Mohamed Soua
email: mohamed.soua@etap.com.tn

Time series (Orbital cycles) analysis of the latest Cenomanian -Early Turonian sequence on the southern Tethyan margin using foraminifera

Keywords: Time series analysis, Heterohelix spp, Guembelitria spp, Milankovitch cyclicity, cyclostratigraphy, Cenomanian-Turonian boundary

Time series analysis has been performed for the first time on the Cenomanian-Turonian sequence in Central Tunisia in order to shed light on its Milankovitch-like cyclicity. This analysis was applied to two foraminiferal genera: the biserial Heterohelix, an oxygen-minimum zone (OMZ) dweller, and the triserial Guembelitria, a eutrophic surface dweller. Average sedimentary rates and the duration of the OAE2 in each studied section were estimated. The fluctuations in abundance of these two opportunistic species can be related mainly to both precessional (ca. 20 kyr) and eccentricity (100 and 400 kyr) cyclicity suggesting that changes in surface water fertility were linked to climate changes in the the Milankovitch frequency band .

Introduction

Understanding of the biotic and sedimentary events that marked Earth history is of great interest in the geoscience community (e.g. [START_REF] Haq | Chronology of fluctuating sea levels since the Triassic[END_REF][START_REF] Sepkoski | Ten Years in the Library: New Data Confirm Paleontological Patterns[END_REF]Kauffeman, 1995;[START_REF] Sageman | Multiple Milankovitch cycles in the Bridge Creek Limestone (Cenomanian-Turonian), Western Interior basin[END_REF][START_REF] O'dogherty | Rates and Pattern of Evolution among Cretaceous Radiolarians: Relations with Global Paleoceanographic Events[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. The Cenomanian-Turonian (C/T) boundary lies in a time interval characterized by a cluster of significant events, some of which are biotic (mass, step-by-step or even pseudo-extinction, O'Dogherty, personal communication), progressive recolonization of new habitats, etc…), others are sedimentary (forced regression following an intense transgression) (e.g. [START_REF] Robaszynski | A tentative integrated stratigraphy in the Turonian of Central Tunisia : Formations, zones and sequential stratigraphy in the Kalaat Senan area[END_REF][START_REF] Hardenbol | Mesozoic and Cenozoic Sequence Stratigraphy of European BasinsSoc[END_REF]De Wever et al., 2003;[START_REF] Zhao | New palaeointensity results from Cretaceous basalt of Inner Mongolia[END_REF]. The chronometric scale across the C/T boundary has been defined by (1) radiometric ages, e.g. 40Ar/39Ar determined from bentonite layers at the Pueblo section (e.g. Obradovich, 1993;Kowallis et al., 1995), (2) ammonite biostratigraphy (e.g. Kennedy and Cobban, 1991), and (3) linear interpolation (where by the sedimentation rate is assumed to be constant) inside the magnetic anomaly C34 (Cretaceous Normal Super-Chron).

It has been suggested that the marl-limestone alternations characterizing the C/T transition in Central Tunisia may have originated from orbital forcing [START_REF] Vonhof | Synchronous strontium and carbon isotope excursions across the Cenomanian-Turonian Oceanic Anoxic Event[END_REF][START_REF] Nederbragt | Stratigraphy and paleoceanography of the Cenomanian-Turonian Boundary Event in Oued Mellegue, north-western Tunisia[END_REF][START_REF] Caron | Estimation de la durée de l'événement anoxique global au passage Cénomanien Turonien. Approche cyclostratigraphique dans la Formation Bahloul en Tunisie centrale[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. The thus induced climatic changes produced alternations between terrigenous input and pelagic-hemipelagic carbonate sedimentation.

Geological framework

According to the tectonic setting, this area is regarded as being a transitional zone between the Tunisian Northern Atlas, dominated by diapiric salt structures, and the Tunisian Central Atlas, dominated by a NE-SW trending fold axis, which is intersected by many trough faults bordering on Neogene-filled half-graben systems [START_REF] Soua | Structural context of the paleogeography of the Cenomanian -Turonian anoxic event in the eastern Atlas basins of the Maghreb[END_REF]. The C/T interval is represented by the black shales of the Bahloul Formation [START_REF] Robaszynski | A tentative integrated stratigraphy in the Turonian of Central Tunisia : Formations, zones and sequential stratigraphy in the Kalaat Senan area[END_REF]Maamouri et al., 1994;Caron et al., 1999;Nederbrag and Fiorentino, 1999;[START_REF] Soua | Biostratigraphie de haute résolution des foraminifères planctoniques du passage Cénomanien Turonien et impact de l'événement anoxique EAO-2 sur ce groupe dans la marge sud de la Téthys, exemple régions de Jerissa et Bargou[END_REF][START_REF] Soua | Radiolarian biotic responses to the Latest Cenomanian global event across the southern Tethyan margin (Tunisia)[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF][START_REF] Soua | Structural context of the paleogeography of the Cenomanian -Turonian anoxic event in the eastern Atlas basins of the Maghreb[END_REF] in some localities, the sedimentation was controlled by basin morphology created either by Triassic salt halokinesis (Fig. 1A) affecting the Cretaceous series or by other syn-sedimentary tectonic activities. The eastern part belongs to the Bargou area that is connected palaeogeographically to central Tunisia. It is characterized by (1) emerged palaeohighs displaying gaps and discontinuities, and by (2) subsiding zones affected by deep water sedimentation. This area is dominated by N140° and N70° trending faults limiting several blocks.

Uniquely, in the Bargou (COK) and Guern Halfaya (GH) sections, the top of the Bahloul Formation represents many Cenomanian olistolith levels marking syndepositional tectonic activities. Elsewhere, these syn-sedimentary features are represented by local slumping (e.g. in the Jerissa (CES) and Hammem Mellegue (HM) sections.

