Sarah Bellini
email: sarah.bellini@irstea.fr

Ryad Bendoula

Eric Latrille

Jean-Michel M Roger

Potential of a spectroscopic measurement method using Adding-Doubling to retrieve the bulk optical properties of dense microalgal media

Keywords: Dense microalgal culture monitoring, multiple light scattering, inverse adding-doubling, bulk optical properties, radiative transfer theory

In the context of algal mass cultivation, current techniques used for the characterization of algal cells require time-consuming sample preparation and a large amount of costly, standard instrumentation. As the physical and chemical properties of the algal cells strongly affect their optical properties, the optical characterization is seen as a promising method to provide an early diagnosis in the context of mass cultivation monitoring. This article explores the potential of a spectroscopic measurement method coupled with the inversion of the radiative transfer theory for the retrieval of the bulk optical properties of dense algal samples. Total transmittance and total reflectance measurements were performed over the 380-1020nm range on dense algal samples with a double integrating sphere setup. The bulk absorption and scattering coefficients were thus extracted over the 380-1020nm range by inverting the radiative transfer theory using inverse-adding-doubling computations. The experimental results are presented and discussed: the configuration of the optical setup remains a critical point. The absorption coefficients obtained for the four samples of this study appear not to be more informative about pigment composition than would be classical methods in analytical spectroscopy, however there is a real added value in measuring the reduced scattering coefficient, as it appears to be strongly correlated to the size distribution of the algal cells.

Introduction

Autotrophic microalgae are seen as a promising source of biomass for various applications such as high-value chemicals extraction, [START_REF] Dufossé | Microorganisms and microalgae as sources of pigments for food use: a scientific oddity or an industrial reality?[END_REF] animal and human food 2 and energy production. [START_REF] Cadoret | La production de biocarburant lipidique avec des microalgues : promesses et défis[END_REF] Consequently, the global mass production of microalgae has largely increased over the last decade. [START_REF] Cadoret | La production de biocarburant lipidique avec des microalgues : promesses et défis[END_REF] However, the current techniques used for the characterization of the algal cells all along the growth process require time-consuming sample preparation, a large amount of costly, standard instrumentation and cannot usually be performed in situ.

New tools are needed to optimize the monitoring of the cultivation process by providing a faster and simpler measurement of the microalgal cells physical and chemical states. For this purpose, utilizing visible (VIS) and near infrared (NIR) spectroscopy [START_REF] Williams | Near-Infrared Technology in the Agricultural and Food Industries[END_REF] is looked as a promising solution since the measurements can be performed with minimum or no sample preparation, with instruments presenting a high signal-to-noise ratio. Moreover, previous studies demonstrated that the absorption and scattering coefficients of microalgal suspensions in the VIS-NIR domain depend heavily on the chemical characteristics [START_REF] Morel | Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications[END_REF][START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF] (mainly nature and concentration of pigments) and physical characteristics [START_REF] Williams | Near-Infrared Technology in the Agricultural and Food Industries[END_REF][START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF][START_REF] Zaneveld | The variation in the inherent optical properties of phytoplankton near an absorption peak as determined by various models of cell structure[END_REF][START_REF] Aas | Influence of shape and structure on light scattering by marine particles[END_REF][START_REF] Ciotti | Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient[END_REF][START_REF] Morel | Theoretical results concerning light absorption in a discrete medium, and application to specific absorption of phytoplankton[END_REF][START_REF] Quirantes | Light scattering by marine algae: two-layer spherical and non-spherical models[END_REF][START_REF] Kirk | A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters. I. General treatment of suspensions of pigmented cells[END_REF][START_REF] Kirk | A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters. II. Spherical cells[END_REF][START_REF] Kirk | A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters. III. Cylindrical and spheroidal cells[END_REF] of the cells (size, density of the cells). Retrieving the bulk optical properties of dense microalgal media has great potential for the advanced diagnosis in micro-algae cultivation processes. [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF][START_REF] Lee | Spectral optical properties of selected photosynthetic microalgae producing biofuels[END_REF][START_REF] Cornet | Modeling photoheterotrophic growth kinetics of Rhodospirillum rubrum in rectangular photobioreactors[END_REF] In a context of an algal cultivation process, cell density is very high (10 6 -10 9 cell/mL) which makes the scattering phenomena significant. Recent studies [START_REF] Reis | Spectroscopic on-line monitoring of reactions in dispersed medium: Chemometric challenges[END_REF][START_REF] Lu | Comparison of Methods for Reducing the Effects of Scattering in Spectrophotometry[END_REF] have showed that the data extraction from spectroscopic measurements performed on turbid samples is highly complicated by the influence of the scattering phenomena on the spectra. Yet, several studies [START_REF] Burger | Quantitative Determination of the Scattering and Absorption Coefficients from Diffuse Reflectance and Transmittance Measurements: Application to Pharmaceutical Powders[END_REF][START_REF] Steponavicius | Extraction of chemical information of suspensions using radiative transfer theory to remove multiple scattering effects: application to a model two-component system[END_REF][START_REF] Steponavicius | Extraction of chemical information of suspensions using radiative transfer theory to remove multiple scattering effects: application to a model multicomponent system[END_REF] demonstrated that the separate consideration of the absorption and scattering coefficients could greatly improve the extent of information extracted from the spectral measurements. In particular, the prospects of a method to retrieve the bulk optical properties from diffuse reflectance and transmittance measurement by inverting the radiative transfer equation have been showed [START_REF] Dzhongova | Changes in the Absorption and Scattering Properties in the Near-Infrared Region During the Growth of Bacillus subtilis in Liquid Culture[END_REF] for the monitoring of bacterial growth.

Several research groups have investigated methods to measure simultaneously the absorption and scattering properties of algal samples. [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF][START_REF] Berberoglu | Experimental measurements of the radiation characteristics of Anabaena variabilis ATCC 29413-U and Rhodobacter sphaeroides ATCC 49419[END_REF][START_REF] Daniel | Optical properties measurements in suspensions of unicellular algae[END_REF] However, they generally involve sample preparation such as filtering [START_REF] Floc'h | An automatic device for in vivo absorption spectra acquisition and chlorophyll estimation in phytoplankton cultures[END_REF] or may have to be combined with additional measurements in order to determine completely both the absorption and scattering signals. [START_REF] Davies-Colley | Optical properties and reflectance spectra of 3 shallow lakes obtained from a spectrophotometric study[END_REF] Certain technical difficulties [START_REF] Berberoglu | Experimental measurements of the radiation characteristics of Anabaena variabilis ATCC 29413-U and Rhodobacter sphaeroides ATCC 49419[END_REF][START_REF] Davies-Colley | Optical properties of some freshwater phytoplanktonic algae[END_REF] still have to be overcome in the measurement of scattering.

This study is a first approach to investigate the potential of a spectroscopic method coupled with inverse-addingdoubling (IAD) computation [START_REF] Prahl | Determining the optical properties of turbid media using adding doubling method[END_REF] applied to microalgal samples. The method is tested on four dense microalgal samples over the [380-1020nm] range. The soundness of the absorption and reduced scattering coefficient spectra obtained is analyzed. The interest of using these coefficients to characterize the algal samples in addition or in place of classical spectral measurement is also investigated.

This study shows that the method remains hard to apply in practice. The configuration of the optical setup [START_REF] Pickering | Two integrating spheres with an intervening scattering sample[END_REF] is a critical point that may be difficult to achieve properly, what can introduce significant light losses in the measurements and errors in the estimation of the absorption and reduced scattering coefficient absolute values [START_REF] Vries | The effect of light losses in double integrating spheres on optical properties estimation[END_REF] . The absorption coefficients obtained for the four samples of this study appear not to be more informative about pigment composition than would be classical methods in analytical spectroscopy, like processing on reflectance and transmittance spectra. However there is probably a real added value in measuring the reduced scattering coefficient, as it appears to be strongly correlated to the size distribution of the algal cells.

Theory

Microalgal cells can be considered as suspended particles in water that significantly absorb and scatter incident light. In that case, the transport theory [START_REF] Bohren | Absorption and scattering of light by small particules[END_REF] is the rigorous expression of the light radiance variation in space:

d ( , , λ) d = -μ λ . , , λ + μ λ 4π ( , ′) ( , ′, λ)dω′ + ε , , λ (1)
Where I(r, s, λ) is the spectral radiance at point r of input radiation propagating along direction s, ( , ′) is the phase function measuring the angular distribution of scattered light with respect to the input direction, µ ext (λ) [=µ a (λ)+µ s (λ)] is the bulk extinction coefficient, µ s (λ) (mm -1 ) is the bulk scattering coefficient, µ a (λ) (mm -1 ) is the bulk absorption coefficient and ε , , λ is a source term. In this study, the phenomena of fluorescence introduced by the photopigments were considered as negligible, which sets the source term to zero.

