et al., 2003) was used with slight modifications. In brief, sample aliquots (40 mL) were acidified to a pH < 1 by adding concentrated sulfuric acid and were then extracted with MTBE (4 mL). 2,3-dibromopropionic acid was added to the extracts as a surrogate. Subsequently, the resulting organic phase was transferred into 15 mL vials to which acidified methanol was added and placed in a water bath at 50 °C for 2 h to transform the HAAs into their methyl ester derivatives. After cooling, 4 mL of saturated sodium bicarbonate solution were added before collecting the organic phase containing the HAA esters in chromatographic vials.

Analytical methods for water analysis

Free residual chlorine and total chlorine were measured on-site by the colorimetric DPD method using a portable spectrophotometer (AQUALYTIC-AL 800, Germany). Bromide levels in water were measured using an ICS-3000 Dionex ion chromatography system, 30 mM NaOH eluent with a flow rate of 1.5 ml/min at 30 °C. A Dionex IonPac AS11-HC (4 × 250 mm) analytical column and a Dionex Ionpac AG11-HC (4 × 50 mm) guard column were used (Thermo Scientific, USA). Total Organic Carbon (TOC) and Total Nitrogen (TN) were measured using high temperature catalytic oxidation technique (Multi N/C 2100, Analytik Jena, Germany). The pretreated sample was injected (50 µl) into the furnace filled with a Pt preconditioned catalyst.

The combustion was realized at 800 °C and the combustion products were carried by high purity oxygen (Linde Gas) allowing detection of CO 2 by non-dispersive infrared (NDIR) and detection of NO by chemiluminescence (CLD). Organic extracts containing DBPs were analyzed using a gas chromatograph coupled to a 63 Ni electron-capture detector (GC-ECD model Clarus 580, Perkin Elmer, Norwalk, CT, USA). An Elite 5MS capillary column was used for the separation. Helium 5.0 was used as a carrier gas at 1 mL/min. Nitrogen was used as a make-up gas at 30 mL/min. For the analysis of THMs, HPs, HANs and HKs, the temperature program was as follows: initially 35 °C increasing to 145 °C at a rate of 10°C/min, then at a rate of 20 °C/min up to 225 °C and finally at 10 °C/min to 260 °C, held for 2 min. For the analysis of HAAs, the temperature was initially set to 40 °C, then increased to 75 °C at a rate of 15 °C/min, then increased to 100 °C at 5 °C/min, and finally temperature reached 135 °C at 10 °C/min and held for 2 min. External calibration was performed using a set of 7 standard solutions. The solutions were prepared by adding aliquots of the standard stock solution in reconstituted seawater and later conducting the same treatment as pool water samples. Reconstituted seawater was prepared according to ASTM International standard practice for the preparation of substitute ocean water (method D1141-98, 2013). Analysis of organic halides was performed using a combustion/microcoulometer system. Coulometric titration with silver ions was performed using organic halide analyzer (TOX-300, Mitsubishi, A1-Envirosciences, France). The analyzer was coupled to an automatic boat controller (ABC-210, Mitsubishi, A1-Envirosciences, France). An aliquot of 50 µL of the MTBE extracts obtained using LLE was injected using an autosampler (ASC-250L, Mitsubishi, A1-Envirosciences, France) equipped with a syringe of 100-µL capacity. Samples were introduced into the combustion tube under a flow of O 2 and Ar adjusted at 200 mL/min. The combustion of the extracted organohalides was followed by pyrolysis at 900 °C resulting in the formation of hydrogen halides (HX) which were then determined with micro-coulometric titration. Calibration was performed by spiking reconstituted seawater with bromoform. Precision and recovery were determined by injecting 50 µL of MTBE extracts obtained from seawater spiked with bromoform at 376 µgCl -/L. Average percent recovery was 91.5% and relative standard deviation was 4.4% based on 4 replicates of the 376 µgCl -/L solution. Data processing was performed using the software TOX-300 (version 1.0.0, A1-Envirosciences, France). For quality control, reconstituted seawater was extracted and used as a blank to demonstrate absence of contamination from the high chloride concentrations typically present in seawater. Seawater and water reagent blanks were included with each sequence. Analysis of samples was conducted in triplicate. Limits of detection (DL) and the limits of quantification (QL) for the analyzed chemicals and parameters are presented in Table S2.

Analytical methods for air analysis

Analysis of air samples collected in canisters was carried out with a proton-transfer-reaction time-of-flight mass spectrometry (PTR-ToF-MS 8000, Ionicon Analytik GmbH, Innsbruck, Austria) equipped with a switchable reagent ion module. O 2 + mode was used to investigate the presence of halogenated volatile organic compounds (VOCs). O 2 + can be used as reagent ion to increase the detection ability of the PTR-ToF-MS, since VOCs with proton affinities lower than water can then be ionisable. Mass spectra up to an m/z ratio of 500 were recorded, with a resolution m/Δm of 3500. Parameters of the PTR-ToF-MS during the experiments were as follows: T drift = 50 °C, P drift = 2.04 mbar, E/N = 95 Td, U drift = 400 V. U drift is the electric potential applied to the drift tube; T drift and P drift are the temperature and the pressure in the drift tube, respectively. E is the strength of the electrical field in V/cm and N is the gas number density in cm 3 . The ratio E/N in Townsend (1 Townsend = 10 -27 cm 2 /V) is a defining characteristic of the drift tube. Data from PTR-ToF-MS were analyzed with the software Tofware (version 2.5.7, Tofwerk). The air concentrations were calculated using the following equation:

[VOC + ] = [O 2 + ] 0 .[VOC].k.t
Where [O 2 + ] 0 and [VOC+] are the transmission corrected densities of the primary ion O 2 + and of the VOC + ions respectively, expressed in counts per second (cps). k is the reaction rate constant between the VOC and O 2 + (cm 3 /s) and t is the residence time of the ions in the drift tube (t = 100 µs). Concentrations were calculated based on O 2 + reaction collisional rate of 2.10 -9 cm 3 /s.

Results and Discussion

Physicochemical parameters

Physicochemical parameters including air temperature, water temperature, pH, conductivity, TOC, TN, bromide content, levels of free residual chlorine, and total chlorine were determined. Table 1 presents the values of the physicochemical parameters measured in the studied pools.