Material and Methods

A total of 219 samples were collected throughout the Bahloul Formation, which is well exposed in these four sections (Fig. 1A,B). Calcium carbonate (CaCO 3 ) analysis was conducted in the Geochemistry Laboratory at the Faculty of Science of Tunis University, the total organic carbon (TOC) was determined on crushed samples with a Rock-Eva1 II type machine in ETAP. Thin section analysis was conducted in the geological laboratory of the Office National des Mines (ONM). High-resolution biostratigraphical and geochemical studies have previously been undertaken [START_REF] Soua | Biostratigraphie de haute résolution des foraminifères planctoniques du passage Cénomanien Turonien et impact de l'événement anoxique EAO-2 sur ce groupe dans la marge sud de la Téthys, exemple régions de Jerissa et Bargou[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF] and the essential foraminiferal zone and subzone divisions have been established there. In the present paper, only the abundances of Heterohelix spp. (total Heterohelix species) and Guembelitria spp. (total Guembelitria species) in each section were used for time series analysis. Spectral analysis was carried out using an integrated software package (PAST, [START_REF] Hammer | PAST: Paleontological Statistics software package for education and data analysis[END_REF]. Spectral estimation was applied to the Heterohelix spp. and Guembelitria spp. frequency (%) data series. The use of the spectral estimation ensures a better confidence factor when spectral analysis is used as a cyclostratigraphic tool.

Results

The Bahloul Formation in the studied sections (Fig. 1B) consists of alternating limestone, argillaceous limestone and rhythmically bedded marls. Uniquely, in the Bargou and Guern Halfaya areas (COK and GH sections) it is represented by an original organic-rich and siliceous facies [START_REF] Soua | Radiolarian biotic responses to the Latest Cenomanian global event across the southern Tethyan margin (Tunisia)[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]Fig.2-photo 3). The Bahloul limestone consists of wackstone/packstone clay-poor carbonates rich in microfossils (filaments, Fig. 2-photo 1; radiolarians, Fig. 2-photo 2; foraminifera Fig. 2-photo 4, and calcispheres, Fig. 2-photo 5) and macrofossils (ammonites), whereas marls consist of clay-rich carbonates [START_REF] Robaszynski | A tentative integrated stratigraphy in the Turonian of Central Tunisia : Formations, zones and sequential stratigraphy in the Kalaat Senan area[END_REF]Maamouri et al., 1994;[START_REF] Caron | Estimation de la durée de l'événement anoxique global au passage Cénomanien Turonien. Approche cyclostratigraphique dans la Formation Bahloul en Tunisie centrale[END_REF][START_REF] Nederbragt | Stratigraphy and paleoceanography of the Cenomanian-Turonian Boundary Event in Oued Mellegue, north-western Tunisia[END_REF][START_REF] Soua | Biostratigraphie de haute résolution des foraminifères planctoniques du passage Cénomanien Turonien et impact de l'événement anoxique EAO-2 sur ce groupe dans la marge sud de la Téthys, exemple régions de Jerissa et Bargou[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. According to [START_REF] Caron | Estimation de la durée de l'événement anoxique global au passage Cénomanien Turonien. Approche cyclostratigraphique dans la Formation Bahloul en Tunisie centrale[END_REF], periods of low sea levels generally coincide with high detrital influx (marls) and increased erosion and are predominantly associated with arid and/or cooler climatic conditions. Periods of high sea levels are generally characterized by increased carbonate production (limestone) and low detrital influx under warm and humid climatic conditions. The Bahloul black shales are on average about 20 m thick. A prominent microconglomeratic limestone, 50cm thick on average, marks the base of the Bahloul.

It contains a late Cenomanian ammonite assemblage of the Metoicoceras geslinianum zone in the Jerissa (CES) section [START_REF] Accarie | Stratigraphie événementielle au passage Cénomanien -Turonien dans le secteur occidental de la plateforme de Tunisie centrale (Formation Bahloul, région Kalaat Senen[END_REF], and a planktonic foraminiferal assemblage indicative of the uppermost Rotalipora cushmani zone. It is composed of gray limestone beds overlain by thinly bedded marls with a few laminated darker limestone beds. These layers are overlain by increasingly clayey limestone beds. In the middle part, the microfauna display a more dissolved aspect and dwarfism. Ammonite-rich and ichnofossil-rich beds are present in the Jerissa (CES), Guern Halfaya (GH) and Bargou (COK) sections (Fig. 1B) and they are used as a correlation tool.

Two opportunistic species (the biserial Heterohelix and the triserial Guembelitria spp.) were selected for this study to carry out spectral analysis. Heterohelix is considered to be a global biomarker that reflects the expansion of the oxygen-minimum zone (OMZ) [START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. This low oxygen tolerant species dominates the faunal assemblages, averaging up to 80% in the Bahloul black shales (Fig. 3), and especially in the lower W. archaeocretacea zone [START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]Fig. 1B; Fig. 3). The Guembelitria species thrived in eutrophic surface waters with variable salinities at times of severe ecological stress [START_REF] Soua | Biotic response during times of severe ecological stress, how paleoceanographic changes in latest Cenomanian-earliest Turonian Ocean induced step-by-step extinction and dwarfism[END_REF]Soua and Trbovillard, 2007).

Time series analysis

In the stratigraphic record, sedimentary rhythmicity has been well discussed and debated (see mainly Berger et al., 1989;[START_REF] House | Orbital forcing timescales: an introduction[END_REF][START_REF] Weedon | Time-Series Analysis and Cyclostratigraphy[END_REF]. Such records are often interpreted as orbitally controlled especially with the hierarchical stacking of limestone-marl couplets [START_REF] Berger | Long-term variations of caloric insolation resulting from the Earth's orbital elements[END_REF][START_REF] House | Orbital forcing timescales: an introduction[END_REF][START_REF] Negri | Tethyan Cenomanian pelagic rhythmic sedimentation and Pleistocene Mediterranean sapropels: is the biotic signal comparable? Palaeogeography[END_REF]Scopelliti et al., 2006). It is believed that periodicities of precession and obliquity were not the same in the past as today (e.g. Berger et al. 1989;Strasser et al., 2006).