For a medium composed of different species, the usual assumption [START_REF] Steponavicius | Extraction of chemical information of suspensions using radiative transfer theory to remove multiple scattering effects: application to a model two-component system[END_REF] is to consider that the bulk scattering and absorption coefficients are the sums of the coefficients of each individual species j:

μ λ = μ , (λ) (2) μ λ = μ , (λ)
The phase function p can be approximated by a function of the scattering angle θ and the anisotropy factor g (defined as = < cos θ > ). It is usual to choose the empirical Henyey-Greenstein phase function [START_REF] Flock | Total attenuation coeffcients and scattering phase functions of tissues and phantom materials at 633nm[END_REF] expressed by:

(cos θ) = 0.5 1 - (1 + -2 cos θ) . (3)
It is usual to define also the reduced scattering coefficient µ s' such that:

μ = μ (1 -) (4)
Equation ( 1) thus describes spectral radiance of a beam as it propagates inside a medium as a function of the bulk optical properties, µ a , µ s and g of that medium. With proper boundary conditions depending on the geometry of the system, it is possible to retrieve the light variations when µ a , µ s and g of the sample are known. Adding-doubling method was introduced in atmospheric sciences by van de Hulst 33 to solve the transport equation in slab geometry. A comprehensive software was developed by Prahl [START_REF] Prahl | The Adding-Doubling Method[END_REF] for his own work on light distribution in biological tissues and is available on the website http://omlc.ogi.edu/software/. The method is adapted to solve (1) in any situation with no restriction on the ratio between scattering and absorption, no restriction on the scattering anisotropy and it includes reflection at the boundaries of the sample. A reduced set of assumptions [START_REF] Prahl | Everything I think you should know about Inverse Adding-Doubling[END_REF] specifies the scope of validity of the method: no time dependence, description of the sample as the union of optically uniform layers of finite thickness and infinite extent along directions parallel to the surface, uniform illumination by collimated or diffuse light.

In adding-doubling theory, the reflection and transmission properties of a slab are described by its reflection and transmission matrices that give the signals reflected and transmitted by the slab at different solid angles in space.

If the transmission and reflection matrices of two individual layers are known, one can compute the successive reflection and transmission between the two layers and can thus deduce the reflection and transmission matrices of their combination. With that principle, the reflection and transmission properties of a homogenous slab of sample of thickness z can be computed by starting with an infinitely thin layer represented by its optical characteristics: the anisotropy factor g, the albedo a and the optical thickness τ such that:

= μ + μ d (5)

= μ μ + μ

With dz the unite thickness of the slab. Equation (1) can be discretised for an infinitely thin layer and solved thanks to the diamond initialization method. [START_REF] Wiscombe | On initialization, error and flux conservation in the doubling method[END_REF] The reflection and transmission matrices of the initialization layer are thus obtained.

Once the reflection and transmission of the initialization layer are known, it is possible to calculate the new reflection and transmission matrices of the combination of two initialization layers. By iterating that process one can calculate the reflection and transmission matrices of any slab of thickness z.

The inverse problem is the retrieval of the bulk optical coefficients from measurements describing light variations in space: it can be solved with inverse-adding-doubling. [START_REF] Prahl | Determining the optical properties of turbid media using adding doubling method[END_REF] The radiance throughout the sample can be characterized by measuring total reflectance , total transmittance and regular transmittance with a dedicated double integrating sphere setup. In that case the inversion makes it possible to retrieve all three coefficients µ a , µ s and g. The inverse algorithm first calculates with the adding-doubling principle the values of total reflectance and total transmittance from an initial triplet of optical characteristics (a,τ,g). The error between the estimated reflectance and transmittance and the measured values is then estimated by the quantity M:

, τ, = | - | + 10 + | - | + 10 (6)
The optimization of the triplet (a,τ,g) is obtained by minimizing the error M by means of an n-dimension minimization algorithm. It is thus possible to deduce a triplet of optical characteristics (a,τ,g) that matches the one of the measured sample.

Because the measurement of T coll is generally problematic, [START_REF] Steponavicius | Extraction of chemical information of suspensions using radiative transfer theory to remove multiple scattering effects: application to a model two-component system[END_REF] it is also usual to apply inverse adding-doubling with only two measurements (of R tot and T tot ). In that case, the anisotropy coefficient g is fixed and only the absorption coefficient µ a and the reduced scattering coefficient µ s' are calculated by the inversion process. As illustrated by the study of Dzhongova et al. [START_REF] Dzhongova | Effects of sample thickness on the extracted nearinfrared bulk optical properties of bacillus subtilis in liquid culture[END_REF] and as discussed by Prahl, [START_REF] Prahl | Everything I think you should know about Inverse Adding-Doubling[END_REF] using poor collimated transmittance signals with inverse-adding-doubling method generates many errors in the computation of scattering and absorption coefficients. Better results are obtained by only using and and approximating the phase function p with the empirical Henyey-Greenstein phase function. [START_REF] Flock | Total attenuation coeffcients and scattering phase functions of tissues and phantom materials at 633nm[END_REF] That is why the latter solution was implemented in the case of this study.

Material and methods

Experimental design

Four mixed populations of Scenedesmus and Chlorella were grown in four distinct external ponds numbered S1, S2, S3 and S4, at Laboratoire de Biotechnologie de l'Environnement (LBE), Narbonne (INRA France). Illumination was provided by the sun and no specific temperature regulation was applied. Mixing and bubbling were carried out with a pump system. Nutrients were provided by regular inputs of fertilizer (ANTYS®8, Fertil France). Samples were taken at 3 p.m. from each pond and entirely characterized using standard methods in the shortest time possible in order to minimize the impacts caused by a change in the algal culture environment. In the meantime the spectroscopic measurements of R tot and T tot were performed on each sample.

Measurement of total reflectance and total transmittance spectra

Optical setup

A detailed description of the optical measurement setup and its principle can be found elsewhere. [START_REF] Pickering | Two integrating spheres with an intervening scattering sample[END_REF][START_REF] Pickering | Double integrating-sphere system for measuring the optical properties of tissue[END_REF] Figure 1 illustrates the different measurement configurations. Total reflected signal I R,tot was collected in the first integrated sphere (Figure 1 (a)) in contact with the sample side reached by the incident light beam I 0 . The incident light beam was tilted with an angle θ of 8° from the optical axis to ensure that the regular reflected signal (1) was collected inside the reflectance sphere. Total reflectance signal I R,tot thus measured included both regular (1) and diffuse (2) reflected light. Total transmitted signal I T,tot was collected with the second integrating sphere (Figure 1 (b)) aligned with the incident beam direction and in contact with the other side of the sample. I T,tot included both regular (3) and diffuse (4) transmitted light. Total reflectance R tot and total transmittance T tot were calculated such that:

= , -, , -,
Author-produced version of the article published in Applied Spectroscopy, 2014, N°10 (68), p. 1154-1167. The original publication is available at http://www.ingentaconnect.com http://dx.doi.org/10.1366/13-07308

(7) = , -, , -, (8)
Where I R,std is the signal measured in the reflectance sphere when the sample is replaced by a standard reflectance. The standard reflectance used in this study was a spectralon (LabSphere) with a spectral reflectivity r std close to 0.98 on the spectral domain considered. The values of r std were provided by the manufacturer. I T,1 is the signal measured in the transmittance sphere when the input beam directly reaches the transmittance sphere (sample removed). I R,0 and I T,0 are the signals measured respectively in the reflectance and transmittance spheres when the input light beam I 0 is stopped.

The double integrating sphere configuration imposed that the sample cell was positioned outside of the spheres: in practice this meant that for one sphere, the actual solid angle where the reflected or transmitted light was collected was smaller than 2π sr. A significant amount of light ((5) on figure 1) could thus leak in directions that were not detected by the spheres, at the edges of the sample cell and at the sphere ports. In order to limit at best those effects, the sample cell thickness, the sample cell position, the incident light beam size upon the sample and the diameters of the spheres ports were carefully adapted. In the case of this study, the solid angle detected by one sphere could be optimized to reach approximately 1.7π sr.

Ten measurements of R tot and T tot were collected for each sample, what made it possible to limit the effects of the experimental conditions. The measurements were conducted using 30mm-diameter reflectance and tramsittance spheres (AvaSphere-30, Avantes) fibered with 1mm-core low OH optical fibers (Ocean Optics). Illumination was provided by a tungsten halogen light source (HL -2000, Ocean Optics) and the spectral acquisition was carried out using a spectrometer (MMS1, Zeiss). The temperature fluctuations of the light source were limited by turning on the lamp at least one hour before beginning the measurements: this lapse of time was observed to be sufficient for the light source to be as stable as possible. The integration time varied between 4000 and 6500ms depending on the signal measured. Liquid samples were put in quartz cells (100-QS, Hellma) with a 10mmoptical thickness and maintained between the two spheres thanks to a customized cell holder fitted to the bench dimensions. The measurements were made in the spectral region between 380 and 1020nm with 10nm resolution intervals and 3nm step intervals.

Determination of the errors in the spectroscopic measurement procedure Ten measurements of T tot spectra were conducted on the same algal sample and put in a matrix X with dimension 10 x p where p is the number of wavelengths:

× X was analyzed by means of a Principal Component Analysis (PCA) [START_REF] Martens | Multivariate Calibration[END_REF] which made it possible to approximate it by the matrix such that:

= × × ×
Where S and L are respectively the matrices of the scores and of the loadings, and k the number of loadings. The loadings obtained were the eigenvectors describing a new linear vector space where T tot spectra were represented by the values of their scores, which were their coordinates in that space. The advantage of the vector space found with PCA was that it had a smaller dimension than the original space of description of the T tot spectra and was thus easier to analyze. A hundred noise spectra were then simulated by randomly choosing the values of the scores, and put in the matrix N: Where ℵ is a normal law centered on zero with standard deviation 1 and the diagonal matrix of the scores satandard deviation values. Those simulated noise spectra were added to an averaged T tot spectrum in order to simulate a hundred replicates of total transmittance measurements on the same sample.