The measured pH values ranged between 8.3 and 8.5. These pH values do not conform to the French recommendations for swimming pools, according to which pH should be maintained between 6.9 and 7.7 for pools treated with chlorine. This recommendation has been established to avoid decrease in the disinfecting ability, which takes place at higher pH due to the formation of the less potent hypochlorite ions (OCl -) (ANSES, 2010). The latter recommendation targets swimming pools without considering the type of pool filling water and a recommendation regarding pH that is specific to seawater pools or pools disinfected with bromine does not exist so far. However, in chlorinated seawater pools bromine is the disinfectant that is formed from the reaction of chlorine with bromide present in seawater. Thus, equilibrium between HOBr/BrO - (pKa = 8.63) should be considered instead of equilibrium between HOCl/ClO -(pKa = 7.54). In this way, the pH between 8.3 -8.5 should not compromise disinfection. Pool temperatures ranged from 30.9 to 33.1 °C and 21.5 to 24.2 °C in water and air, respectively. Bromide levels were relatively high ranging from 75.0 to 88.5 mg/L. Typically, seawater contains around 65 mg/L bromide [START_REF] Magazinovic | Bromide levels in natural waters: its relationship to levels of both chloride and total dissolved solids and the implications for water treatment[END_REF]. Conductivity of water ranged from 65.6 to 73.2 mS/cm. This high conductivity is in agreement with the high salt content expected in seawater. However, the higher conductivity and bromide concentrations measured in the pools compared to those typically measured in seawater could be due to evaporation especially that waters of these pools were heated. TOC levels ranged between 2.7 and 3.9 mg/L. Previously, heterogeneous TOC levels varying from as low as 1.5 mg/L to as high as 39.3 mg/L have been reported in swimming pools [START_REF] Chu | Distribution and determinants of trihalomethane concentrations in indoor swimming pools[END_REF][START_REF] Hang | Occurrence and health risk assessment of halogenated disinfection byproducts in indoor swimming pool water[END_REF]. In seawater pools, [START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF] reported levels ranging between 2.8 and 8.6 mg/L. More recently, TOC levels reaching 11.88 mg/L were detected in seawater swimming pools in Southeastern France during summer period [START_REF] Manasfi | Identification of disinfection by-products in freshwater and seawater swimming pools and evaluation of genotoxicity[END_REF]. This variability in TOC levels is related to characteristics of the filling water as well as to swimmers behavior and activities since the latter are main contributors to TOC observed in pools [START_REF] Simard | Variability of chlorination by-product occurrence in water of indoor and outdoor swimming pools[END_REF]. The lower levels of TOC measured in this study compared to other studies could be related to lower frequentation rates in the investigated pools. In addition, the type of activity of pools was mainly soft which could reduce the discharge of sweat in comparison to other pools where swimmers' activities could be more vigorous. TN levels ranged between 1.4 and 2.3 mg/L. Human body fluid discharges in swimming pools are believed to be a major source of nitrogen in swimming pools (Chowdhury et al., 2014b). [START_REF] Keuten | Definition and quantification of initial anthropogenic pollutant release in swimming pools[END_REF] studied the release of anthropogenic pollutants in swimming pools and estimated that TN released per person is 46 mg within the first minute of showering. During a 30-min exercise, it was estimated that TN release reaches 77.3 mg/bather [START_REF] Keuten | Quantification of continual anthropogenic pollutants released in swimming pools[END_REF]. Free residual chlorine levels ranged between 1.0 and 1.6 mg/L. The latter level is slightly higher than the maximal level recommended in France for free residual chlorine (between 0.4 and 1.4 mg/L) (ANSES, 2010).

Occurrence of DBPs

Table 2 provides an overview of the concentrations of DBPs measured in water and air of the studied pools. tribromoacetic acid; HAA-9: sum of the nine haloacetic acid concentrations; N.D: Not Determined, for compounds which were not detected or at detected at levels below quantification limits

DBPs in pool water

In all the pools, the speciation of the occurring DBPs was predominantly brominated (Table 2). This speciation is linked to the relatively high levels of bromide present in the filling seawater, since bromide ions react with the added chlorine resulting in the formation of bromine [START_REF] Deborde | Reactions of chlorine with inorganic and organic compounds during water treatment-Kinetics and mechanisms: A critical review[END_REF]. Consequently bromine reacts with organic compounds leading to the formation of brominated DBPs [START_REF] Heeb | Oxidative treatment of bromide-containing waters: Formation of bromine and its reactions with inorganic and organic compounds -A critical review[END_REF][START_REF] Hua | Effect of Bromide and Iodide Ions on the Formation and Speciation of Disinfection Byproducts during Chlorination[END_REF]. Bromine is even more potent than chlorine in halogenating organic compounds [START_REF] Gallard | Rate constants of reactions of bromine with phenols in aqueous solution[END_REF]. Brominated DBPs detected in the pools included HAAs, THMs, HANs and THAs. Figure 1 shows the distribution of THMs in water. Among THMs, bromoform was the most abundant compound with concentrations that ranged from 49.7 to 101.3 µg/L. Dibromochloromethane was also detected at lower levels (ranged from 2.1 to 5.5 µg/L). In average, TTHM level in the three pools was 83.2 ± 28.1 µg/L. Data reported in the literature about levels of TTHMs in seawater pools is limited. [START_REF] Beech | Nitrates, chlorates and trihalomethanes in swimming pool water[END_REF] reported high levels of TTHM (657 ± 354 µg/L) in seawater pools in USA.

Recently, [START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF] reported an important variability in TTHM levels in seawater pools in France with levels ranging from as low as 32.2 µg/L to as high as 995.6 µg/L. In a previous report, [START_REF] Manasfi | Identification of disinfection by-products in freshwater and seawater swimming pools and evaluation of genotoxicity[END_REF] reported levels ranging from 50.4 to 91.8 µg/L in seawater pools during summer period. Unlike in seawater pools, the occurrence of THMs in swimming pools filled with tap water has been well documented [START_REF] Chu | Distribution and determinants of trihalomethane concentrations in indoor swimming pools[END_REF][START_REF] Fantuzzi | Occupational exposure to trihalomethanes in indoor swimming pools[END_REF][START_REF] Guilherme | Occurrence of regulated and non-regulated disinfection by-products in small drinking water systems[END_REF][START_REF] Lourencetti | Trihalomethanes in chlorine and bromine disinfected swimming pools: Air-water distributions and human exposure[END_REF][START_REF] Richardson | What's in the Pool? A Comprehensive Identification of Disinfection By-products and Assessment of Mutagenicity of Chlorinated and Brominated Swimming Pool Water[END_REF][START_REF] Righi | Bromate, chlorite, chlorate, haloacetic acids, and trihalomethanes occurrence in indoor swimming pool waters in Italy[END_REF][START_REF] Simard | Variability of chlorination by-product occurrence in water of indoor and outdoor swimming pools[END_REF]Zwiener et al., 2007b). In these pools, chloroform has been determined as the predominant THM. [START_REF] Chu | Distribution and determinants of trihalomethane concentrations in indoor swimming pools[END_REF] reported average concentration of 125.2 µg/L in 8 indoor swimming pools in England. [START_REF] Richardson | What's in the Pool? A Comprehensive Identification of Disinfection By-products and Assessment of Mutagenicity of Chlorinated and Brominated Swimming Pool Water[END_REF] reported a TTHM average levels of 49.6 µg/L and 60.2 µg/L in chlorinated and brominated tap water pools in Spain, respectively. [START_REF] Simard | Variability of chlorination by-product occurrence in water of indoor and outdoor swimming pools[END_REF] reported an average TTHM level of 64 µg/L in indoor swimming pools in Canada. Figure 2 shows the distribution of HAAs in water. Among HAAs, dibromoacetic acid (DBAA) was the most abundant compound followed by tribromoacetic acid (TBAA). These two compounds alone represented about 88% of the total HAA (HAA-9) content by weight. Chlorodibromoacetic (CDBAA), bromochloroacetic acid (BCAA), and bromodichloroacetic acid (BDCAA) were also detected at levels far lower than those of DBAA and TBAA. In total, HAA-9 ranged between 68.0 and 214.6 µg/L with an average concentration of 150.9 ± 75.2 µg/L. These levels tend to be situated in the lower range of HAA-9 levels that have been reported in swimming pools previously. [START_REF] Parinet | Exposure levels to brominated compounds in seawater swimming pools treated with chlorine[END_REF] reported HAA-9 levels ranging between 84.01 and 2232.89 µg/L in seawater pools. [START_REF] Simard | Variability of chlorination by-product occurrence in water of indoor and outdoor swimming pools[END_REF] reported an average level of 412.9 µg/L in indoor tap water pools. [START_REF] Tardif | Assessment of air and water contamination by disinfection by-products at 41 indoor swimming pools[END_REF] reported levels ranging from 109.2 to 886.2 µg/L in indoor tap water pools. In tap water pools, dichloroacetic acid (DCAA) and trichloroacetic acid (TCAA acid), the chlorinated analogues of DBAA and TBAA respectively, represent the most abundant HAAs [START_REF] Lee | Production of various disinfection byproducts in indoor swimming pool waters treated with different disinfection methods[END_REF][START_REF] Tardif | Assessment of air and water contamination by disinfection by-products at 41 indoor swimming pools[END_REF].