Well established correlations between rhythmic sequences and geochemical and biotic parameters have been described by many authors (e.g. Ditchfield and Marshall 1989; Weedon and Jenkyns 1990), confirming temperature dependence and correlations with %CaCO3, nannofossils and foraminifera frequencies (%), which might be expected to be controlled by temperature or other parameters related to Milankovitch cyclicity [START_REF] House | Orbital forcing timescales: an introduction[END_REF][START_REF] Negri | Tethyan Cenomanian pelagic rhythmic sedimentation and Pleistocene Mediterranean sapropels: is the biotic signal comparable? Palaeogeography[END_REF]. The frequency distribution of limestone-marl alternations and their relation to the Milankovitch parameters is commonly tested by time series analysis (e.g. House, 1986;[START_REF] House | Orbital forcing timescales: an introduction[END_REF][START_REF] Weedon | Time-Series Analysis and Cyclostratigraphy[END_REF]. The power spectrum shows generally squared amplitudes and wavelengths that represent the periods of regular components in the time series [START_REF] Weedon | Time-Series Analysis and Cyclostratigraphy[END_REF]. Conventionally, the horizontal axis of the power spectrum represents Frequency (Frequency = 1/period) with highest frequencies (i.e. shortest oscillations) appearing on the right and the vertical axis represents Power spectra (Fig. 3). Zero frequency usually corresponds to oscillations that have periods exceeding the length of the whole data set [START_REF] Weedon | Time-Series Analysis and Cyclostratigraphy[END_REF]. The Heterohelix spp. and Guembelitria spp. relative abundance curves in the four localities clearly exhibit strong cyclic signals (Fig. 3), which allowed us to perform a spectral analysis study, computed using the PAST software [START_REF] Hammer | PAST: Paleontological Statistics software package for education and data analysis[END_REF], to test for the existence of periodicities through the OAE2 deposits in Central Tunisia. The results of the spectral analysis are illustrated in Figure 3. The strongest peaks point to a period of 25 m (Heterohelix spp) in the HM Section (Fig. 3A) and a period of 17.54 m (Guembelitria spp) in the CES section (Fig. 3D).

Hammam Mellegue (HM section) [START_REF] Nederbragt | Stratigraphy and paleoceanography of the Cenomanian-Turonian Boundary Event in Oued Mellegue, north-western Tunisia[END_REF] argued that in the nearby Mellegue section the Bahloul Formation is suggestive of Milankovitch cycles due to its regular strata (Fig. 1B). Average accumulation rates of about 10 cm/kyr for the same Bahloul interval was previously determined by [START_REF] Vonhof | Synchronous strontium and carbon isotope excursions across the Cenomanian-Turonian Oceanic Anoxic Event[END_REF] suggesting that each 2-m-thick pair of laminated limestone and bioturbated marly limestone represents a precession cycles (20 kyr) rather than obliquity cycle (40 kyr) as seen in other C/T intervals (e.g. [START_REF] Arthur | The Cenomanian-Turonian oceanic anoxia event: II. Paleoceanographic controls on organic matter production and preservation[END_REF][START_REF] Kuhnt | Cyclicity of Cenomanian-Turonian organic-carbon-rich sediments in the Tarfaya Atlantic coastal basin (Morocco)[END_REF][START_REF] Sageman | Multiple Milankovitch cycles in the Bridge Creek Limestone (Cenomanian-Turonian), Western Interior basin[END_REF]. Time series analysis performed on Heterohelix spp. shows that the strongest peak points to a period of 25 m (Fig. 3A). Other statistically significant peaks are found at 11.9 and 5.26m. This latter peak, although statistically significant, falls in the low-energy field of the spectrum. The spectral curve of the Guembelitria spp. shows significatant peaks at about 15.62m and 7.14 m.

The 4.54m and 3.12m peaks (Fig. 3A) recorded in the low energy field of the spectrum are very close, and they might be considered as components of the same periodicity.

Dir Ouled Yahia (COK section) and Guern Halfaya (GH section)

The COK section, about 24 m thick (Fig. 1B), is exposed in Oued El Kharroub (Dir Ouled Yahia area) (Fig. 1A), whereas the GH section, about 17m thick, is located between Hammem Mellegue and Tajerouine and is one of the most expanded C-T transitions in Tunisia [START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. The results of the spectral analysis are also shown in Figure 3 (B andC). At the COK and GH sections, the Bahloul Formation is characterized by several radiolarian-rich siliceous beds [START_REF] Soua | Radiolarian biotic responses to the Latest Cenomanian global event across the southern Tethyan margin (Tunisia)[END_REF]; Fig. 2

-photo 3). The time series analysis performed on

Heterohelix spp shows that the strongest peak points to a period of 17.85 m (Fig. 3B). Other significant values are represented at 9.1, 5m and 3.84 m.

Dealing with Guembelitria time series analysis, we observe strong peaks at 13.16 and 12.82m respectively in the GH and COK sections (Fig. 3B; Fig. 3C).

Jerissa (CES section)

The Heterohelix signal was filtered and three significative peaks of different wavelengths were detected (i.e. 19.6 m, 7.69 m, and 4.1m; Fig. 3D). They were selected for this study because they represent accurate values for time series analysis. These values are normalised to the shortest periodicity (i.e. 4.1) and then compared to the relative precession ratios of classical Milankovitch periodicities (see Tab. 1). Table 1 shows the relationship between the ratios obtained by the normalisation both of the eccentricity (100-400 kyr) and obliquity (40 kyr) to the precession ( 20kyr). All wavelengths (related respectively to Heterohelix and Guembelitria in the four sections) are normalised to the related shortest periodicity.

Cyclostratigraphy

According to the [START_REF] Park | Milankovitch rhythms in the Cretaceous : a GCM modelling study[END_REF] model, which reproduces Cretaceous Milankovitch cyclicity, the Bahloul sequence may display a Milankovitch style climatic cyclicity corresponding to a 20 kyr precession cycle that prevailed at low latitudes during the C/T transition. In this study we have tried to calculate the palaeolatitudes of the Kef and Bargou areas (where the four studied sections are situated) during the C/T transition, i.e about 93.5 Ma. The calculated palaeolatitudes are about 15 to 17 ° N according to [START_REF] Philip | Late Cenomanian (94-92 Ma)[END_REF], or 16-19 ° N according to [START_REF] Camoin | Late Maastrichtian (69.5-65 Ma)[END_REF]. In contrast they are 37 ° to 37.5 ° N according to the ODSN Plate Tectonic Reconstruction Service [START_REF] Hay | The evolution of Cretaceous ocean/climate systems[END_REF]. These latter sequences represent variable indurate levels that also show %TOC, %CaCO 3 and ‰ 13 C fluctuations (Figure 5). [START_REF] Negri | Tethyan Cenomanian pelagic rhythmic sedimentation and Pleistocene Mediterranean sapropels: is the biotic signal comparable? Palaeogeography[END_REF] discussed the duration of the orbital cycles in time-equivalent Bonarelli black shale level, and have shown that they can be normalised and tuned to precession cycles. The Heterohelix and Guembelitria signals in the studied sections were filtered, and show significant fluctuations in the OMZ and eutrophic surface dweller signals (see figure 4). This time series analysis allowed us to develop a cyclostratigraphic approach in order to estimate the duration of the organic-rich Bahloul Fm in the four studied sections. The evaluation of the OAE2 duration was the subject of several studies and was originally estimated based mainly on biostratigraphic (ammonites and foraminiferal) ranges (e.g. [START_REF] Hardenbol | Mesozoic and Cenozoic Sequence Stratigraphy of European BasinsSoc[END_REF] and/or orbital cyclicity. Estimates are: 720 kyr in the Pueblo section (Meyers et al., 2004), about 400 kyr in Tarfaya and Wadi Bahloul [START_REF] Kuhnt | Cyclicity of Cenomanian-Turonian organic-carbon-rich sediments in the Tarfaya Atlantic coastal basin (Morocco)[END_REF], Caron et al., 1999), 320 kyr in western Canada and the Bottaccione section in Central Italy [START_REF] Prokoph | Geochronology and calibration of global Milankovitch cyclicity at the Cenomanian-Turonian boundary[END_REF]Scopelliti et al., 2006), 450 ky for the Douvres section (Gale, 1991), 500 kyr to 600 kyr for the Thomel level [START_REF] Morel | Stratigraphie à haute résolution du passage Cénomanien-Turonien[END_REF].