× = ℵ × 0,1 × ( ) × × Author-
× = × + ×
The spectral standard deviation of the set of T tot spectra stored in M Ttot was then calculated and used to characterize the errors on the measurement procedure of T tot .The same method was applied to estimate the error on the total reflectance measurement, and the matrix M Rtot of one hundred simulated R tot spectra was calculated. This procedure was conducted for the four algal samples: for each sample the M Ttot and M Rtot matrices were obtained.

Computation of absorption and reduced scattering spectral coefficients

Inverse-adding-doubling computations were performed on the measured spectra of R tot and T tot using software developed by Prahl [START_REF] Prahl | The Adding-Doubling Method[END_REF] and run with MatLab (R2012b version). The real part of the refractive index of the cell slab was set as 1.46 according to manufacturer data and considered as constant over the spectral region studied. The real part of the refractive index of the sample solutions was measured at 598 nm using an Abbe refractometer (NAR-1T, Atago) and assumed to be constant as well over the visible spectral range, and set as n algal sample =1.334.

According to the measurements published by Lee et al., [START_REF] Lee | Spectral optical properties of selected photosynthetic microalgae producing biofuels[END_REF] the anisotropy factor g was fixed to 0.98 throughout the [380-1020nm] spectral domain.

Propagation of the measurement procedure errors in the IAD computation For each sample, the impact of the measurement errors on the IAD results was estimated by calculating the absorption and scattering coefficient spectra of a hundred possible doublets of R tot and T tot . Those doublets were built by randomly associating a vector of the matrix M Ttot to a R tot coming from M Rtot .

For each sample, one hundred spectra of possible absorption coefficient and one hundred spectra of possible reduced scattering coefficient were obtained. It was thus possible to estimate the variation of the µ a and µ s' spectra originating from the errors in the measurements. The mean value and the standard deviation of the µ a and µ s' spectra were calculated.

Measurement of cell number and size

Cell number and size of each sample were determined by mean of a Z2 Coulter Counter (Beckman Coulter): samples were diluted in isotonic solution by a factor of 1/200 and the counting was carried out on a 0.5mL volume aliquot. The particle volume was represented in terms of equivalent spherical diameter (ESD), i.e. the diameter of the sphere having the same volume as the particle of interest. By summing the volumes occupied by the cells of increasing size, the total biovolume of the sample was obtained (figure 2). The size distribution was calculated by normalizing by the total biovolume (figure 3). Microscopic observations and counting were conducted concurrently using a BX40 phase-contrast microscope (BX40, Olympus) and Toma counting cells.

Measurement of Chlorophyll concentrations

Chlorophyll a (Chl a) and chlorophyll b (Chl b) contents of the algal samples were determined through pigment extraction and colorimetric measurements. Solutions containing 2 × 10 6 cells were obtained after centrifugation (19000 × g, 10min). 1mL of acetone was added and mixed by vortexing. The volume solution was completed at 2mL with acetone and mixed again. The sample was then put in ultrasound tub for 60min and centrifuged (19000 × g, 8 min). Absorption coefficient of the obtained supernatant at 664nm and 647nm was then measured using a Shimadzu spectrophotometer, and correction was applied by subtracting acetone absorption. The pigment concentrations [Chl a] and [Chl b] were calculated using the spectrophotometric equations of Porra et al. [START_REF] Porra | Determination of accurate extinction coefficients and simultaneous equations for assaying chlorophylls a and b extracted with four different solvents: verification of the concentration of chlorophyll standards by atomic absorption spectroscopy[END_REF] The intracellular pigment concentration was computed according to Bricaud et al. definition [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF] :

ℎ = ℎ . π. 6 (9)
Where N/V is the cell number density in the medium, d the mean cell diameter (m) and [Chl] the concentration of chlorophyll in the extraction (g.m -3 ).

Results and discussion

Sample characteristics Sample composition

Microscopic observations revealed that the main mesoscopic constituents of the samples were microalgal cells: no significant amount of detrial particles was observed, and no particular bacterial population was detected, which was confirmed by the granulometric results indicating no significant amount of small particles (< 3µm). In a first approach, the samples were thus considered to be exclusively composed of algal cells and water. The impact of dissolved nutrients was also judged negligible in the framework of this study.

Cell size distribution

On the ordinate axis, figure 2 shows the total biovolume in mm 3 taken up by algal cells whose diameters are inferior to the value given on the abscissa axis. Cell diameters are distributed over a range from 3µm to 10µm. Total biovolume is read for x = 10µm. Sample S4 biovolume is the smallest. S2 and S3 present the same total biovolume. Figure 3 shows the same results but this time the biovolume is normalized by the total biovolume: this makes it possible to directly compare the size distribution profiles of the cells in the different sample algal suspensions. Consequently we observe that S3 biovolume is mainly made up of big cells, whereas S2 biovolume principaly consists of small cells. This indicates that two pairs of samples can be clearly differentiated: the pair 1-4 with samples having similar size distribution profiles but significantly different total biovolumes, and the pair 2 -3 with samples presenting considerably distinct size distribution profiles but similar total biovolumes.

Chlorophyll concentrations

Table I shows the intracellular pigment concentrations measured for Chl a, Chl b and the total pigment concentration, approximated as the sum of the two chlorophylls. The four sample algal populations are distinctly pigmented: the intracellular total chlorophyll concentration for S4 is 6 times that of S1 and S3 and reaches the value of 12. 2±0.6 × 10 3 g.Chl.m -3 . S1 and S3 present intracellular total pigment rates that are comparable. However Chl a proportion is much higher in S1 (74% of total pigment) than in S3 (64% of total pigment). S2 has the lowest concentration in chlorophyll with an intracellular total pigment concentration that is half those of S1 and S3, for a value of 1.03±0.05 × 10 3 g.Chl.m -3 .

Raw reflectance and transmittance spectra

Total transmittance and total reflectance Total transmittance and total reflectance spectra were measured using the double-integrating sphere setup. Figure 4 (a) shows the raw total reflectance spectra measured for the four samples. The error bars are set to plus or minus twice the standard deviation.

For the four samples, the measurements were made with a relative error that does not exceed 6% of the value on the [400-950nm] spectral range. As expected, the uncertainty grows dramatically at the upper and lower limits of the detection range of the spectrometer, reaching up to 20% at 1020nm and 10% at 380nm. The position of the sample cell, the fluctuations in time of the light source and the noise of the spectrometer at the limits of its detection bands were identified as the major experimental factors introducing variation in the measurements. It had been observed that the angular position of the sample significantly influenced the signals measured, and particularly the regular reflected signal. This explained why a small angular deviation of the cell would dramatically change the amount of total reflected light collected in the sphere. Therefore, special care was taken in positioning the sample cell at each replicate to limit the impact of the cell position.

R tot spectra consistently illustrate the chemical composition of the samples: they show three major spectral regions where the reflected signal is lower: the [400-550nm], [650-700nm] and [900-1020nm] bands. This originates from the significant absorption phenomena occurring at these wavelengths, due to the presence of pigments ([400-550nm] and [650-700nm] bands) and water ([900-1020nm] band) in the samples. The measurements of T tot were conducted with a relative error lower than 4% throughout the [400-1000nm] spectral domain. As for R tot , the limitation of the spectrometer introduces higher uncertainty for the lower wavelengths. T tot measurements appear to be less sensitive to the experimental conditions than R tot measurements. This is explained by the fact that the Signal To Noise (SNR) ratio is higher for the T tot than for R tot due to higher levels. Moreover, the transmitted signal collected is less dependent on the angular cell position than R tot.

T tot spectra show the same absorption bands as observed for R tot .

Figure 5 (a) shows the fraction of incident light that has not been collected in the double-sphere setup: it is expressed as 1-(R tot +T tot ) . It can be seen that less than 100% of the incident light is actually detected by the measurement system, which originates from expected absorption phenomena inside the sample as well as supplementary, unwanted light losses depending of the configuration of the optical setup.

A qualitative analysis of the shape of the spectra makes it possible to identify three major effects, as shown by figure 5 (b): a baseline, a decreasing trend with increasing wavelength and absorption peaks.

The baseline indicates that a portion of incident light has been lost in a way that does not depend on the wavelength. Those losses may originate from the geometrical configuration of the measurement setup and the thickness of the sample as explained previously.

The linear decreasing trend with increasing wavelength may represent light losses due to scattering phenomena, that are expected to be wavelength dependant and higher in the lower wavelengths. A linear approximation of the four different spectra shows that the slope is the highest for sample S4. In decreasing order come S3, S1 and S2.

Finally, a significant amount of light is absorbed within the sample with a particular spectral pattern depending on the chemical absorbers. The three majors absorption bands previously identified are also clearly visible on the spectra.