In the present study, HAAs represented the most abundant chemical class (by weight) among the determined DBPs. The occurrence of HAAs at highest concentrations by weight has been observed for HAAs in tap water swimming pools also (Chowdhury et al., 2014b). This abundance of HAAs in chlorinated swimming pool water is distinct than that typically identified in drinking water. In the latter, THMs are the most abundant class of DBPs rather than HAAs. In swimming pools, the high abundance of HAAs is favored by anthropogenic organic inputs brought into water by swimmers [START_REF] Kanan | Formation of disinfection by-products in indoor swimming pool water: The contribution from filling water natural organic matter and swimmer body fluids[END_REF]. In addition, HAAs exist in the ionic form at pH relevant to swimming pools and thus tend to accumulate in water without suffering from outgassing due to high volatility as in the case of THMs (Chowdhury et al., 2014a). Among HANs, dibromoacetonitrile (DBAN) was detected in the three pools at levels that ranged from 18.3 to 34.5 µg/L and an average concentration of 26.9 ± 8.2 µg/L. Interestingly, the highest concentration of HANs occurred in pool J where TN was the highest (2.3 mg/L). The contribution of N-containing compounds to the formation of HANs has been previously demonstrated [START_REF] Shah | Halonitroalkanes, halonitriles, haloamides, and N-nitrosamines: A critical review of nitrogenous disinfection byproduct formation pathways[END_REF]. [START_REF] Kim | Formation of disinfection by-products in chlorinated swimming pool water[END_REF] observed that the presence of compounds such as urea and proteins of human origin promote the formation of HANs in chlorinated pool water. The N-containing amine precursors are present extensively in body fluids released by swimmers [START_REF] Teo | Chemical contaminants in swimming pools: Occurrence, implications and control[END_REF]. Furthermore, the formation of HANs from precursors such as body fluid analogs was shown to increase in the presence of bromide ions [START_REF] Hansen | Effect of selection of pH in swimming pools on formation of chlorination byproducts[END_REF], Chowdhury et al., 2014b). Occurrence of HANs in seawater pools has been very scarcely documented. Levels comparable to those detected in this study were reported by [START_REF] Manasfi | Identification of disinfection by-products in freshwater and seawater swimming pools and evaluation of genotoxicity[END_REF] in seawater pools where DBAN levels ranged between 14.0 and 28.6 µg/L. Recently, [START_REF] Daiber | Progressive Increase in Disinfection Byproducts and Mutagenicity from Source to Tap to Swimming Pool and Spa Water: Impact of Human Inputs[END_REF] reported levels of DBAN ranging between 35.3 and 1102 µg/L in brominated pools and spas. HANs occurrence in tap water swimming pools has been investigated by fewer studies compared to the occurrence of THMs and HAAs (Chowdhury et al., 2014b). [START_REF] Lee | Production of various disinfection byproducts in indoor swimming pool waters treated with different disinfection methods[END_REF] reported dichloroacetonitrile (DCAN) as the predominant HAN in tap water pools with an average level of 3.9 µg/L. [START_REF] Hang | Occurrence and health risk assessment of halogenated disinfection byproducts in indoor swimming pool water[END_REF] reported levels of DCAN varying from less than 0.5 up to 205.5 µg/L in chlorinated tap water swimming pools. Among THAs, bromal hydrate (BH), which is the hydrated form of tribromoacetaldehyde, was detected in the three pools at levels that ranged from 8.5 to 12.4 µg/L with a mean concentration of 10.0 ± 2.1 µg/L. The occurrence of BH in seawater pools has been very poorly documented. However, recent evidence about its mutagenic and genotoxic potential warrants further investigations concerning the occurrence of this compound in swimming pools [START_REF] Manasfi | Assessing the genotoxicity of two commonly occurring byproducts of water disinfection : Chloral hydrate and bromal hydrate[END_REF]. In tap water pools, chloral hydrate, the chlorinated analogue of BH, has been frequently detected. [START_REF] Lee | Production of various disinfection byproducts in indoor swimming pool waters treated with different disinfection methods[END_REF] reported an average level of 10.2 µg/L in swimming pools in Korea. [START_REF] Daiber | Progressive Increase in Disinfection Byproducts and Mutagenicity from Source to Tap to Swimming Pool and Spa Water: Impact of Human Inputs[END_REF] reported levels as high as 556 µg/L in chlorinated public pools in USA.

DBPs in pool air

Bromoform and dibromochloromethane were detected and quantified in the ambient air of the three pools. The main halogenated species detected were assigned their formulae based on the measured exact mass and the isotopic peak patterns: CHBr 2 + (m/z 170.844), and CHClBr + (m/z 126.894). Reactions between halogenated VOCs and O 2 + as reagent ion have been reported to proceed via a dissociative charge transfer reaction, generally resulting in the loss of a halogenated atom [START_REF] Spanel | Selected ion flow tube studies of the reactions of H3O+, NO+, and O2+ with several aromatic and aliphatic hydrocarbons[END_REF]. In the case of THM containing both bromine and chlorine atoms, the loss of a bromine atom is favoured [START_REF] Mayhew | A selected ion flow tube investigation of the positive ion chemistry of a number of bromine containing fully and partially halogenated hydrocarbons[END_REF]. Accordingly, CHBr 2 + and CHBrCl + represented the ions obtained from bromoform (CHBr 3 ) and dibromochloromethane (CHBr 2 Cl) after bromine loss, respectively. Other halogenated species namely BrO + (m/z 94.913) and BrCO + (m/z 106.913) were also detected but their origin has not been elucidated yet.

As shown in Table 2, bromoform was the predominant DBP in air in the three pools at concentrations ranging from 21.7 to 240.1 µg/L and a mean concentration of 133.2 ± 109.3 µg/m 3 . Dibromochloromethane was detected at levels ranging between 3.6 and 20.7 µg/m 3 with a mean concentration of 12.4 ± 8.6 µg/m 3 . In total, TTHM level in air ranged between 25.3 and 260.8 µg/m 3 with a mean concentration of 145.6 ± 117.8 µg/m 3 .