Influence of orbital forcing during Bahloul deposition

Wavelength ratios were tuned to the associated orbital cyclicity of the C/T transition strata (see Tab. 1). Alternatively we may estimate an average sedimentary rate for the Bahloul Fm (OAE2) by tuning each calculated wavelength to the corresponding orbital cyclicity (e.g. 19.6/100; 7.69/40; 4.1/20; Heterohelix data of the CES section). Figure 4 shows that for the CES section, the Heterohelix precession curve (filter 20) exhibits 18 to 19 cycles. This means that a duration of about 400 kyr can be attributed to the Bahloul Formation, which represents the anoxic event. The eccentricity curve exhibits about 4 to 4.5 cycles, which also corresponds to about (i.e. ~ 400 kyr).

The average duration of the Bahloul formation (OAE2) may thus be evaluated to ~ 400 kyr. The results are displayed in Figure 4, and Tab.1.

Discussion

The solar influx which penetrates the atmosphere is controlled by the orbital parameters of the Earth: i.e. eccentricity, obliquity and precession [START_REF] Berger | Long-term variations of caloric insolation resulting from the Earth's orbital elements[END_REF][START_REF] House | Orbital forcing timescales: an introduction[END_REF]. These orbital variations lead to climatic variations, which then influence oceanic circulation and the sedimentary systems. A dominance of precession cycles on climate change and sedimentation can be discerned during the C/T interval [START_REF] Berger | Long-term variations of caloric insolation resulting from the Earth's orbital elements[END_REF]. In addition, ignoring the obliquity signal component will greatly simplify data interpretation [START_REF] Vonhof | Synchronous strontium and carbon isotope excursions across the Cenomanian-Turonian Oceanic Anoxic Event[END_REF][START_REF] Nederbragt | Stratigraphy and paleoceanography of the Cenomanian-Turonian Boundary Event in Oued Mellegue, north-western Tunisia[END_REF][START_REF] Caron | Estimation de la durée de l'événement anoxique global au passage Cénomanien Turonien. Approche cyclostratigraphique dans la Formation Bahloul en Tunisie centrale[END_REF][START_REF] Negri | Tethyan Cenomanian pelagic rhythmic sedimentation and Pleistocene Mediterranean sapropels: is the biotic signal comparable? Palaeogeography[END_REF][START_REF] Scopelliti | High-resolution geochemical and biotic records of the Tethyan 'Bonarelli Level' (OAE2, latest Cenomanian) from the Calabianca-Guidaloca composite section, northwestern Sicily, Italy[END_REF]. Eccentricity is Thus, high abundance of Heterohelix indicates an expanded oxygen minimum zone [START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF].

The triserial heterohelicacea Guembelitria species thrived in eutrophic surface waters with variable salinities at times of severe ecological stress [START_REF] Leckie | Paleoecology of mid-Cretaceous planktic foraminifera: a comparison of open ocean and epicontinental sea assemblages[END_REF][START_REF] Kroon | Ecology and palaeoecology of triserial planktic foraminifers[END_REF][START_REF] Soua | Biotic response during times of severe ecological stress, how paleoceanographic changes in latest Cenomanian-earliest Turonian Ocean induced step-by-step extinction and dwarfism[END_REF]Soua and Trbovillard, 2007).

Relationship between paleoecology and the orbital cycles

We have shown that in the four studied sections strong cyclicity is reflected not only in the lithological pattern but also in the biotic signal. Specially, our data recognize a strong precessional signal that is comparable to other identified all over the world [START_REF] Kuhnt | Cyclicity of Cenomanian-Turonian organic-carbon-rich sediments in the Tarfaya Atlantic coastal basin (Morocco)[END_REF][START_REF] Morel | Stratigraphie à haute résolution du passage Cénomanien-Turonien[END_REF][START_REF] Caron | Estimation de la durée de l'événement anoxique global au passage Cénomanien Turonien. Approche cyclostratigraphique dans la Formation Bahloul en Tunisie centrale[END_REF]Meyers et al., 2004;[START_REF] Prokoph | Geochronology and calibration of global Milankovitch cyclicity at the Cenomanian-Turonian boundary[END_REF][START_REF] Negri | Tethyan Cenomanian pelagic rhythmic sedimentation and Pleistocene Mediterranean sapropels: is the biotic signal comparable? Palaeogeography[END_REF]Scopelliti et al., 2006). The palaeoecological preferences of both Heterohelix spp. and Guembelitria spp. seem to be related to areas of enhanced surface water fertility and oxygeneminimum zone (e.g. Nederbragt and Fierontino, 1999;[START_REF] Luning | An integrated depositional model for the Cenomanian-Turonian organic-rich strata in North Africa[END_REF][START_REF] Soua | Depositional model at the Cenomanian/Turonian boundary for the Bahloul Formation, Tunisia[END_REF]. Thus, the long term fluctuations related to both precession and eccentricity suggest that changes in surface water fertility were linked to the Milankovitch parameters.