The first and second derivatives are usual preprocessing methods in analytical spectroscopy to remove additive effects on the spectra [START_REF] Rinnan | Review of the most common pre-processing techniques for near-infrared spectra[END_REF] . The first derivative removes only the baseline and the second derivative removes both baseline and linear trend. It can be achieved by the Savitzky-Golay derivation method. [START_REF] Savitzky | Soothing and differentiation of data by simplified least squares procedures[END_REF] Figure 5 (c) shows the spectra obtained by calculating the second derivative of the quantity 1-R tot -T tot. Eight main absorption peaks can thus be identified, and are presented in table II. They are consistent with many studies on microalgal pigments reported in Aguirre-Gomez et al. [START_REF] Aguirre-Gomez | Identification of algal pigments using high order derivatives[END_REF] It has to be noted that convergence of the inverse-adding-doubling program appears to be erroneous for sample S2 beyond λ = 700nm since the reduced scattering coefficient obtained is null. This indicates that the results computed with the IAD in the case of this study must be handled critically. In particular, the effect of the unwanted light losses in the measurement setup described previously (figure 1, ( 5)) has to be taken into consideration. The study of de Vries et al. [START_REF] Vries | The effect of light losses in double integrating spheres on optical properties estimation[END_REF] showed that in the case of samples with low absorption and high scattering coefficients, those unwanted light losses may be interpreted by the IAD algorithm as absorption phenomena inside the sample rather than losses in the outside world, which would lead to an overestimation of the absorption coefficient. The quantitative values of the µ a and µ s' computed with IAD may then be dependent on the optical setup with which the measurements were conducted. It can also be conjectured that the results obtained with a given optical setup for two objects with different ranges of optical characteristics (distinct order of magnitude for the optical thickness and albedo) could not be compared. This is why the absorption and reduced scattering coefficients computed in the framework of this study should only be treated qualitatively.

Absorption

From figure 6 (a) it can be seen that the relative estimation error on the µ a values computed largely depend on the wavelength. It is quite high throughout the spectrum (more than 6% and up to 17% at 750nm) except on the main absorption bands (the [400-550nm], [650-700nm] and [900-1000nm] bands) where it is as low as 4%. This is probably explained by the fact that the absorption coefficient is much higher on those spectral domains, what significantly reduces the relative error. As what was observed on R tot and T tot spectra (figure 4), absorption spectra are mainly shaped by the absorption of the photosynthetic pigments. µ a spectra show the same absorption peaks as those previously identified with the second derivative on the raw measurement spectra (table II).

For two samples, the overlap of the error bars indicate that their µ a values at that wavelength cannot be considered as different. From this it appears that the µ a spectra of the four samples are quite similar throughout the considered spectral domain, except on the [380-550nm] and [650-710nm] bands where they can be distinct. It can be observed in particular that the four µ a spectra are completely overlapping on the [900-1000nm] band corresponding to the absorption of water. This is not surprising, as the water volume was significantly higher than the algal volume in the four samples. The comparison of µ a values at peaks 1 and 6 can be done. µ a (S1) and µ a (S2) are distinct at peaks 1 and 6 with the following order: µ a (S1)> µ a (S2). µa (S1) and µ a (S3) are overlapping at peak 1 and are different at peak 6 where µ a (S1)> µ a (S3). It is the same thing for S1 and S4, overlapping at peak 1 but distinct at peak 6 with µ a (S4)> µ a (S1). µ a (S2) and µ a (S3) are very similar and cannot be distinguished. Again these observations are consistent with the pigments measurements given in table I. The information of relative Chla quantity in the samples appears to be more represented by peak 6. For Chlb at peak 2 we can only conclude that µ a (S1)>µ a (S2) and that µ a (S4)>µ a (S2) ; µ a (S4)>µ a (S3). S1 and S4, S1 and S3 and S2 and S3 are not distinct at 492nm. This gives a first idea of the results found by the pigment measurement (table I).

As for what was found with the second derivative on (1-R tot -T tot ) spectra, the information on relative pigment quantity in the sample given by the analysis of µ a spectra is only qualitative. Indeed, µ a values are not proportional to the pigment concentrations at absorption peaks: the ratio at 680nm is only 1.42 while the ratio ( ) ( ) is 9.4. The absorption coefficient spectra are "flattened" compared to the expected values. This is surely explained by an erroneous estimation of the absolute value of µ a coefficients by the IAD due to the effect of unwanted light losses in the optical setup.

While remaining critical concerning the µ a absolute values computed for the four algal samples in this study, it can be reported still that they seem to be consistent with the results that can be found in literature. This may indicate that the errors of estimation of the µ a introduced by the IAD process remain reasonable relatively to the actual value of the absorption coefficient. In order to take into account the dependency of absorption on the physical structure of the algal population, the dimensionless efficiency factors , and are usually considered. [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF] They are the ratio between the energies that are respectively absorbed, scattered and attenuated within the medium and the input energy. For a suspension of microalgal cells, a simple relation exists between μ and :

, = μ , (10)
Where Ω is the geometrical cross section of one cell, N the number of cells of uniform size in a volume V , and i= a, s or ext. Here µ i,cell is the bulk optical coefficient of one cell. If the algal cells are approximated as spheres the value for Ω can be easily deduced from the cell diameter d: Ω = π ² 4 ⁄ . As the efficiency factors take into account the influence of cell size and density in the medium, it is more relevant to use them instead of bulk absorption coefficient μ in order to compare distinct measurements of the absorption properties of various algal polydispersions. Table III, adapted from the article of Sathyendranath et al. [START_REF] Sathyendranath | Variations in the spectral values of specific absorption of phytoplankton[END_REF] compares the efficiency factors for absorption obtained in this study with those obtained by other previous studies. Table III shows that the efficiency factors computed from the measurements on the four samples of this study are consistent with the literature [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF][START_REF] Savitzky | Soothing and differentiation of data by simplified least squares procedures[END_REF] regarding their order of magnitude and their dependency upon the characteristics of the algal population. Fluctuations of the values observed can be both intra and inter species and originate from difference in the relative amount of pigments in the algal cells as well as from variation in the cell density and size between two samples.

Reduced scattering coefficients

The mean reduced scattering coefficient spectra have been obtained for the four samples and are shown in figure 6 (B). The relative error is higher throughout the spectral domain than it was for µ a spectra. It increases with increasing wavelengths, and varies from 5% at 380nm to 17% at 920nm for S4. This trend is explained because the µ s' values decrease with increasing wavelengths. The relative error for S2 grows dramatically beyond 700nm and exceeds 50%. This is surely due to convergence failure of the iad computation for sample S2 at higher wavelengths, meaning this part of the spectrum should not be taken into account for S2.

The four reduced scattering coefficient spectra are more dissimilar the one from the other than what was observed for µ a spectra: there is less overlap of the spectra throughout the spectral domain considered. Although S2 and S3 show very similar µ a spectra, their µ s' spectra seem more distinct the one from the other. On the contrary, S1 and S4 spectra are very similar. However they are distinct from S2 and S3 spectra. This seems to be explained by the granulometric properties of the samples, and more particularly by the size distribution of the algal cells. Unlike what could have been expected, the total quantity of biomass inside the sample does not appear to be influential on the reduced scattering coefficient in the case of this study: indeed figure 2 shows that S1 and S4 have different total biovolumes but their µ s' spectra are similar. However, the size distribution of the algal cells is the same for those two samples, as shown in figure 3. On the contrary, S2 and S3 biovolumes are the same but the size distributions of the cells are dissimilar: in that case it is observed that the µ s' spectra of S2 and S3 are quite distinct. From this analysis it seems that the size distribution of the algal cells inside the sample is very influential on the values of µ s' spectra.

From figure 6 (b) the general shape of µ s' spectra can be described: firstly, they are a decreasing function of wavelength and secondly, they show pronounced enhancements in the vicinity of the absorption bands. Unlike what is usually thought in analytical spectroscopy, those peaks in the reduced scattering spectra appear not to be erroneous: they are actually expected, and consistent with the Lorentz-Mie [START_REF] Mie | Beitrage zur optik trüber medien, speziell kolloidaler metallösungen[END_REF] theory and Ketteler-Helmholtz's theory of anomalous dispersion. [START_REF] Van De Hulst | Light scattering by small particles[END_REF] If the algal cells are considered as homogeneous spheres whose refractive index is close to that of the surrounding medium (here water), their efficiency factors throughout the visible spectrum depend upon the optical size parameter ρ, defined as [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF][START_REF] Van De Hulst | Light scattering by small particles[END_REF] :

ρ = 2. π. λ . ( -1) (11)
Where d is the cell diameter, n the real part of the cell complex refractive index relative to water defined as = + ′ and λ the wavelength in the surrounding medium. For absorbing particles, the efficiency factors are given [START_REF] Van De Hulst | Light scattering by small particles[END_REF] by: = -

= 2 -4 cos -1 ρ . sin ρ --1 + cos -1 ρ . cos ρ -2 -1 + 4 cos -1 ρ . cos 2 -1 (12)
= 1 + . 2ρ tan -1 + 1 -1 2ρ tan -1 (13)
If the particles are polydisperse with respect to size according to a law P(ρ), the efficiency factors must be averaged:

ρ = ρ (ρ)ρ ρ (ρ)ρ ρ (15)
Author -If ρ is lower than ρ throughout the spectrum increases with ρ i.e. with decreasing λ -If the range of variation of ρ includes ρ , has a maximum inside the spectrum -If ρ remains close to but higher than ρ , decreases with increasing ρ, i.e. with decreasing λ -For high values of ρ, is almost constant throughout the spectrum.

variations (and consequently those of μ ) follow the same patterns, given by the relationship between and as shown by eq (8). Bricaud et al. [START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF] computed that ρ ranges between 2 and 4 and depends on the size distribution law in the case of algal suspensions.