Figure 3 shows the distribution of TTHM levels in the air and water of the pools. While water in pool H had two-fold higher TTHM concentration than in pool F (105.8 and 51.8 µg/L, respectively), air in pool H contained lower TTHM concentration than in pool F (150.7 and 260.8 µg/m 3 , respectively). Furthermore, while pools H and J had comparable TTHM concentrations in water (105.8 and 92.0 µg/L, respectively), they had considerably different TTHM concentrations in air (150.7 and 25.3 µg/m 3 , respectively). Previously, THM concentrations in pool water and air have not been strongly correlated [START_REF] Aggazzotti | Survey of volatile halogenated organics (VHO) in Italy. Levels of VHO in drinking waters, surface waters and swimming pools[END_REF]. Several factors could affect the outgassing of volatile compounds into the air including water temperature, air temperature, concentration in water, intensity of air circulation (ventilation), and the turbulence in water caused by vigorous activity of pool users (Chowdhury et al., 2014b). In this study, the high TTHM level in the air in pool F seems related to poor ventilation in this facility (partially defective ventilation system as described by the pool operator). To our knowledge, this is the first paper reporting the levels of THMs in the ambient air of chlorinated indoor seawater pools. The air concentrations of bromoform reported here are comparable to levels reported for chloroform in the air of tap water pools. Chloroform concentrations ranging from 36 to 241 µg/m 3 has been reported in the ambient air of indoor swimming pools in Germany [START_REF] Lahl | Distribution and balance of volatile halogenated hydrocarbons in the water and air of covered swimming pools using chlorine for water disinfection[END_REF]. [START_REF] Aggazzotti | Survey of volatile halogenated organics (VHO) in Italy. Levels of VHO in drinking waters, surface waters and swimming pools[END_REF] reported chloroform levels ranging from 48.0 to 459.5 µg/m 3 in indoor swimming pools in Italy. More recently, [START_REF] Richardson | What's in the Pool? A Comprehensive Identification of Disinfection By-products and Assessment of Mutagenicity of Chlorinated and Brominated Swimming Pool Water[END_REF] reported mean TTHM levels of 72.1 and 89.5 µg/m 3 in the air of chlorinated and brominated pools in Spain, respectively.

Extractable Organic Halides (EOX) contents

Table 3 shows the measured EOX contents in waters. EOX ranged between 510 and 920 µgCl -/L with a mean level of 706 ± 205 µgCl -/L. The highest EOX was detected in pool J that also had the highest DBP content (by weight). The contribution of DBPs quantified in water to the total EOX ranged between 11 and 17% approximately. As a result, unknown halogenated species represented between 89 and 83% of the EOX contents of the pool waters. Figure 4 presents the mean contribution of the identified chemical classes of DBPs to the mean EOX in the three pools. HAAs represented the highest EOX fraction among the identified DBPs (7.2%) followed by THMs (5.3% of TOX). HANs (DBAN) and THAs (BH) represented 1.3% and 0.5% of EOX, respectively. Consequently, an average 85.7% of EOX is still unaccounted for by the quantified DBPs in the indoor seawater pools. In drinking water, it has been estimated that around 70% of the EOX is still unknown [START_REF] Richardson | Drinking Water Disinfection By-products[END_REF]. A higher unknown fraction of EOX in swimming pools is not surprising knowing that complex cocktails of organic precursors are introduced into pool waters [START_REF] Lakind | The good, the bad, and the volatile: Can we have both healthy pools and healthy people?[END_REF]. The introduced organic loads react with disinfectants generating complex profiles of halogenated byproducts beyond those which are classically quantified [START_REF] Daiber | Progressive Increase in Disinfection Byproducts and Mutagenicity from Source to Tap to Swimming Pool and Spa Water: Impact of Human Inputs[END_REF][START_REF] Richardson | What's in the Pool? A Comprehensive Identification of Disinfection By-products and Assessment of Mutagenicity of Chlorinated and Brominated Swimming Pool Water[END_REF]. Precursors such as personal care products worn by swimmers can also react with disinfectants leading to the production of halogenated transformation products [START_REF] Teo | Chemical contaminants in swimming pools: Occurrence, implications and control[END_REF]. Previous reports have shed the light on the implication of emerging precursors such as UV filters in the generation of DBPs in swimming pools [START_REF] Manasfi | Degradation Products of Benzophenone-3 in Chlorinated Seawater Swimming Pools[END_REF][START_REF] Santos | The degradation products of UV filters in aqueous and chlorinated aqueous solutions[END_REF]Zwiener et al., 2007a). Recently, halobenzoquinones were detected in swimming pool waters resulting from chlorination reactions of some personal care products [START_REF] Wang | Halobenzoquinones in swimming pool waters and their formation from personal care products[END_REF].

Conclusions

This study shows that in chlorinated seawater pools the speciation of DBPs in the water and air is predominantly brominated. Bromoform, DBAA and TBAA, DBAN, and BH were the main THMs, HAAs, HANs and THAs detected in the three indoor pool waters, respectively. In the air, brominated THMs were detected with bromoform being the most abundant species. The occurrence of brominated DBPs at relatively high levels is of health concern since several investigations have demonstrated higher toxicities for brominated species [START_REF] Jeong | Occurrence and Comparative Toxicity of Haloacetaldehyde Disinfection Byproducts in Drinking Water[END_REF][START_REF] Manasfi | Assessing the genotoxicity of two commonly occurring byproducts of water disinfection : Chloral hydrate and bromal hydrate[END_REF][START_REF] Richardson | Occurrence, genotoxicity, and carcinogenicity of regulated and emerging disinfection by-products in drinking water: A review and roadmap for research[END_REF][START_REF] Yang | Toxic Impact of Bromide and Iodide on Drinking Water Disinfected with Chlorine or Chloramines[END_REF]. The quantified DBPs represented only a small fraction (an average of 14%) of EOX content measured in the pools. Therefore, most of EOX (86% fraction) was not accounted for by the quantified DBPs and remains unknown. These findings emphasize the need for further research to identify the halogenated DBPs with unknown nature and toxicity and for which users could be exposed to while swimming or in the context of an occupational exposure.

Figure 2 .

 2 Figure 2. Distribution of the detected HAAs in the water of the studied pools.Error bars represent replicate standard deviation.

Figure 3 .

 3 Figure 3. Distibution of total trihalomethanes (TTHM) in the air and water of the studied pools. Error bars represent replicate standard deviation

Figure 4 .

 4 Figure 4. Mean contribution of the identified DBP chemical classes to the measured extractable organic halides (EOX)

Table S1 .

 S1 Characteristics of the studied indoor chlorinated seawater pools

	Pool	Surface	Depth	Volume	Type of	Type of	Age	Mean Daily
		(m 2 )	(m)	(m 3 )	filtration	use	Category	Frequentation
	F	143	1.5	215	Sand	Swimming/	Adult	40
						relaxing
	H	91	0.8-2.2	160	Sand	Swimming/	Adult	65
						relaxing
	J	24	1.3	32	Sand	Swimming/	Adult	45
						sport
						activity*
	*e.g. aerobic exercises in water

Table 1 .

 1 Physicochemical parameters of the studied pools

	Pool Air	Water	pH Conductivity	[Br-]	Free	Total	TOC	TN
		Temperature	Temperature	at 25°C	(mg/L)	Chlorine	chlorine	(mg/L)	(mg/L)
		(°C)	(°C)	(mS/cm)		(mg/L)	(mg/L)
	F	22.7	32.2	8.5 75.0	88.5	1.6	1.75	2.7	1.4
	H	21.5	30.9	8.4 65.6	75.0	1.3	1.50	3.1	1.8
	J	24.2	33.1	8.3 73.2	78.3	1.0	1.10	3.9	2.3

Table 2 .