Conclusion

Four C/T transition sections were sampled in Central Tunisia displaying biotic and lithologic variations. Time series analysis was applied to the abundances of two opportunistic foraminiferal genera (Heterohelix and Guembelitria spp) for all the four sections. This analysis allowed us to calculate and estimate both the average sedimentary rate and the duration of the OAE2 in each section. In addition, the biotic signal represented by the Heterohelix and Guembelitria spp. relative abundance fluctuations in the studied sections is probably driven by Milankovitch B. Distribution and correlation of foraminiferal and radiolarians profiles in the same graphic at Bargou section Table 1 Wavelengths evaluated from the power spectra in Figure 3; average sedimentary rates (cm/kyr) and estimated duration of the OAE2 in each section. Note that the Bahloul Formation is deposited within an interval of 350-410 kyr with a sedimentation rate encompassed between 12 and 20 cm/kyr.

Figures and Tables caption

Figure 1

 1 Figure 1 Location of the studied sections, (A) Bahloul isopach map and C/T palaeogeography in Central Tunisia (B) Stratigraphy and biostratigraphy of Jerissa (CES), Guern Halfaya (GH), Hammem Mellegue (HM) and Bargou (COK) sections.

Figure 2 -

 2 Figure 2 -(1) Micrograph of a filament-rich layer from the upper Bahloul Fm showing elongated and thin forms with imbricated and tangled arrangement enveloping sparitic elements. They display also several features such as tangling and overlapping. Moreover, they display heterogeneous sizes. (2) Micrograph of a radiolarian-rich layer from the Bahloul in COK section showing both nassellarian and spumellarian species. (3) A view of the Bahloul outcrop in GH section showing silica-rich layers characterizing organic-rich and siliceous facies of the GH and COK section. (4) Micrograph of a foraminiferal-rich level showing whiteinellids and hedbergellids. (5) Micrograph of a calcispheres-rich layer from the lower Bahloul Fm.

Figure 3

 3 Figure 3 A-D Time series analyses performed on the two opportunistic C/T foraminiferal species, the OMZ dweller Heterohelix spp and the eutrophic surface dweller Guembelitria spp. showing the power spectrum of their relative abundance logs (%) in the studied interval of the Bahloul in each section. The values on the vertical axis indicate the power while the horizontal axis refers to frequencies in cycles/metre, from low-frequency (left) to high-frequency (right) periodicities. Only the statistically signifcant periodicities are labelled; numbers above the significant peaks are frequencies in cycles/metre. Dashed lines indicate filtered signals

known to be very stable through the Mesozoic time and did not vary significantly through the last 100 Ma (Berger et al., 1992;[START_REF] Laskar | A numerical experiment on the chaotic behaviour of the Solar System[END_REF]Laskar, , 1999)). Figures 3 and Figure 4 show the cyclostratigraphic interpretation of the four studied sections, leading to the recognition of precession cycles and the identification of 100 kyr cycles (short eccentricity). The spectral analysis applied to the Heterohelix/Guembelitria spp. fluctuations (Fig. 3) points to the presence of a metre-scale periodicity, for example at 25 m in the HM section (Fig. 3A), and other major relevant peaks at 11.9m and 5.26m using Heterohelix spp counts. Regarding Guembelitria ssp, there is a metre-scale periodicity at 17.54m in the CES section and other important peaks at 8.33 and 3.84m (Fig. 3D). The relationship between the ratios obtained by the normalisation both of the eccentricity (100-400 kyr) and obliquity (40 kyr) to the precession (20 kyr) are displayed in Tab.1. The high correlation between the spectral peak ratios (of both the Heterohelix and Guembelitria in the four sections) and those of the orbital components is very interesting (Fig. 3A, Tab.1). Calculated average sedimentary rates (Tab.1) are in perfect agreement with the sedimentation rate estimated from [START_REF] Hardenbol | Mesozoic and Cenozoic Sequence Stratigraphy of European BasinsSoc[END_REF] and the relatively close value (10cm/kyr) obtained by Vanhof et al., (1998) for the Mellegue section. This interpretation clearly highlights the existence of cyclicity within the Bahloul Formation that is more complex than that which can be recognised by visual inspection. It implies that orbital forcing has caused the Heterohelix and Guembelitria abundance fluctuations.

Paleoecology of the two opportunistic species

The biserial heterohelicids (Heterohelix spp.), are believed to be as ecological opportunists and low-oxygen tolerant fauna thriving in well-stratified open marine settings with a well-developed oxygen minimum zone (OMZ) [START_REF] Boersma | Atlantic palaeogene biserial heterohelicid Foraminifers and oxygen minima[END_REF][START_REF] Barrera | Productivity across the Cretaceous-Tertiary boundary in high latitudes[END_REF].

frequencies through a climate-controlled productivity model. We can deduce that the fluctuations of these two species are related mainly to both precessional and eccentricity cyclicity, suggesting that changes in surface water fertility were linked to the Milankovitch parameters. Thus the Bahloul Formation in the four studied sections exhibits duration interval between 350-400 kyr and sedimentation rate interval between 12 and 20 cm/kyr.


Pierre Boulenguez
email: pierre.boulenguez@univ-poitiers.fr

Boris Airieau
email: boris.airieau@univ-poitiers.fr

Mohamed-Chaker Larabi
email: larabi@sic.univ-poitiers.fr

Daniel Meneveaux
email: daniel@sic.univ-poitiers.fr

Towards a perceptual quality metric for computer-generated images

Keywords: Quality metric, computer-generated images, global illumination, psychovisual evaluations, statistical analysis

The physical validation of computer-generated images (CGIs) has received a lot of attention from the computer graphics community, as opposed to the assessment of these images' psychovisual quality. The field indeed lacks the proper tools to quantify the perceptual quality of a CGI; this paper engages in the construction of such a metric. A psychovisual experiment was submitted to a representative panel of observers, where participants were asked to score the overall quality and aspects of this quality for several CGIs. An analytical quality model, fit to the data, next gives insight into the relative perceptual importances of these aspects. Accuracy in the simulation of shadows, good contrast and absence of noise were found to have a major impact on the perceived quality, rather than precise anti-aliasing and faithfull color bleeding.

INTRODUCTION

Realistic computer-generated images (CGIs) have emerged as a key component to such wide-ranging fields as architecture, road traffic, tunnel lighting, archeology, cultural heritage and electronic gaming. These images originate from the vibrant discipline of computer graphics realistic rendering, of which the ultimate goal can be seen as the simulation of every light related phenomena occuring within a given virtual environment.