, and variations with respect to ρ were computed in the case of our samples using eq (12), ( 13) and (14). The example of sample S1 at λ = 440 nm is presented on figure 7. It was computed that in the case of our samples, the value of ρ varies slightly around 4. The computation of ρ for the four samples presented on figure 7 shows that throughout the spectral range of interest, the values of ρ remain lower than ρ , which is consistent with the shape of measured μ spectra. Over the [380-1100nm] spectral domain it was computed that ρ ranged between extreme values of 0.5 and 1.8 with slight differences between the samples. This shows the observed decrease of μ as a function of increasing λ is consistent with the predictions given by the Lorentz-Mie theory. [START_REF] Mie | Beitrage zur optik trüber medien, speziell kolloidaler metallösungen[END_REF][START_REF] Van De Hulst | Light scattering by small particles[END_REF] The influence of an absorption band upon scattering properties has been well described by the same authors. [START_REF] Morel | Theoretical results concerning the optics of phytoplankton, with special reference to remote sensing applications[END_REF] By simulating the variations of in the vicinity of an absorption line (occurring at λ = 675nm) for various values of ρ they showed different phenomena may occur depending on the value of ρ:

-For ρ < 2 or 3 the scattering coefficient is enhanced inside and slightly beyond the absorption band, resulting in peaks that may shift slightly towards upper wavelengths compared to the absorption bands. -For ρ > 3 the scattering coefficient is reduced inside the absorption line, which leads to variations of opposite to those of .

In the case of this study, ρ remains below to two on the considered spectrum, which explains the peaks observed on the reduced scattering spectra measured (figure 6) in the vicinity of the absorption bands identified in table II.

Conclusion

This study reports the results obtained while testing the adding-doubling method on the [380-1020nm] spectral range for four non-diluted algal samples extracted from real cultivation ponds. The spectra of absorption and reduced scattering coefficients were computed with inverse-adding-doubling algorithm from total reflectance and total transmittance measurements conducted with a double integrating sphere setup. Several critical points have been encountered, first to optimize the configuration of the optical setup, and second in the convergence of the IAD algorithm from experimental, imperfect measurements of R tot and T tot .

Because the sample cell is positioned outside of the spheres in the double integrating sphere setup, it is impossible in practice to avoid light losses at the sphere ports and at the edges of the sample cell. These effects are all the more important than the sample is highly scattering. Those losses can be limited at best by adapting carefully the optical setup dimensions. In the case of this study however the light losses remained significant. Light losses within the setup introduce errors in the IAD algorithm convergence and the estimation of the absorption and reduced scattering coefficient absolute values may be erroneous and dependent on the setup with which the optical measurements were conducted. [START_REF] Vries | The effect of light losses in double integrating spheres on optical properties estimation[END_REF] In the case of this study, the absorption and reduced coefficient spectra obtained could only be qualitatively analyzed.

The absorption coefficient spectra computed represent qualitatively the difference in pigmentation between the four algal samples. However the same results could be obtained with a classical processing on total reflectance and total transmittance measurements. Nevertheless it appears that the reduced scattering coefficient may be of interest to extract information on the size distribution of the algal cells. It seems to vary significantly with the granulometric properties of the microalgal samples, thus providing information that could not be extracted from classical measurements. This conclusion is consistent with other works. [START_REF] Ciotti | Assessment of the relationships between dominant cell size in natural phytoplankton communities and the spectral shape of the absorption coefficient[END_REF][START_REF] Frankovitch | Investigation of microalgae with photon density waves[END_REF] This could be a promising track to follow up for future application to growth monitoring, and may justify that beyond the complexity in implementing a sound optical setup, adding-doubling could be seen as a potential operational method.

Figure 4 (

 4 Figure 4 (b) shows the raw total transmittance spectra. As previously the error bars show plus or minus twice the standard deviation.The measurements of T tot were conducted with a relative error lower than 4% throughout the [400-1000nm] spectral domain. As for R tot , the limitation of the spectrometer introduces higher uncertainty for the lower wavelengths. T tot measurements appear to be less sensitive to the experimental conditions than R tot measurements. This is explained by the fact that the Signal To Noise (SNR) ratio is higher for the T tot than for R tot due to higher levels. Moreover, the transmitted signal collected is less dependent on the angular cell position than R tot.

Figure 6

 6 Figure 6 shows the absorption (a) and reduced scattering (b) coefficient spectra obtained after IAD computations. The mean absorption and reduced scattering spectra were computed for the samples throughout the spectral range [380-1020nm]. The error bars represent plus or minus twice the standard deviation obtained by repeating one hundred times the IAD computations as explained previously.

  produced version of the article published in Applied Spectroscopy, 2014, N°10 (68), p. 1154-1167. The original publication is available at http://www.ingentaconnect.com http://dx.doi.org/10.1366/13-07308

  The values of the peaks may be linked to the quantity of absorbers inside the samples. If we compare the values of the spectra of the different samples at Chla main absorption peaks (1 and 6), it seems that sample S4 is the most concentrated in Chla and sample S2 is the least pigmented. It is difficult to conclude something about S3 and S1 as their relative position does not remain the same at peak 1 and 6. At 492nm the values of the peaks may indicate the Chlb level of the samples: here again, S4 is clearly more pigmented than S2, S1 and S3, while S2 is the least pigmented. S1 and S3 seem to have quite similar Chlb levels. Those results are consistent with the pigment concentrations measured and shown in table I.

	Absorption and reduced scattering coefficient spectra
	Convergence of the IAD algorithm

Peaks 1, 4,5 and 6 (

Table II) correspond to in vivo absorption by Chl a. Peak 2 is clearly attributable to Chl b. The 590nm peak could be attributed to Chl a-Chl c or to carotenoid-like pigments. Peak 8 corresponds to absorption by water.

  -produced version of the article published in Applied Spectroscopy, 2014, N°10 (68), p. 1154-1167. The original publication is available at http://www.ingentaconnect.com http://dx.doi.org/10.1366/13-07308With i = a, s or ext. Bricaud et al.[START_REF] Bricaud | Optical efficiency factors of some phytoplankters[END_REF] computed the variations of the efficiency factors for simulated algal suspensions. They observed different patterns depending on the value of ρ with respect to the values ρ corresponding to the first maximum in (ρ):

  Author-produced version of the article published in Applied Spectroscopy, 2014, N°10 (68), p. 1154-1167. The original publication is available at http://www.ingentaconnect.com http://dx.doi.org/10.1366/13-07308

		Hymenomonas	9	384	0	7.5	79	333	8.1	13.5	0.693 0.021
		elongata
	12	Hymenomonas elongata	14	781	0	10.3	166	640	17	14	0.618 0.034
	13	Hymenomonas elongata	17	1019	0	22.7	300	769	23	15.1	0.507 0.034
	14	Chaetoceros protuberans	1	172	0	14.9 95.6	73.4	7.5	9.5	0.941 0.090

Author-produced version of the article published in Applied Spectroscopy, 2014, N°10 (68), p. 1154-1167. The original publication is available at http://www.ingentaconnect.com http://dx.doi.org/10.1366/13-07308


Georgios D Evangelidis

Gurkirt Singh

Radu Horaud

Continuous gesture recognition from articulated poses ⋆

This paper addresses the problem of continuous gesture recognition from articulated poses. Unlike the common isolated recognition scenario, the gesture boundaries are here unknown, and one has to solve two problems: segmentation and recognition. This is cast into a labeling framework, namely every site (frame) must be assigned a label (gesture ID). The inherent constraint for a piece-wise constant labeling is satisfied by solving a global optimization problem with a smoothness term. For efficiency reasons, we suggest a dynamic programming (DP) solver that seeks the optimal path in a recursive manner. To quantify the consistency between the labels and the observations, we build on a recent method that encodes sequences of articulated poses into Fisher vectors using short skeletal descriptors. A sliding window allows to frame-wise build such Fisher vectors that are then classified by a multi-class SVM, whereby each label is assigned to each frame at some cost. The evaluation in the ChalearnLAP-2014 challenge shows that the method outperforms other participants that rely only on skeleton data. We also show that the proposed method competes with the top-ranking methods when colour and skeleton features are jointly used.