 2 Concentrations of the identified DBPs in the water (in µg/L) and air (in µg/m 3 ) of the three indoor seawater pools

	Chemical	Pool F Pool H Pool J Mean SD
	In Water (µg/L)
	Chloroform	N.D	N.D	N.D	-	-
	Bromodichloromethane	N.D	N.D	N.D	-
	Dibromochloromethane	2.1	4.5	5.5	4.0	1.7
	Bromoform	49.7	101.3	86.5	79.2	26.6
	TTHM	51.8	105.8	92.0	83.2	28.1
	MCAA	N.D	N.D	N.D	-	-
	MBAA	N.D	N.D	N.D	-	-
	DCAA	N.D	N.D	N.D	-	-
	TCAA	N.D	N.D	N.D	-	-
	BCAA	3.4	6.2	8.7	6.1	2.7
	DBAA	30.5	84.4	103.7	72.9	37.9
	BDCAA	1.1	1.6	3.3	2.0	1.2
	CDBAA	4.5	10.1	15.5	10.0	5.5
	TBAA	28.5	67.8	83.4	59.9	28.3
	HAA-9	68.0	170.1	214.6	150.9	75.2
	CH	N.D	N.D	N.D	-	-
	BH	8.5	9.2	12.4	10.0	2.1
	DCAN	N.D	N.D	N.D	-	-
	BCAN	N.D	N.D	N.D	-	-
	DBAN	18.3	28	34.5	26.9	8.2
	In air (µg/m 3 )
	Chloroform	N.D	N.D	N.D	-	-
	Bromodichloromethane	N.D	N.D	N.D	-	-
	Bromoform	240.1	137.7	21.7	133.2	109.3
	Dibromochloromethane	20.7	13.0	3.6	12.4	8.6

TTHM: sum of four trihalomethane concentrations (or THM-4); MCA: monochloroacetic acid; MBAA monobromoacetic acid; DCAA: dichloroacetic acid; TCAA: trichloroacetic acid; BCAA: bromochloroacetic acid; DBAA: dibromoacetic acid; BDCAA: bromodichloroacetic acid; CDBAA: chlorodibromoacetic acid; TBAA:

Table 3 .

 3 Extractable organic halides (EOX) levels and the percentage contribution of the identified chemical classes of DBPs to the measured EOX in pool waters

	Pool F Pool H Pool J	Mean	SD


Cédric Demonceaux
email: cedric.demonceaux@u-bourgogne.fr

Pascal Vasseur

Yohan Fougerolle

Central Catadioptric Image Processing with Geodesic Metric

Keywords: Catadioptric image, image processing, spherical image

come

Central catadioptric image processing with geodesic metric

Introduction

More and more applications benefit from the use of large or panoramic field of view cameras [START_REF] Benosman | Panoramic vision: sensors, theory, and applications[END_REF]. Indeed, a 360 • view of the camera environment is a very rich source of informations in order to perform tasks such as obstacle avoidance, occupancy map estimation, or beacon tracking even for six degrees of freedom systems... Many different solutions have been proposed in order to obtain panoramic images such as rotating camera, camera network, or the association of a mirror and a classical camera (fig 1). The latter option is often chosen because it provides an omnidirectional image in a single shot and can then be used in dynamic environment. Consequently, this kind of sensor is now ubiquitously used in mobile robotic for tasks such as navigation, surveillance, visual simultaneous localization and mapping (SLAM) [START_REF] Lemaire | Slam with panoramic vision[END_REF], [START_REF] Andreasson | Topological localization for mobile robots using omnidirectional vision and local features[END_REF].

However, because of the distortions observed in such catadioptric images (fig 1), traditional image processing techniques are no longer appropriate and require to be adapted to the new sensor geometry. As shown in figure (fig 2), the influence of a pixel on its neighbours strongly depends on its position in the image. Thus, while the distance between P 1 and P 2 and between P 3 and P 4 is equal, it appears that pixel P 2 does not have the same impact on P 1 as P 4 on P 3 because of the distortions induced by the mirror. In this way, classical operators can not be directly applied to this type of images.

In order to take into account the distortions implied by the sensor during the omnidirectional image processing, the intrinsic parameters have to be considered and used for defining a new representation space. In [START_REF] Bogdanova | Scale-space analysis and active contours for omnidirectional images[END_REF], Bogdanova et al. propose to Demonceaux 1 ), Pascal.Vasseur@univ-rouen.fr (Pascal Vasseur 2 ), yohan.fougerolle@u-bourgogne.fr (Yohan Fougerolle 1 ). perform the image processing directly in the image space by taking into account the deformation due to the mirror thanks to the Jacobian induced by the mirror geometry. While this approach corrects the image distortions during the gradient estimation, it can not be extended to image filtering. Indeed, in this case, the metric change equations allow to consider the new geometry of the space and consequently to obtain the associated differential operator formula by the Jacobian. However, this space change can not be applied to filtering operators which are defined by a convolution product. The unitary sphere represents an other space which is particularly useful for omnidirectional image processing. As demonstrated in [START_REF] Barreto | A unifying geometric representation for central projection systems[END_REF] and [START_REF] Geyer | Catadioptric projective geometry[END_REF], there exists an equivalence between the unitary sphere and single view point (SVP), also called central images and even some fisheye images [START_REF] Ying | Can we consider central catadioptric cameras and fisheye cameras within a unified imaging model[END_REF]. However, this equivalence is related to the knowledge of the intrinsic parameters of the sensor (fig 3) and can be decomposed into a double projection as follows: 3D point P w is projected on the sphere surface according to the sphere center in P s which is then projected on the image plane into P i from the projection center O p located between the center and the north pole of the sphere. The position of O p depends on the type of sensor. This spherical space, which appears to be more natural for central images than Euclidean space, has been considered either for the processing directly, as detailed in the next section or as an intermediate space for a new representation. For example, in [START_REF] Jacquey | Fuzzy edge detection for omnidirectional images[END_REF], the authors proposed to project the central image onto a virtual cylinder in order to avoid the spherical geometry constrains. By considering that this cylinder is locally planar, they apply directly conventional filtering operators. Nevertheless, even if this representation can be considered as a valid approximation, the geometry on the cylinder is not appropriate to spherical images. Indeed, this cylindrical modeling defines operators that are anisotropic on the spherical image and then leads to different operations according to the pixel position in the catadioptric image. In [START_REF] Demonceaux | Markov random fields for catadioptric image processing[END_REF], Demonceaux and Vasseur developed a neighborhood based on the spherical dependency of each image pixel. They proposed to use this approach in order to adapt Markovian methods to omnidirectional images. This representation shows a significant improvement of the Markovian methods but can not be generalized to image filtering since the number of neighbors of one pixel depends on its position in the image. The approach proposed in this paper is based on a direct processing on the sphere. We propose in the next section a presentation of the existing related works in order to bring out the differences and the contributions of our approach.