In view of the theoretical and computational complexity of the task at hand, numerous approaches have specialized in the simulation of diffuse light scattering. [START_REF] Goral | Modeling the interaction of light between diffuse surfaces[END_REF][START_REF] Ward | Irradiance gradients[END_REF] Phenomena induced by non-diffuse light/matter interactions (e.g. gloss, specularity, transparency, caustics, anisotropy) are then rendered separately. [START_REF] Jensen | Global illumination using photon maps[END_REF] A number of studies also have addressed the problem of reducing complexity based on perceptual considerations, [START_REF] Horvitz | Perception, attention, and resources: A decision-theoretic approach to graphics rendering[END_REF][START_REF] Stokes | Perceptual illumination components: a new approach to efficient, high quality global illumination rendering[END_REF][START_REF] Debattista | Selective component-based rendering[END_REF] but the field still lacks a dedicated perceptual quality metric adapted to CGIs. Such a tool would be beneficial to interactive-time rendering, allowing for a focusing on the most perceptually significant phenomena, as well as to off-line simulations, where the stop criterion of the iterative light distribution could be based on perceptual considerations, rather than purely empirical. Comparable perceptually-driven approaches have been employed with great success for speech, audio and video compression. [START_REF]An objective method for end-to-end speech quality assessment of narrowband telephone networks and speech codecs (PESQ)[END_REF][START_REF]Method for objective measurements of perceived audio quality (PEAQ)[END_REF][START_REF]Methodology for the subjective assessment of the quality of television pictures (PEVQ)[END_REF] This paper engages in the construction of such a perceptual quality metric adapted to CGIs. First, the work context at the frontier between rendering and perception is introduced (Section 2). Five criteria of the psychovisual quality of CGIs are then detailed (Section 3). These criteria were assessed by observers through a psychovisual experiment, described along with the statistical tools involved (Section 4). Results obtained are discussed (Section 5). This paper ends with conclusions and perspectives for future research.

RELATED WORK

Work context in rendering

The problem of computing the light distribution within a virtual environment is formalized by the rendering equation. [START_REF] Kajiya | The rendering equation[END_REF] Recursive by nature, it cannot be solved analytically for arbitrary environments and its numerical approximation by realistic rendering approaches is referred to as global illumination.

Monte Carlo integration can be seen as the reference methods for offline simulations. Path-tracing, [START_REF] Kajiya | The rendering equation[END_REF] for instance, estimates radiance impinging on each pixel, following random paths from the camera towards the sources. The approach, although unbiased, results in noisy CGIs unless a considerable number of paths are computed. Refinements such as importance sampling, 11 bidirectional path tracing, [START_REF] Lafortune | Bi-directional path tracing[END_REF] or metropolis methods [START_REF] Veach | Metropolis light transport[END_REF][START_REF] Kelemen | A simple and robust mutation strategy for the metropolis light transport algorithm[END_REF] enhance convergence. Irradiance cache [START_REF] Ward | A ray tracing solution for diffuse interreflection[END_REF][START_REF] Křivánek | Practical global illumination with irradiance caching[END_REF] also reduces computational complexity, using interpolation between accurate samples. They are distributed in the environment and can be reused to compute new images from nearby camera positions. Interpolation results in low-frequency noise and an adequate choice of interpolation parameters is not straightforward. [START_REF] Křivánek | Making radiance and irradiance caching practical: Adaptive caching and neighbor clamping[END_REF] Photon-tracing approaches, 3 on the other hand, construct paths directly from the sources, and simulations are independent from the camera position. The impacts of the paths within the environment are represented as photons, stored in a so-called photon-map. Photon-map-based operators are inherently biased and the resulting CGIs often exhibit low-frequency noise. A final gather stage circumvents the problem but, in turn, introduces high-frequency noise. Photon streaming 18 avoids noise flickering for interactive-time rendering in dynamic environments. Finally, instant-radiosity methods [START_REF] Keller | Instant radiosity[END_REF] represent impacts as virtual point light sources. These methods are unbiased but result in check-pattern-like noise due to multiple shadow casting.

For interactive-time rendering, a compromise has to be found between physical plausibility and severe time constraints. Historically, the ambient term has been seen as the most practical approximation for diffuse lighting. Ambient occlusion 20 can modulate this ambient term using an estimation of occluded light at each viewed position. Finally, environment gather 21 stores light scattered in an environment map.

Work context in perception

The link between perception and rendering is not new. The early years of CGIs were indeed essentially perceptually driven, as the validation of a particular approach was carried out by visual inspection. The orientation towards physically based rendering has lessened the importance of visual assessment for offline simulations, but it remains strong for interactive-time rendering.

In spite of this fundamental relationship, the first formal psychovisual evaluation of CGIs was, to our knowledge, only carried out in a study [START_REF] Wanger | Perceiving spatial relationships in computer-generated images[END_REF] where participants were asked to assess the implications of various visual cues on the rendering of depth. Other experiments were subsequently conducted [START_REF] Wanger | The effect of shadow quality on the perception of spatial relationships in computer generated imagery[END_REF] to evaluate the influence of shadow rendering strategies on the perception of object shape. This research led to the important and somewhat confusing conclusion that less physically accurate shadows may be preferable in some tasks requiring unambiguous perception of the shape.

Another pioneering study 4 concerns the perceptual implications of environment simplifications (e.g. geometry, textures, shading models). An experiment [START_REF] Yu | Perceptual influence of approximate visibility in indirect illumination[END_REF] was, for instance, recently conducted to assess the psychovisual impact of approximate indirect visibility computation and notably their impact on shadow realism.

A number of studies [START_REF] Stokes | Perceptual illumination components: a new approach to efficient, high quality global illumination rendering[END_REF][START_REF] Debattista | Selective component-based rendering[END_REF] have also engaged in selected rendering, which refers to the ability of a given algorithm to deactivate certain features of the rendering process (e.g. direct lighting, indirect diffuse lighting, mirror reflections, glossy reflections, transparency). The perceptual importance of each stage of the rendering process can then assessed by formal psychovisual experiments. In such an experiment, 5 for instance, ten participants were asked to assess the quality of CGIs with indirect diffuse, glossy and direct lighting alternatively activated.