Introduction

Gesture and human action recognition from visual information is an active topic with many potential applications in human-computer interaction. The recent release of depth sensors (e.g., Kinect) led to the development of recognition methods based on depth or RGB-D data. Moreover, recent advances on human pose recognition from depth data [START_REF] Shotton | Real-time human pose recognition in parts from single depth images[END_REF] made the human skeleton extraction possible, so that three information sources are at one's disposal: color, depth, and skeleton. The latter has been proved very effective for human action recognition when used either alone [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF][START_REF] Vemulapalli | Human action recognition by representing 3d skeletons as points in a lie group[END_REF] or in conjunction with color/depth features [START_REF] Xia | Spatio-temporal depth cuboid similarity feature for activity recognition using depth camera[END_REF][START_REF] Ohn-Bar | Joint angles similiarities and hog 2 for action recognition[END_REF].

The majority of gesture (or action) recognition methods consider known boundaries of individual gestures and solve the isolated gesture recognition problem as a single-label assignment (1-of-L) problem, e.g., by invoking a multi-class classfier. However, the continuous case is mostly met in practice, i.e., a video may contain a sequence of gestures in an unknown order and with unknown gesture boundaries. Therefore, one has to solve both the segmentation and the classification problem in order to answer the question: which gesture and when is performed?

In this paper, we address the above problem within an energy minimization framework, that is, we formulate it as a frame-wise labeling problem under the constraint for a piece-wise constant solution. We build on a recent isolated action recognition method [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] and extend it to the continuous case for gesture recognition. Unlike [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF], we use a reduced set of the proposed skeletal descriptors per pose in order to describe the position of the hands with respect to the body. Based on a sliding window, we build frame-wise Fisher vectors that encode the poses of a video segment. Then, a multi-class SVM allows us to assign each label to each frame at some cost, while a binary classifier estimates costs for a "no-gesture" class. All these costs, summarized in a table, are finally exploited by a dynamic programming method that estimates the piece-wise constant labeling which minimizes the total energy. Fig. 1 illustrates the proposed pipeline. We test our method on the ChalearnLAP-2014 dataset [START_REF] Escalera | Chalearn looking at people challenge 2014: Dataset and results[END_REF] and we compare our method with other challenge participants. Note that our primary goal is to first extensively investigate the potential of the skeleton information in a continuous recognition framework, before combining skeletal data with other modalities.

The remainder of the paper is organised as follows. We summarise the related work in Sec. 2 and we present the skeleton-based representation in Sec. 3. Sec. 4 presents the energy minimization framework, while our method is tested on public datasets in Sec. 5. Finally, Sec. 6 concludes this work.

Related work

Regardless of the continuous nature of the recognition problem,1 one initially has to extract features from the available modalities in order to encode the footage. While the potential of color information to provide informative features in a recognition scenario has been extensively studied [START_REF] Wang | Action recognition with improved trajectories[END_REF], the release of depth sensors led to the development of depth descriptors, e.g, local occupancy patterns [START_REF] Wang | Mining actionlet ensemble for action recognition with depth cameras[END_REF][START_REF] Vieira | On the improvement of human action recognition from depth map sequences using spacetime occupancy patterns[END_REF] and histogram of spatio-temporal surface normals [START_REF] Oreifej | Hon4d: Histogram of oriented 4d normals for activity recognition from depth sequences[END_REF][START_REF] Yang | Super normal vector for activity recognition using depth sequences[END_REF]. More interstingly, the articulated human pose estimation from depth data [START_REF] Shotton | Real-time human pose recognition in parts from single depth images[END_REF] inspired many researchers to use skeleton as third modality along with RGB-D data, thus building several skeletal descriptors: joint position differences [START_REF] Yang | Eigenjoints-based action recognition using naive-bayes-nearestneighbor[END_REF][START_REF] Wang | Mining actionlet ensemble for action recognition with depth cameras[END_REF], joint angles [START_REF] Chaudhry | Bio-inspired dynamic 3d discriminative skeletal features for human action recognition[END_REF], joint motion characteristics [START_REF] Zanfir | The moving pose: An efficient 3d kinematics descriptor for low-latency action recognition and detection[END_REF], poses of spatio-temporal joint groups [START_REF] Wang | An approach to pose-based action recognition[END_REF], relative positions of joint quadruples [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF], relative position of joint edges [START_REF] Vemulapalli | Human action recognition by representing 3d skeletons as points in a lie group[END_REF], joint angle trajectories [START_REF] Ohn-Bar | Joint angles similiarities and hog 2 for action recognition[END_REF]. The benefit of combing features from multiple visual sources has been also illustrated [START_REF] Xia | Spatio-temporal depth cuboid similarity feature for activity recognition using depth camera[END_REF][START_REF] Ohn-Bar | Joint angles similiarities and hog 2 for action recognition[END_REF][START_REF] Wang | Mining actionlet ensemble for action recognition with depth cameras[END_REF].

The features are typically translated into a single vector, e.g. Bag-of-Words (BoW) histograms [START_REF] Xia | Spatio-temporal depth cuboid similarity feature for activity recognition using depth camera[END_REF] or Fisher vectors [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF], while a classifier, e.g. SVM, does the 1-of-L label assignment in isolated case. Such a strategy is only locally applicable in a continuous recognition scenario and one has to deal with the temporal nature of the labeling, like in speech recognition. The latter inspired people to develop continuous gesture/action recognition models.

The first continuous sign-language recognizers used hidden Markov models (HMM) [START_REF] Vogler | ASL recognition based on a coupling between HMMs and 3D motion analysis[END_REF][START_REF] Starner | Real-time american sign language recognition using desk and wearable computer based video[END_REF] for both modeling and recognition. CRF models [START_REF] Sminchisescu | Conditional models for contextual human motion recognition[END_REF][START_REF] Wang | Hidden conditional random fields for gesture recognition[END_REF] have been also proposed to avoid HMM's narrow temporal dependencies. Dynamic programming (DP) constitutes a standard framework as well, either in one-pass or two-pass mode, while it can be used in conjunction with either generative or discriminative classifiers [START_REF] Lv | Recognition and segmentation of 3-d human action using HMM and multi-class AdaBoost[END_REF][START_REF] Shi | Human action segmentation and recognition using discriminative semi-markov models[END_REF][START_REF] Hoai | Joint segmentation and classification of human actions in video[END_REF]. In the DP context, action templates (temporal models that replace HMMs) were recently proposed to be used in a dynamic warping framework [START_REF] Kulkarni | Continuous action recognition based on sequence alignment[END_REF]. We refer the reader to the latter for a detailed discussion about the pros and cons of all the above models.

ChalearnLAP-2014: Several methods have been proposed in the context of the ChalearnLAP-2014 challenge [START_REF] Escalera | Chalearn looking at people challenge 2014: Dataset and results[END_REF] for the continuous gesture recognition problem. The majority of the methods exploit features from both RGB and depth data [START_REF] Neverova | Multi-scale deep learning for gesture detection and localization[END_REF][START_REF] Monnier | A multi-scale boosted detector for efficient and robust gesture recognition[END_REF][START_REF] Chang | Nonparametric gesture labeling from multi-modal data[END_REF][START_REF] Pigou | Sign language recognition using convolutional neural networks[END_REF][START_REF] Wu | Deep dynamic neural networks for gesture segmentation and recognition[END_REF][START_REF] Chen | Multi-modality gesture detection and recognition with un-supervision, randomization and discrimination[END_REF][START_REF] Liang | Multi-modal gesture recognition using skeletal joints and motion trail model[END_REF], while [START_REF] Camgoz | Gesture recognition using template based random forest classifiers[END_REF] and [START_REF] Peng | Action and gesture temporal spotting with super vector representation[END_REF] rely on single modalities, i.e., skeleton and RGB respectively. The silence-based pre-segmentation of sequences is proposed by [START_REF] Chen | Multi-modality gesture detection and recognition with un-supervision, randomization and discrimination[END_REF][START_REF] Liang | Multi-modal gesture recognition using skeletal joints and motion trail model[END_REF], while the rest of the methods simultaneously solve the segmentation and recognition problems, e.g., with the help of a temporal model [START_REF] Chang | Nonparametric gesture labeling from multi-modal data[END_REF][START_REF] Wu | Deep dynamic neural networks for gesture segmentation and recognition[END_REF]. A deep learning framework that employs convolutional neural networks obtained the best results in the challenge [START_REF] Neverova | Multi-scale deep learning for gesture detection and localization[END_REF]. We refer the reader to [START_REF] Escalera | Chalearn looking at people challenge 2014: Dataset and results[END_REF] for a detailed categorization of the above methods in terms of several features.

Gesture representation

We rely on [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] in order to encode a set of articulated poses into an informative vector. This approach uses skeletal features, referred to as skeletal quads, to describe a sequence for isolated action recognition. A set of skeletal features is then encoded as a Fisher vector with the help of a trained GMM that explains the generation of any feature set. We briefly discuss these two steps below, that are slightly modified for a gesture recognition scenario.