Spherical Image Processing: an overview

In order to process central omnidirectional images, some authors ( [START_REF] Makadia | Correspondence-free structure from motion[END_REF], [START_REF] Bigot | Spherical edge detector: Application to omnidirectional imaging[END_REF], [START_REF] Daniilidis | Image processing in catadioptric planes: Spatiotemporal derivatives and optical flow computation[END_REF], [START_REF] Bogdanova | Scale-space analysis and active contours for omnidirectional images[END_REF]) propose to consider them as spherical images and develop specifically dedicated tools for such images. They used the spherical harmonic analysis in order to define the convolution and the Fourier analysis. We develop such different methods to provide clear comparison with our approach. Precisely, we describe the different steps required to evaluate the spherical gradient and to filter such image.

Spherical Gradient

The unit sphere S 2 can be parameterized by spherical coordinates:

∀x ∈ S 2 , x = (cos(φ) sin(θ), sin(φ) sin(θ), cos(θ)), (1)
where

φ ∈ [0, 2π[, θ ∈ [0, π].
With this parameterization, the spherical gradient is defined by:

∇ S 2 I(θ, φ) = ∂I ∂θ e θ (θ, φ) + 1 sin(θ) ∂I ∂φ e φ (θ, φ). (2)
Thus, if we adopt a regular sampling of the sphere based on θ i and φ j , the spherical gradient can be computed thanks to finite differences [START_REF] Bigot | Spherical edge detector: Application to omnidirectional imaging[END_REF] as:

∇ S 2 I(θ j , φ k ) 2 = |I(θ j+1 , φ k ) -I(θ j , φ k )| 2 + 1 sin 2 (θ j ) |I(θ j , φ k+1 ) -I(θ j , φ k )| 2 .
(

) 3
We can note that the formulation of the spherical gradient depends of the latitude θ because the distance between the points (θ j , φ k ) is not regular (fig. 4). This problem more clearly appears when we want to compute a discrete Laplace operator:

S 2 = 1 sin θ ∂ ∂θ (sin θ ∂ ∂θ ) + 1 sin 2 θ ∂ 2 ∂ 2 φ . (4)
In order to avoid the computation of differential operators on the sphere, Bogdanova et al. [START_REF] Bogdanova | Scale-space analysis and active contours for omnidirectional images[END_REF] proposed to consider the equivalent projection between the catadioptric image plane and the spherical image proposed by [START_REF] Geyer | Catadioptric projective geometry[END_REF]. For example, for a paracatadioptric image which is equivalent to a spherical image by stereographic projection, the metric induced on the sphere is equivalent to:

dl S 2 = dθ 2 + sin 2 θdφ 2 = 4 (1 + x 2 + y 2 ) 2 (dx 2 + dy 2 ). (5)
Thus, the spherical gradient can be computed thanks to the classical Euclidean gradient by multiplying with a scaling factor:

∇ S 2 = (1 + x 2 + y 2 ) 2 4 ∇ R 2 . ( 6
)
The main advantage of this formulation is that we can compute the image gradient directly in the planar image with cartesian coordinates while respecting the non planar geometry of the mirror. However, the equation ( 6) is valid only for a parabolic miror and the formulation is different if we consider an hyperbolic mirror.

Spherical Filtering and Harmonic Analysis

On the sphere, the classical convolution used in Euclidean metric is not valid.

Driscoll and Healy [START_REF] Driscoll | Computing fourier transforms and convolutions on the 2-sphere[END_REF] have developed new tools based on spherical harmonics.

Let us note < ., . > the inner product on the sphere:

f, g ∈ L 2 (S 2 ), < f, g >= π 0 2π 0 f (θ, φ)g(θ, φ) sin θdθdφ. (7)
The spherical harmonics Y m l (θ, φ), defined by Legendre polynomials, form an orthonormal basis of L 2 (S 2 ), and a function f can be decomposed by (see [START_REF] Driscoll | Computing fourier transforms and convolutions on the 2-sphere[END_REF]):

f = l 0 |m| l f (l, m)Y m l (θ, φ) , where f (l, m) =< f, Y m l > . (8)
Driscoll and Healy define the spherical convolution as:

f, g ∈ L 2 (S 2 ), (f * g)(η) = SO(3) f (Rn 0 )g(R -1 η)dR, (9)
where η ∈ S 2 , n 0 = (0, 0, 1) is the North of the sphere. Similar definition can be seen in [START_REF] Bülow | Multiscale image processing on the sphere[END_REF] and [15].

This convolution can be computed in Fourier domain thanks to the convolution theorem:

f, g ∈ L 2 (S 2 ), ( f * g)(l, m) = 2π 4π 2l + 1 f (l, m)ĝ(l, 0). (10)
With these notations, the spherical Gaussian function G (which solves the spherical So, we can smooth a spherical image using ( 11), [START_REF] Makadia | Correspondence-free structure from motion[END_REF], and ( 8). Nevertheless, we can note that the spherical convolution is not commutative (f * g = g * f ) and does not verify the derivative relation which is very useful for edge detection in perspective image (f * g) = f * g = f * g [START_REF] Bigot | Spherical edge detector: Application to omnidirectional imaging[END_REF]. Thus, the image gradient can not be computed by using a low-pass filter as it is commonly done in perspective image processing.

diffusion equation S 2 u = ∂ t u) is given by: G(., t)(l, m) =                2l+1 4π e -l(l+1)t if m = 0 0 else (11)
In this paper, we propose a new definition of the neighborhood between pixels of a central catadioptric image. We show that this definition allows to use the same operators than in classical image processing techniques. In the next section, we examine the necessity of modifying the notion of neighborhood in catadioptric images and present the choice of the geodesic metric. The section 4 is dedicated to the definition of the new convolution product and its use in catadioptric image filtering. Different experimental results on edge detection and interest point detection will be presented and evaluated. Point matching methods derived from the new neighborhood definition will be proposed in Section 5 before a conclusion.

Introduction

In perspective image processing, most methods are developed from Euclidean metric:

∀x, y ∈ R 2 , d R 2 (x, y) = ||x -y|| l 2 (R 2 ) . (12)
From this metric, a neighborhood can be derived to define pixels dependency be-

tween

Neighborhood Definition

Let note P the projection that transforms a central catadioptric image which belongs to R 2 into his equivalent spherical image on S 2 : P :

R 2 → S 2 x → x s = (θ, φ) . ( 13
)
Fig. 6. Spherical coordinates and local basis.

In order to process spherical images, we propose to use the following geodesic distance:

∀x s = (θ, φ), y s = (θ , φ ) ∈ S 2 d S 2 (x, y) = arcos                              cos(φ) sin(θ) sin(φ) sin(θ) cos(θ)               T .               cos(φ ) sin(θ ) sin(φ ) sin(θ ) cos(θ )                             
.

Let note x s ∈ S 2 the projection of an image pixel x onto the unitary sphere (x s = P(x)). We then define the continuous neighborhood V r (x) of pixel x in the image as follows:

V r (x) = {y s ∈ S 2 , d S 2 (x s , y s ) r |P(x) = x s }. ( 14
)
This neighborhood results from the intersection between the cone with apex O, direction Ox s , angle r, and the sphere S 2 . In order to use discrete convolution filters with this neighborhood, it is then necessary to introduce a discrete version of [START_REF] Bülow | Multiscale image processing on the sphere[END_REF]. In this way, we consider the tangent plane π to S 2 at x s . This plane has the following equation x s + a e θ + b e φ , (a, b) ∈ R 2 , where ( e θ , e φ ) are vectors of the basis at x s = (θ, φ) (fig 6) :

e θ = ∂ OM ∂θ =               cos φ cos θ sin φ cos θ -sin θ               , e φ = 1 sin θ ∂ OM ∂φ =               -sin φ cos φ 0              
.