The aformentioned studies aim at reducing the rendering time of a given algorithm while maintaining an acceptable level of perceived quality. To our knowledge, no formal inter-algorithms psychovisual evaluations were conducted. For instance, there is no way to know how, for the diffuse lighting component, the empirical ambient term compares to a physically accurate global illumination simulation, in terms of perceptual quality.

A SET OF CGI'S PSYCHOVISUAL QUALITY CRITERIA

Let {C 1 , . . . , C n } be a set of criteria and Q the overall pyschovisual quality of a CGI. The ultimate goal of this research is to find an optimal function f such that:

Q = f (C 1 , . . . , C n ).
(1)

Ideally, the set {C 1 , . . . , C n } would encompass every possible aspect of a CGI's psychovisual quality. Such a set would obviously have exceedingly large cardinality, and contain criteria that might be fuzzy or non-intuitive. Yet, as each criterion has to be explained to and assessed by participants during the psychovisual experiment, a first set of five criteria, empirically known as important in diffuse environments, was constructed. Those criteria are: color bleeding C b , shadow C s , noise C n , aliasing C a and contrast C c . They are described in the remainder of this section. Color bleeding, denoted C b , is a subtle phenomenon by which the light reflected by a colored surface becomes tinted by the color of that surface. Figure 1 illustrates the effect with colored paper sheets and a diffuse white plate. Closely related to the interreflections in the environment, the phenomenon is difficult to render faithfully without a complete global illumination simulation. Shadows are another key challenge as their appearance has already been identified as critical to a CGI's perceptual quality. The luminosity gradient across a shadow, which tends to be darker in the vicinity of the occulting object, is a particularly difficult aspect to render. Figure 2 illustrates the phenomenon.

Color Bleeding C b

Noise C n

The noise criterion, illustrated in Figure 3, can be distinguished into high and low frequency noise. As stated in Section 2.1, many stochastic rendering approaches, despite accurate global light distribution, are also prone to produce noise.

Aliasing C a

Edge aliasing is a common issue with some rendering methods. Figure 4a details a jagged junction between two walls in the background, while Figure 4b shows the same image with anti-aliasing. Contrast and luminosity are well known attributes of an image. In the context of CGIs, they are dependent on both the main light distribution process, as well as on the quantification stage (or tone mapping), that converts high dynamic range images into standard 8-bit per component images. Figure 5 presents renderings of the same environment with varying contrast and luminosity settings.

SUBJECTIVE QUALITY EXPERIMENT

To evaluate the influence of the criteria {C b , C s , C n , C a , C c } on the overall perceived quality Q, a subjective quality experiment was constructed and carried out. This section describes the procedure in detail. Seven rendering algorithms that produce the effects described in Section 3 were selected: ambient term (AT), ambient occlusion [START_REF] Landis | Production-ready global illumination[END_REF] (AO), environment gather 21 (EG), photon streaming 18 (PS), photon mapping 3 (PM), photon mapping with a final gather pass 3 (FG) and Metropolis light transport 14 (ML). The latter is the most computationally intensive and is considered the most physically plausible.

Seven views from four widely used scenes in computer graphics (see Figure 6) were also chosen. They represent a suitable variability of content for the intended experiment and are freely available. Each scene has been used as input to the aforementioned algorithms in order to generate the subjective experiment stimuli.

Algorithms parametrization

The ML algorithm has been tuned to provide the most accurate rendering, independent of any computational complexity considerations. The other methods were voluntarily used with degraded parameters in order to highlight each criteria.

Precisely, PM and FG CGIs were generated by tracing 200,000 initial photons and storing 1,000,000 photons in the photon-map. The final gather pass was done with 32 rays. AT values have been experimentally set for each scene. AO images were generated with ray-tracing using 64 rays. PS images were generated with 1,024 virtual light sources and 120,000 photons stored. For EG, 128 rays of final gather have been used.

Regarding computation time, PM images were rendered in a few seconds, while their FG counterparts needed several minutes. All other methods only needed a few milliseconds to compute.

Test environment

The experiment was conducted in a dedicated room constructed following the ITU recommendations [START_REF]Methodology for the subjective assessment of the quality of television pictures (PEVQ)[END_REF] and equipped with a 30" LCD monitor with a native resolution of 2,560 × 1,600 pixels. The ratio of inactive screen luminance to peak luminance was kept below a value of 0.02. Lighting was ensured using 4 controlled neon tubes delivering a D50 light, and oriented to obtain 64 lux at the display while avoiding direct illumination. The calibration of the screen was performed using a Gretag Macbeth EyeOne calibration device. The viewing distance was set at 4 times the height of the presented images.

Overall test procedure 4.2.1 Participants

Thirty non-CG-experts participated in the experiment. This number complies with the minimum requirement, 9 even if some outliers are rejected.

The panel of participants has been characterized in terms of gender, occupation and age, but also in terms of knowledge in computer science and computer graphics. In particular, 21 males and 9 females participated. They were, overall, university staff and students, and their ages were distributed in the range of 23 to 51 years with the average age being 31.4 years.

Stimuli presentation

The experiment was constructed as a three-staged procedure: Initially, background information on the participant was gathered. Notably, visual acuity and color blindness were checked (using FrACT 26 and Ishihara plates) and a small quiz waz administered (see questionnaires 25 ).

Next, the evaluation procedure and the significance of each criterion were explained to the participant. A normalized speech illustrated by slides was used. The participant was invited to ask questions if needed and had access to the slides during the evaluation stage.

Finally, the evaluation per se consisted in presenting the 49 CGIs in a fully random order (in order to average training bias). For each CGI, the participant was asked to assess its overall quality Q and the five criteria {C b , C s , C n , C a , C c } (cf. Section 3). As there is no reference in the field (although ML can be seen as the most physically accurate), the selected protocol is a single-stimulus one without time limitation. The scoring was done on a continuous scale without numbers but divided in an odd number of sections with two quality adjectives (poor and excellent).

Statistical analysis 4.3.1 MOS and confidence intervals

The Mean Opinion Score (MOS) ūk was computed for each presentation:

ūk = 1 N N i=1 u ik , (2)
where u ik denotes the score of the i th observer for the k th image and N = 30 is the number of participants. The confidence interval associated with the MOS is given by:

⌊ū k -δ k , ūk + δ k ⌋. (3)
The deviation term δ k is given for a 95% confidence interval, calculated as follows:

9 δ k = 1.96 σ k √ N , (4)
where σ k is the standard deviation.