Skeletal quads

In order to describe a gesture instance, and in particular the hand pose with respect to the body, we use the skeletal quad [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF]. This descriptor encodes the geometric relation of joint quadruples thus leading to a low-dimensional descriptor (see Fig 2). This idea originates in [START_REF] Lang | Astrometry.net: Blind astrometric calibration of arbitrary astronomical images[END_REF], while it has been successfully adopted to video synchronisation [START_REF] Evangelidis | Efficient and robust alignment of unsynchronized video sequences[END_REF][START_REF] Evangelidis | Efficient subframe video alignment using short descriptors[END_REF]. In short, if (x 1 x 2 x 3 x 4 ) is an ordered set of four joints, i.e., x i ∈ R 3 , it is encoded as q = [S(x 3 ); S(x 4 )],2 with q ∈ R 6 , where

S(x i ) = sR[x i -x 1 ], i = 1 . . . 4, (1)
and s, R are the scale and rotation respectively, such that S(x 1 ) = [0, 0, 0] ⊤ and S(x 2 ) = [1, 1, 1] ⊤ . In other words, a similarity normalization is applied to the quadruple, whereby a gesture descriptor is obtained. When the actor looks at the camera (e.g., ChalearnLAP dataset), the above scheme is sufficient. When the camera viewpoint or the body orientation drastically change, any rotation around the local axis x 1 x 2 (axis NH in Fig. 2) must be also normalised, i.e., R should account for this further rotation as well. This would lead to a fully view-invariant code with less discriminability in principle. Unlike [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] that enables all possible quads, we choose 14 specific quads based on the upper-body joints, as shown in Fig. 2 (right). Note that this list is not crossvalidated based on some data-sets, but it intuitively describes the relation among upper-body joints, by taking into account the body symmetry. For example, the first quad encodes the coordinates of the two hands when the origin is the Hip-Center and the Head coincides with the point [1, 1, 1] ⊤ .

Gesture encoding

Fisher vectors have been proved more discriminative than the the popular BoW representation in a recognition context [START_REF] Perronnin | Improving the fisher kernel for large-scale image classification[END_REF]. We adopt this representation in order to describe a gesture sequence as a set of gesture instances. Note that the low dimension of the skeletal quads compensates for the large inherent dimensionality associated with Fisher vectors.

If statistical independence is assumed, a set of M skeletal quads,

Q = {q i , 1 ≤ i ≤ M }, can be modelled by a K-component Gaussian mixture model (GMM), i.e., p(Q|θ) = M i=1 K k=1 w k N (q i |µ k , σ k ), (2)
where θ = {w k , µ k , σ k } K k=1 is the set of the mixture parameters with mixing coefficients w k , means µ k ∈ R 6 and diagonal covariance matrices, represented here as vectors, i.e., σ k ∈ R 6×1 . Once the GMM parameters are estimated, e.g., via the standard EM algorithm, any set Q may be described by its Fisher score [START_REF] Jaakola | Exploiting generative models in discriminative classifiers[END_REF], namely the gradient of the log-probability with respect to the GMM parameters,

J Q θ = ∇ θ log p(Q|θ).
The quadratic form of two such gradient vectors and the inverse information matrix defines the Fisher kernel, which can be written as a linear kernel of the so called Fisher vectors (FV), denoted here as J . The reader is referred to [START_REF] Jaakola | Exploiting generative models in discriminative classifiers[END_REF] for a detailed analysis.

By considering the gradients with respect to µ k and σ k , the FV consists of the concatenation of two vectors J Q µ k and J Q σ k . One can easily show (see [START_REF] Perronnin | Improving the fisher kernel for large-scale image classification[END_REF]) that the (6k -6 + j)-th element of the above vectors (1 ≤ j ≤ 6, 1 ≤ k ≤ K), that is the j-th entry for the k-th block, is given by

J Q µ k (j) = 1 M √ π k M i=1 γ k,i q j i -µ j k σ j k , J Q σ k (j) = 1 M √ 2π k M i=1 γ k,i q j i -µ j k σ j k 2 -1 , (3)
where γ k,i is the posterior probability that q i belongs to kth cluster conditioned by Q. The normalization by M is added to avoid dependence on the Q's cardinality. Since quads live in R 6 , the Fisher vectors are reasonably long, i.e., of dimension 12K. Once the FV is computed, we apply a power-normalisation step, i.e., each vector element x is transformed to sgn(x) * |x| α , and the resulting vector is further normalized by its l 2 norm. Note that the power-normalization eliminates the inherent sparseness of the FV; the benefit is discussed in detail in [START_REF] Perronnin | Improving the fisher kernel for large-scale image classification[END_REF]. Unlike [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF], we do not use a temporal pyramid since we are going to describe the gestures locally. As a consequence, it is only the following energy minimization scheme that takes into account the temporal nature of gestures towards a continuous labelling.

Continuous gesture recognition

We formulate the continuous gesture recognition problem as a labeling problem. In particular, every frame t∈{1, ..., T } must be assigned a label f t ∈L that denotes the gesture ID the frame belongs to. As a consequence, the goal is to find the frame-wise labeling f = {f 1 , . . . , f t , . . . , f T } subject to: i) f is consistent with the observations, ii) f is piece-wise constant. Note that a frame-wise labeling direclty answers the question "which gesture and when is performed?".

Such a global labeling problem can be cast into an energy minimization framework, that is, one estimates the labeling f that minimizes the energy

E(f ) = E D (f ) + E S (f ), (4)
where E D (f ) (the data term) measures the dissimilarity between f and observations and E S (f ) (the smoothness term) penalizes labelings that are not piece-wise constant.

The data-term is typically defined as

E D (f ) = T t=1 D t (f t )
, where D t (f t ) measures how appropriate the label f t is for t-th frame. Here, we use a mutliclass SVM classifier to evaluate this appropriateness. Note that the framework of [START_REF] Wu | Probability estimates for multi-class classification by pairwise coupling[END_REF] allows one to compute an empirical probability of assigning a label to an input. We train a multi-class SVM in a one-versus-all manner using FVs of isolated gesture examples. During testing, FVs are built based on a sliding temporal window centered at each frame. Instead of a fully varying window size, we suggest the use of three windows: a narrow, a mid-size and a wide window. By denoting as p t (f t ) the probability of assigning the label f t to frame t, the above appropriateness is computed by the following convex combination

D t (f t ) = 1 - 3 j=1 w j p j t (f t ) (5)
where j stands for different windows and w j can balance their contribution.

The smoothness term penalizes the assignment of different labels to successive frames. If we consider that each frame interacts with its immediate neighbors (first-order Markov assumption), the smoothness term can be written as a summation of pairwise potentials

E S (f ) = T -1 t=1 V (f t , f t+1 ). ( 6
)
Since we seek a piece-wise constant labeling, we define the potential function

V (f t , f t+1 ) = 0 if f t = f t+1 β otherwise. ( 7
)
To efficiently solve the global optimization problem

min f E(f ), (8)
we use a dynamic programming approach, while we leave more sophisticated solutions for a future paper. If C t [f t ] denotes the minimum labeling cost for the first t frames provided that the t-th frame has label f t , the following recursive equation (t is increasing) fills in a table C of size |L| × T :

C 1 [f 1 ] = D 1 (f 1 ) C t [f t ] = D t (f t ) + min ft-1 (C t-1 [f t-1 ] + V (f t-1 , f t )) . ( 9
)
Once the table is filled, the optimal solution can be obtained by first finding the label of the last frame, i.e., f * n = arg min fn C n [f n ], and then by tracing back in order of decreasing t:

f * t = arg min fi C t [f t ]) + V (f t , f * t+1 ) . (10)
In order to take into account the silent part of a gesture sequence, we train a binary classifier based on silent and non-silent parts of a sufficient number of training examples (see details in Sec. 5). This leads to an extra row in table C that corresponds to a "no-gesture" class. Note that this does not imply a presegmentation, but rather, we let the energy minimizer decide which frames are silent or no.

Note that if one wants to solve the isolated recognition problem, dynamic programming is not required (C reduces to a vector). In such a case, the single label is directly obtained by f * = arg max f p(f ).

Experiments

MSR-Action3D Dataset

Although we focus on the continuous recognition problem, it is important to show that our gesture representation is quite discriminative in the isolated recognition scenario. Our method reduces to [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] for isolated case, being the only difference the few quads that are considered here. We refer the reader to [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] for a performance analysis of the method in isolated case. Here, we just present an updated comparison table based on the widely used MSR-Action3D dataset, by including very recent methods that are missed in [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF].

We skip the details of the dataset (see [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF]). We just notice that 20 actions are performed by 10 actors and that a cross-subject splitting is considered, i.e. five actors for training and five actors for testing. FVs are built based on 128component GMM, while they are power-normalized with α = 0.3. Instead of all possible joint quadruples (4845) in [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF], only 44 meaningful quads are used; they relate hand and leg joints with the body. 3 Note that this leads to a more efficient recognition since the running time of building FVs is reduced by a factor of 100.

Table 1 shows the performance of various methods for this dataset. We do not observe significant loss in performance when using fewer quads. Our method achieves similar performance with the state-of-the-art methods that count on skeleton joints, while it competes with the best-performing methods that use multi-modal features.

Multi-modal Gesture Dataset 2014

The Multi-modal Gesture dataset was released for the ChalearnLAP-2014 challenge (Track3) [START_REF] Escalera | Chalearn looking at people challenge 2014: Dataset and results[END_REF]. More than 14, 000 gestures drawn from a vocabulary of 20 Italian sign gesture categories were performed by several actors. Each actor, being captured by a Kinect camera, performed a non-fixed number of gestures. Multi-modal data are available, i.e., skeleton (20 joints), RGB and depth image sequences.