Since we want a regular mesh with constant geodesic distance, we obtain (2N +1) 2

points of π as follows :

x s + tan(nr) e θ + tan(pr) e φ , -N ≤ n, p ≤ N (15)
i.e. (2N + 1) 2 points of S 2 as:

V N r (x) = {x s (n, p) =
x s + tan(nr) e θ + tan(pr) e φ x s + tan(nr) e θ + tan(pr) e φ , -N ≤ n, p ≤ N, x s = P(x)}.( 16)

In V N r (x), the points are all equidistant in term of geodesic metric:

∀y ∈ V N r (x), min z∈V N r (x)\y d S 2 (y, z) = r.
Note that this geodesic neighborhood depends on r. This value corresponds to the distance between two points of the neighborhood. In order to compare our results with conventional methods, we will set r such that the geodesic neighborhood is equivalent to the Euclidean neighborhood in the center of the catadioptric image where the distortions are negligible.

Application to Catadioptric Image Processing

In order to demonstrate the validity of the approach, we propose to adapt some conventional image processing methods by using the geodesic metric. We show that this metric allows to apply the classical methods to catadioptric images very easily.

However, it is worth noting that practically, this new neighborhood requires that the luminance of each point to be known. In order to avoid a computationally expensive interpolation method for each point (x s (n, p)), we propose to use a simple nearest neighbour approach. We show that our method significantly improves the results, even with such rough interpolation.

First, we focus on linear catadioptric image filtering by defining the convolution product from the geodesic metric. We propose to apply this filtering for derivates computation and Harris corner detection. Then, we will see that feature matching methods based on similarity can also be adapted to central catadioptric images.

Linear Catadioptric Image Filtering

Linear image filtering consists in applying a weighted mask in each image point through convolution product. According to the previously mentioned reasons, the conventional convolution product can not be applied to catadioptric images. Consequently, the first step consists in defining the convolution product based on geodesic metric in order to process every pixel of the catadioptric image. We show that this new definition implies that the conventional operators remain valid.

Convolution

Let consider an omnidirectional image I and let note

I V N r (x) = I(P -1 (V N r (x))),
where I V N r (x) represents the (2N + 1) 2 grey level values of the regular grid centered at x s = P(x) (where P is defined by ( 13)).

I V N r (x) (n, p) = I(P -1 (x s (n, p))) -N ≤ n, p ≤ N.
Let H be a filter with size (2N + 1) × (2N + 1), we define the convolution product of image I by filter H on point x ∈ R 2 as follows:

∀x ∈ R, IH(x) = I V N r (x) * H(x) = N i=-N N j=-N I V N r (x) (i, j)H(i, j). ( 17
)

Geodesic Neighborhood vs Euclidean Neighborhood on the Tangent Plane

It is also possible to define a regular sampling at x s on the tangent plane π by using the distance d R 2 (x, y). This neighborhood is given by:

V N r,R 2 (x) = {x s + tan(r)(n e θ + p e φ ), -N ≤ n, p ≤ N }. (18)
In V N r,R 2 (x), points are equidistant in term of Euclidean distance: size 9 × 9, the both extreme points of π according to the neighorhoods

∀y π ∈ V N r,R 2 (x), min zπ∈V N r,R 2 (x)\yπ d R 2 (y π , z π ) = tan r. V N r,R 2 (x) and V N r (
V N r,R 2 (x)
and V N r (x) are less than 0.02 pixel distant. This is why the geodesic neighborhood can be considered as a valid approximation of the spherical projection of the tangent plane Euclidean neighborhood. Consequently, the classical filters used on the tangent plane can be applied directly on the geodesic neighborhood.

Derivative Filter

According to the previous considerations, the derivative in x s can be computed by a classical Sobel filter such as:

||∇I(x s )|| 2 |I V 1 r (x) * S| 2 + |I V 1 r (x) * S T | 2 ,
where

S =               -1 -2 -1 0 0 0 1 2 1              
.

In order to verify the behaviour of this geodesic filtering, we applied it to a synthetic image (fig 7) and compared the results with the classical Sobel filter (fig 8) and with the Bogdanova's method ( 6). This synthetic image simulates a catadioptric camera placed inside a rectangular parallelepiped. This configuration is not optimal for the geodesic neighborhood. Indeed, as mentioned before, the geodesic neighborhood is optimal for the case of a spherical scene captured from its center by a catadioptric camera. However, we can note a slight qualitative improvement of the gradient computation. We more clearly distinguish the edges in the center of the image and their thickness is more regular along the radial lines in the geodesic approach (fig 8(f)). Note that Bogdanova's approach globally improves the detection but reduces the detection of lines near the image center Fig. 8(c)). This phenomenon is more clearly visible in the real case image in (Fig. 9(a)). Figure 9 presents the gradient computation in the case of a real image (fig 9(a)). In these results, we consider only pixels with a gradient norm greater than half times the maximum gradient value. It is important to note that the adapted gradient provides better results than the classical method essentially on the periphery of the image where the edges are qualitatively more precisely detected.

We have illustrated that the geodesic distance improves gradient computation for catadioptric images and that the obtained results are comparable to Bogdanova's method which can not be directly adapted to other filtering techniques, whereas our Geodesic approach, (d) Bogdanova's method [START_REF] Bogdanova | Scale-space analysis and active contours for omnidirectional images[END_REF] approach remains valid in a more general framework.

Gaussian and Laplacian Filters

Similarly to the previous case, Gaussian and Laplacian filters remain valid with the geodesic neighborhood. Indeed, we can consider the Gaussian filtering as a weighting of the points according to their distance with the central point. This leads to substitute the Gaussian:

G x (y, σ) = 1 2πσ 2 e -||x-y|| 2 2σ 2 (x, y) ∈ R 2 , by G x (y, σ) = 1 2πσ 2 e - d S 2 (x,y) 2σ 2 (x, y) ∈ S 2 . ( 19
)
The Laplacian of Gaussian can also be defined as:

LoG x (y) = - 1 πσ 4 [1 - d S 2 (x, y) 2σ 2 ] exp - d S 2 (x, y) 2σ 2 . ( 20
)
Thus, while the Gaussian or Laplacian of Gaussian definitions using spherical harmonic analysis for spherical image processing needs their own rewording [START_REF] Bigot | Spherical edge detector: Application to omnidirectional imaging[END_REF] [14][15], our approach provides a straightforward adaptation to such conventional filters. Indeed, thanks to (19, 20) and the convolution product defined in ( 17), the masks used in perspective image processing remain valid.