One of the objectives of the statistical analysis was to be able to eliminate from the final results either a particular score or observer (outlier). In this paper, the method based on the Kurtosis coefficient 9 was employed.

Analytical modeling

Although the construction of an optimal quality function f (cf. Equation 1) is the ultimate goal of this research, as a first step, a linear regression was applied to establish a hierarchy in the contribution of each criterion on the overall perceived quality Q:

Q = β b C b + β s C s + β n C n + β a C a + β c C c + β 0 , (5)
where {β b , β s , β n , β a , β c } are the independent contributions of the criteria {C b , C s , C n , C a , C c } and β 0 is the intercept term.

RESULTS AND DISCUSSION

Figure 7 provides Mean Opinion Scores (MOS) and associated intervals for the seven view/algorithm combinations (as well as the average over the whole data set). The scores are presented with radar graphs in order to ease their interpretation. Figure 7h shows that noise C n was easy to score because the values are spread over almost the entire scale range. As expected, ML obtained the highest scores for all the psychovisual criteria and can be used to calibrate the data in order to fill a larger range.

The results for the seven views are quite consistent with the average, especially for noise C n . However, some differences related to the content exist. For example, the shadow criterion C s has a different shape from one view to the other. The same can be said for the overall quality Q. Figure 7e and 7f show that even if two views come from the same scene, the judgment of the observers can be singularly different. Indeed, there is important variation in terms of structures, lighting effects, etc.

An analysis of covariance (ANCOVA) was conducted to compare one criterion in two or more groups, taking into account variability of other criteria. Table 1 gives the output of the covariance analysis for the five criteria {C b , C s , C n , C a , C c }. For each criterion, two different questions were addressed: (1) Is the overall quality Q related significantly to the criterion? and (2) For the same MOS of a criterion, does the overall quality Q vary according to the view? To answer those questions, the F of Fisher and its associated probability (Pr) were used. Very low values of Pr mean that the variables provide significant information to the model. For example, the Pr related to contrast C c is extremely low (compared to the threshold of 0.05), leading to the conclusion that this criterion is significantly related to the overall quality Q; it is indeed the case for the five selected criteria. For the second question, the statistical analysis indicates that appart from noise C n and aliasing C a , the relationship between a criterion and the overall quality Q is not affected by scene or viewpoint. 5) for the five criteria. An immediate and major observation is that color bleeding C b and aliasing C a have significantly lower contributions (i.e. observers have not given a high importance to these attributes) than the other criteria. A possible explanation for this lower contribution could be the implicit combination of these attributes with the others. On the other hand, contrast C c has an important effect on the overall quality Q (approx. 39%), followed by shadow C s and noise C n . In Section 3) on the seven views (cf. Figure 6) and for the seven algorithms (cf. Section 4.1.2). Average of the seven views is plotted in 7h.

addition to this, R 2 , which measures the quality of the regression, indicates that the criteria selected explain up to 50% of the variation of the overall quality Q. It also means that there are other criteria that have to be taken into account, some of them may be implicit or difficult to formulate.

CONCLUSION

Study of the perceptual quality of computer-generated images through psychovisual experiments is vibrant. In this paper, such an experiment was presented, to assess the influence of five measurable psychovisual criteria, color bleeding, shadows, noise, aliasing and contrast, on the overall quality. Seven computer graphics rendering algorithms were used for the construction of the evaluation. A reprensentative panel of thirty observers participated to the experiment. The statistical analysis showed that among the five criteria, contrast, noise and shadows have a major effect on the overall quality, rather than color bleeding and aliasing. The future direction of this work is to study the correlation between automatically measured human judgment criteria.

Figure 1 :

 1 Figure 1: Illustration of the color bleeding criterion (real case).

3. 2

 2 Shadows C s (a) Flat shadow. (b) Gradient shadow.

Figure 2 :

 2 Figure 2: Illustration of the shadows criterion.

  (a) High frequency noise. (b) Low frequency noise.

Figure 3 :

 3 Figure 3: Illustration of the noise criterion.

  (a) Aliased rendering. (b) Anti-aliased rendering.

Figure 4 :

 4 Figure 4: Illustration of the aliasing criterion.

3. 5

 5 Contrast C c (a) Uneasy contrast. (b) Comfortable contrast.

Figure 5 :

 5 Figure 5: Incidence of the contrast criterion.

  Sponza I. (f) Sponza II. (g) Cornell Box.

Figure 6 :

 6 Figure 6: The seven views and corresponding scenes used for the experiment. The whole data set (49 CGIs) was made available online.25

25

 25 Figure 6: The seven views and corresponding scenes used for the experiment. The whole data set (49 CGIs) was made available online.25

  Color Bleeding C b Shadows C s Noise C n Aliasing C a Contrast C c

Figure 7 :

 7 Figure7: MOS and confidence intervals for the five criteria (cf. Section 3) on the seven views (cf. Figure6) and for the seven algorithms (cf. Section 4.1.2). Average of the seven views is plotted in 7h.

Table 1 :

 1 Analysis of covariance between criteria {C b , C s , C n , C a , C c } and overall quality Q. For each criterion, the first line answers question (1) and the second line question (2).

		Df Sum Sq Mean Sq	F value	Pr(>F)
	C b C b :view	1 6	16.377 0.402	16.377 0.067	319.261 < 2.2 × 10 -16 1.305 0.252
	C s C s :view	1 6	22.127 0.421	22.127 0.070	459.857 < 2.2 × 10 -16 1.458 0.189
	C n	1	10.957	10.957	201.1214	< 2.2e-16
	C n :view	6	1.229	0.205	3.761	0.001
	C a C a :view C c C c :view	1 6 1 6	9.354 1.524 32.330 0.205	9.354 0.254 32.330 0.034	173.704 < 2.2 × 10 -16 4.717 9.146 × 10 -05 778.832 < 2.2 × 10 -16 0.824 0.551

Table 2 :

 2 Regression coefficients and output.

	β b	β s	β n	β a	β c	β 0	R 2	Std. Err.	DF
	0.0693 0.2507 0.2138 0.0322 0.3888 -0.0519 0.507	0.1806	1375

Table 2

 2

gives the linear regression coefficients (cf. Equation

AKNOWLEDGEMENTS

The authors wish to thank the projects UE-FEDER NAVII and ANR QUIAVU for funding, Romuald Perrot for his help on the implementation of the ML algorithm, and the thirty participants to the experiment.