The dataset is divided into three parts, development data (7, 754 manually labeled gestures), validation data (3, 362 labelled gestures) and evaluation data (2742 gestures). Training and parameter cross-validation was done on development and validation data respectively; testing was done on the evaluation data.

Skeleton

EigenJoints [START_REF] Yang | Eigenjoints-based action recognition using naive-bayes-nearestneighbor[END_REF] 82.33% Joint Angles [START_REF] Ohn-Bar | Joint angles similiarities and hog 2 for action recognition[END_REF] 83.53% FV of skeletal quads (less quads) 89.07% Skeleton Lie group [START_REF] Vemulapalli | Human action recognition by representing 3d skeletons as points in a lie group[END_REF] 89.45% FV of skeletal quads [START_REF] Evangelidis | Skeletal quads: Human action recognition using joint quadruples[END_REF] 89.86% Pose Set [29] * 90.22% Moving pose [START_REF] Zanfir | The moving pose: An efficient 3d kinematics descriptor for low-latency action recognition and detection[END_REF] 91.70%

Skeleton, RGB-D Joints+Actionlets [START_REF] Wang | Mining actionlet ensemble for action recognition with depth cameras[END_REF] 88.20% HON4D [18] * 88.89% Joints + Depth Cuboids [START_REF] Xia | Spatio-temporal depth cuboid similarity feature for activity recognition using depth camera[END_REF] 89.30% Super Normal vectors [START_REF] Yang | Super normal vector for activity recognition using depth sequences[END_REF] 93.09% Joints+STIP [ In particular, the GMM and the linear multi-class SVM 4 were learned on the development data while the parameter β of the smoothness term was crossvalidated on the validation set; best performance was obtained with β = 3. As mentioned, 14 quads were invoked (see Fig. 2). We used a GMM with 128 components that led to 1536D Fisher vectors, which were power-normalized with α = 0.5. While we observed that less components lead to a lower performance in validation set, we did not test more components to avoid very long FVs. The size of the three sliding windows were 15, 37 and 51, while equal weights (w j = 1/3) were used to compute the cost of assigning each label per frame. There was no significant difference in the performance when changing the window size and the weights. As with the multi-class classifier, the cost of assigning a "no-gesture" label is the average cost obtained from three classifications of short windows, i.e., with 5, 7 and 9 frames. We used 50 videos of the development data for this training, by considering each FV of a window as an example. The performance of the recognition was quantified by the average Jaccard index.

Table 2 summarizes the Jaccard indices of the participants in the challenge. We first sort out the methods that count on skeleton data, and then the methods that combine different modalities. The proposed method and Camgoz et al. [START_REF] Camgoz | Gesture recognition using template based random forest classifiers[END_REF] achieve the best performance when only skeleton joints are used (almost same index). Note that the Jaccard index 0.745 corresponds to the performance of the software version submitted to the challenge. A fixed bug led to a higher index, i.e., 0.768. As previously, the best performing methods use multi-modal features. Neverova et al. [START_REF] Neverova | Multi-scale deep learning for gesture detection and localization[END_REF] exploit all the modalities, thus obtaining the highest Jaccard index (0.850). Note that Peng et al. [START_REF] Peng | Action and gesture temporal spotting with super vector representation[END_REF] performs quite well by using only RGB data.

Table 2. Results of the ChalearnLAP-2014 challenge (Track 3) [START_REF] Escalera | Chalearn looking at people challenge 2014: Dataset and results[END_REF] Team Modality Jaccard index Camgoz et al. [START_REF] Camgoz | Gesture recognition using template based random forest classifiers[END_REF] Skeleton 0.746 FV of quads (this work) Skeleton 0.745 (0.768 * ) Team-13 (Terrier) Skeleton 0.539 Team-17 (YNL) Skeleton 0.271 Neverova et al. [START_REF] Neverova | Multi-scale deep learning for gesture detection and localization[END_REF] Skeleton, Depth, RGB 0.850 Monnier et al. [START_REF] Monnier | A multi-scale boosted detector for efficient and robust gesture recognition[END_REF] Depth, RGB 0.834 Ju Yong Chang [START_REF] Chang | Nonparametric gesture labeling from multi-modal data[END_REF] Skeleton, RGB 0.827 FV of quads+HOF (this work) Skeleton, RGB, 0.816 Peng et al. [START_REF] Peng | Action and gesture temporal spotting with super vector representation[END_REF] RGB 0.792 Pigou et al. [START_REF] Pigou | Sign language recognition using convolutional neural networks[END_REF] Depth, RGB 0.789 Di Wu and Ling Shao [START_REF] Wu | Deep dynamic neural networks for gesture segmentation and recognition[END_REF] Skeleton, Depth 0.787 Team-9 (TelePoints) Skeleton, Depth, RGB 0.689 Chen et al. [START_REF] Chen | Multi-modality gesture detection and recognition with un-supervision, randomization and discrimination[END_REF] Skeleton, Depth, RGB 0.649 Bin Liang and Lihong Zheng [START_REF] Liang | Multi-modal gesture recognition using skeletal joints and motion trail model[END_REF] Skeleton, Depth 0.597 Team-12 (Iva.mm) Skeleton, Depth, RGB 0.556 Team-14 (Netherlands) Skeleton, Depth, RGB 0.431 Team-16 (vecsrel) Skeleton, Depth, RGB 0.408 * A fixed software bug led to a higher index We also report the performance of our method when skeletal features are combined with color features, i.e., histograms of flows (HOF) [START_REF] Wang | Action recognition with improved trajectories[END_REF]. We reduce the dimensionality of HOF feature from 108 to 48 using PCA, and then, we learn another GMM with 64 components which led to 6144D Fisher vector. An early fusion is performed, i.e., the two FVs are concatenated into a single input to be classified. This leads to a higher index (0.816) and makes the proposed method comparable with the top-ranking methods. Note that we did not investigated what is the best color feature to be combined with the quads. It is worth noticing that the performance when using only HOF features is 0.693. Apparently, the combination of skeletal quads with more sophisticated features [START_REF] Wang | Action recognition with improved trajectories[END_REF] would lead to a higher index.

Fig. 3 depicts the confusion matrices for the continuous case when each frame is considered as an example (the reader should not confuse these numbers with the Jaccard indices of Table 2). We also show the confusion matrices that correspond to the isolated recognition scenario, i.e. when the gesture boundaries are known. The accuracy of our method in the isolated case is 90%, 86% and 94% when using skeleton, HOF and both features, respectively. The proposed representation is quite discriminative in either case. However, quite similar gestures like "Le vuoi prendere" (id 14) and "Non ce ne piu" (id 15) may be confused without finger joints. The confusion matrix in the continuous case is more sparse since the confusions are concentrated in the column of the no-gesture class (label 00), owing to the frame-wise labeling. It is important to note that the recognition accuracy of this class, i.e., 89%, 86% and 91%, is based on the final global labeling, as with any other class. Apparently, the use of color features improves the discrimination and the matrices tend to be more diagonal. Note that the percentages do not sum up to 100 since we keep the integer part of the numbers.

Conclusions

We dealt with the continuous gesture recognition problem from series of articulated poses. The problem was cast into a labeling framework and it was solved as a global energy minimization problem. We proposed a dynamic programming solver that exploits the outputs of multiple SVMs and provides a piece-wise constant labeling. We mainly tested our method on the Moltabagno Gesture dataset, released for the ChalearnLAP-2014 challenge purposes. Despite the use of the skeleton information only, the proposed method achieved high recognition scores, while its performance was boosted when extra modalities, e.g. colour data, were used. Future work consists of extending Fisher vectors to deal with the temporal nature of a pose sequence, and of investigating the optimal fusion with other modalities.

Fig. 1 .

 1 Fig. 1. A Gaussian Mixture Model (GMM), learnt on training data, is supposed to generate skeletal quads. Based on the GMM parameters, the skeletal quads of a gesture segment are encoded into a Fisher vector, and a multi-class SVM assigns a cost per label. A global energy minimizer uses these costs to provide a piece-wise constant labeling.

Fig. 2 .

 2 Fig. 2. (Left:) A sketch from [7] that illustrates the coding when (x1 x2 x3 x4) correspond to the joints {Neck, Hand, Shoulder, Elbow}; the quad descriptor is q = [Sx, Sy, Sz, Ex, Ey, Ez] ⊤ . (Right:) The 14 joint quadruples whose quads are locally describe the upper-body pose.

Fig. 3 .

 3 Fig. 3. Confusion matrices of our recognition method for Multi-modal gesture dataset when using skeletal quads (a,b), HOF (c,d), skeletal quads + HOF (e,f) in isolated (left) and continuous recognition scenario (right).

Table 1 .

 1 Recognition accuracy on MSRAction3D datasets.

	Modality	Methods	Average Accuracy

we do not distinguish the problems of human action and gesture recognition, since the latter can be roughly seen as the former when the upper-body part is used

the notation [•; •] denotes vertical vector concatenation

we used the code provided by https://team.inria.fr/perception/research/icpr2014/

The scikit-learn Python package was used

⋆ Support from the European Research Council (ERC) through the Advanced Grant VHIA (#340113) is greatly acknowledged.