In the following, we propose to verify the behaviour of these filters by the application of the Harris corner detector [START_REF] Harris | A combined corner and edge detection[END_REF]. Harris corner detector has been massively used in computer vision applications. In perspective image processing, the corner detection by Harris method consists in studying the eigenvalues of matrix M in each point X:

M (X) =         L 2 x (X, σ) L x L y (X, σ) L x L y (X, σ) L 2 y (X, σ)         , (21)
where

L i (X, σ) = ∂ ∂i G X (X, σ) * I(X).
This matrix M has been computed with classical filter, with spherical convolution [START_REF] Makadia | Correspondence-free structure from motion[END_REF], and spherical Gaussian function [START_REF] Bigot | Spherical edge detector: Application to omnidirectional imaging[END_REF]. Note that in the case of the spherical convolution, since the formula (f * g) = f * g no longer holds, we first have to perform the convolution of the spherical Gaussian with I, then derive the obtained signal using (3) to obtain L i . With our approach, if we consider the relations defined in ( 17) and ( 19), M can be easily computed. First, we compare the adapted Harris corner detection with a classical Harris and a Harris computed on the sphere, for the synthetic image proposed in figure [START_REF] Makadia | Correspondence-free structure from motion[END_REF]. We report only the 100 best responses to the detectors.

Matching

Feature matching between consecutive images of a sequence is a very important problem in computer vision for motion estimation for example. We are particularly dealing with corner matching, but our approach can be applied to any method based (ZNCC):

ZN CC(x, y) = i∈V(x) j∈V(y) (I 1 (i) -I 1 (x))(I 2 (j) -I 2 (y)) i∈V(x) (I 1 (i) -I 1 (x)) 2 j∈V(y) (I 2 (j) -I 2 (y)) 2 , ( 22
)
where I 1 (x) and I 2 (y) are the grey level mean of image I 1 and I 2 in neighborhood V(x) and V(y)), respectively.

For a perspective image, the neighborhood is once again defined from Euclidean distance between points (12). However, for the same reasons previously exposed, this neighborhood can not be applied in catadioptric images. Moreover, a neighborhood on the unitary sphere defined from a regular sampling of the spherical coordinates θ and φ is also not adapted. Indeed, such definition does not provide the same neighborhood for each point on the grid (fig 4). Consequently, we also propose to use the geodesic metric to define the neighborhood ( 16) for measuring the similarity of the detected corners.

We then compare previous images using a classical neighborhood of size 7 × 7

and an geodesic neghborhood V 3 r . If we consider the same corners in both cases obtained by the classical Harris detector with the same thresholds, the use of the here to compare the conventional detection and matching with the adapted detec-tion and matching results. In this way, we want to exhibit more significantly the benefits of the geodesic neighborhood. Green bars (respectively red) correspond to the number of matched corners in each image while the blue bars (respectively black) describe the number of outliers for each method. It is worth noting that the geodesic approach provides a better matching since the number of matched corners is greater while the number of outliers is less than for the classical method. Indeed, over the 21 images, the geodesic method provides 152 matchings in average while the classical methods gives 116 matchings. In the same time, the outlier rate is equal to 3.5 in the geodesic case while the classical approach presents a rate of 14.5.

Conclusion

In this paper, we deal with central catadioptric image processing. Because of the distortions introduced by the mirror, these images can not be processed as classical perspective images. In this way, we consider a geodesic metric rather the Euclidean one in order to define the dependency neighborhood between pixels. We show that this approach allows to directly adapt the classical perspective image processing

Fig. 1 .

 1 Fig. 1. Catadioptric camera and catadioptric image

Fig. 3 .

 3 Fig. 3. Equivalence between the catadioptric projection and the two-step mapping via the sphere.

Fig. 4 .

 4 Fig. 4. Sampling of the sphere. This irregular sampling is unappropriate for the matching by Zero mean Normalized Cross-Correlation function (ZNCC).

Fig. 5 .

 5 Fig. 5. Image formation and neighborhood dependency. (a) Orthographic image, Euclidean metric, (b) perspective image, Euclidean metric, (c) omnidirectional image, Euclidean metric, (d) omnidirectional image, geodesic metric.

  x) are obviously different because tan nr = n tan r. Nevertheless, if we consider a viewing angle equal to r = 5 • , which corresponds to a sampling of the sphere in 180/5 × 360/5 = 36 × 72 pixels and a neighborhood of

Fig. 7 .

 7 Fig. 7. Synthetic catadioptric test image.

Fig. 8 .Fig. 9 .

 89 Fig. 8. Gradient norm results on synthetic image. (a),(b) Classical approach, (c) (d) Bogdanova's method [4], (e)(f) Geodesic approach

Figure 10 (

 10 b) corresponds to the detection using classical Harris. We observe some double corner detections whereas some other corners are not detected (17 corners have been detected). Inversely, Harris detection through spherical analysis detects 21 corners but more corners at the image center where there is a blind spot in a real image (Fig9(a)), but does not detect corners at the periphery (Fig.10(c)). The proposed method therefore seems being a good compromise (Fig10(d)), 19 corners have been detected and the results show that the geodesic distance seems capable to correctly detect corners with only slight modifications of the traditional technique. We now verify the behavior of our approach with real images.Harris detector results are shown for two consecutive real images extracted from a sequence in figure11. Table1presents a comparison of the repeatability rate developed in[START_REF] Schmid | Evaluation of interest point detectors[END_REF] between both detectors. If we focus on the particular part in the image which corresponds to the lockers, we can note that 50 corners were detected in l 1 with the adapted Harris (figure11(b)) while 55 were found with the conventional approach (figure11(d)). In the second image, 51 corners were detected with the adapted method while the classical only detected 36 corners. In the classical Harris results, only 29 corners are common between the two images, which represents a repeatability equal to 80%. The geodesic Harris detector presents 43 common corners between images, i.e. a repeatability rate of 86%.

Fig. 10 .

 10 Fig. 10. Harris corner detection. (a) Test Image, (b) Classical Harris corner, (c) Spherical Harris corner, (d) Adapted method.

Fig. 11 .

 11 Fig. 11. Harris corner detection results. (a)-(b) Classical method, (c)-(d) Geodesic method.

Fig. 12 .

 12 Fig. 12. Matching by ZNCC. (a) Classical method: 65 total matchings, 53 correct matchings, (b) Geodesic method: 71 total matchings, 63 correct matchings.

Figure 13 (

 13 Figure 13(c) compares results for corner detection and matching over an outdoor sequence of 21 consecutive images (figures 13(a) and 13(b)). Contrary to the previous matching results obtained from the classical Harris corner detector, we propose

Fig. 13 .

 13 Fig. 13. Corner detection and matching. (a) (b) 2 images from the real sequence. (c) Matching results.

techniques to central catadioptric images, and more generally to spherical images. Indeed, this geodesic metric allows to apply filtering masks similarly to perspective images while taking into account the distortions of catadioptric images. Experimental results on gradient computation, corner detection, and point matching show a significant improvement of the quality despite the use of the nearest neighbour interpolation. Thanks to this formulation, every method based on pixel mutual dependency can be straightly adapted to central catadioptric images (Markov Random Fields, mathematical morphology, image segmentation...). Moreover, it is worth noting that contrary to methods based on spherical harmonic analysis, we process points only in the image plane. Consequently, pyramidal methods such as proposed by Burt et Adelson [START_REF] Burt | The laplacian pyramid as a compact image code[END_REF] remain valid in our approach. It is also important to note that our approach can be applied to any type of single view point sensor, such as perspective camera, central catadioptric camera, but also fish-eye camera [START_REF] Ying | Can we consider central catadioptric cameras and fisheye cameras within a unified imaging model[END_REF], since they all provide images equivalent to spherical images. Perspectives will then consist in applying these processing techniques to heterogeneous central sensor network in order to improve their efficiency and interest.