Abderraouf Soukeur

Anthony Szymczyk
email: anthony.szymczyk@univ-rennes1.fr

Yassine Berbar

Mourad Amara

Extraction of rare earth elements from waste products of phosphate industry

Keywords: Rare earths, liquid/liquid extraction, industrial waste product, Djebel Onk fluorapatite, valorization

Rare earths are critical elements in our modern societies and the ever-increasing demand raises fears of supply risks in the coming years. This work dealt with the feasibility of extracting rare earth elements (REEs) from an industrial waste product from the exploitation of phosphate ores of "Djebel Onk" in Tébessa eastern region of Algeria. The solid residue was first leached at room temperature with three different inorganic acids (HNO3, H2SO4 and H3PO4) at various concentrations and leaching times. It was possible to recover almost 100 % of La, Ce, Eu, Gd and Y with HNO3 3 N in 24 h. However, only about 10 % of Yb were leached. The leachates were further treated with two organophosphorous extractants, trioctylphosphine oxide (TOPO) and di-(2-ethylhexyl) phosphoric acid (D2EHPA) at various concentrations in chloroform. A virtually total extraction of Eu, Gd, Y and Yb was achieved with TOPO at 0.3 M. The extraction efficiency of light rare earth elements (LREEs), La and Ce, was only 38 and 55 %, respectively. Very good selectivities between heavy rare earth elements (HREEs), and LREEs as well as between medium rare earth elements (MREEs) and LREEs were obtained but TOPO was unable to selectively separate HREEs from MREEs. Although D2EHPA led to lower REEs extraction efficiency than TOPO, it showed interesting performance for the selective separation of REEs into three fractions corresponding to LREEs (La and Ce), MREEs (Eu and Gd) and HREEs (Y and Yb).

Introduction

Rare earth elements (REEs), i.e. scandium, yttrium and the lanthanides, are considered as strategic metals for both civil and military applications. They have been increasingly used in the high-tech sector as they play a crucial role in the development of high-end smart materials [START_REF] Du | Global in-use stocks of the rare earth elements: A first estimate[END_REF][START_REF] Alonso | Erratum: Evaluating rare earth element availability: A case with revolutionary demand from clean technologies[END_REF][START_REF] Tukker | Rare earth elements supply restrictions: Market failures, not scarcity, hamper their current use in high-tech applications[END_REF]. Since the last two decades, a few producers (mainly from China) have conducted intensive extraction and commercialization of REEs [START_REF] Wang | Production forecast of China's rare earths based on the generalized Weng model and policy recommendations[END_REF][START_REF] Weng | A detailed assessment of global rare earth element resources: Opportunities and challenges[END_REF]. The worldwide demand grows by about 10% per year in various applications such as permanent magnets, batteries for hybrid cars, wind turbine generators, luminophores, etc. [START_REF] Barteková | National strategies for securing a stable supply of rare earths in different world regions[END_REF][START_REF] Rollat | Prospective analysis of the flows of certain rare earths in Europe at the 2020 horizon[END_REF]. Meanwhile, the European Union imports more than 90% of its needs in REEs [START_REF]European Rare Earths Competency Network -Enterprise and Industry[END_REF].

REEs are relatively abundant on Earth but not in concentrated forms, which makes them economically challenging to obtain [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF]. The main commercial sources of rare earth elements are monazite, xenotime and bastnasite [START_REF] Kumar | Solid-liquid extraction of heavy rare-earths from phosphoric acid solutions using Tulsion CH-96 and T-PAR resins[END_REF][START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF]. Besides the historical mines Mountain Pass in California and Mount Weld in Australia, numerous new regions, such as in Tamtor (Russia), Strange lake (Canada), Araxà (Brazil), Ngualla (Tanzania), Zandkopsdrift (South Africa) and Norra Karr (Sweden), have begun exploration [START_REF] Hoshino | REE Mineralogy and Resources[END_REF][START_REF] Kanazawa | Rare earth minerals and resources in the world[END_REF]. However, the continuous development of advanced technologies over the past decades has created increasing demand for REEs [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF] and co-production is now considered as a promising alternative route allowing the valorization of REEs, especially for the heavy rare earth elements [START_REF] Schulze | Recycling and its effects on joint production systems and the environmentthe case of rare earth magnet recycling -Part I -Production model[END_REF][START_REF] Wu | Recovery of rare earth elements from phosphate rock by hydrometallurgical processes -A critical review[END_REF]. In contrast to end-of-life products [START_REF] Jha | Review on hydrometallurgical recovery of rare earth metals[END_REF], mining process residues typically contain low concentrations of REEs but they are produced in very large amount. Consequently, they are likely to become a significant source of REEs [START_REF] Borra | Leaching of rare earths from bauxite residue (red mud)[END_REF][START_REF] Davris | Selective leaching of rare earth elements from bauxite residue (red mud), using a functionalized hydrophobic ionic liquid[END_REF][START_REF] Al-Thyabat | Extraction of rare earth elements from upgraded phosphate flotation tailings[END_REF].

A large number of REE-bearing phosphate minerals have been found in nature, thus indicating that REEs have a strong affinity towards phosphates [START_REF] Jha | Review on hydrometallurgical recovery of rare earth metals[END_REF]. In this regard, apatite ores (Ca10(PO4)6A2 with A = F, OH or Cl), used for the production of phosphate fertilizers or phosphoric acid, have been treated for extraction of REEs as secondary products [START_REF] Peelman | Hydrometallurgical Extraction of Rare Earth Elements from Low Grade Mine Tailings[END_REF][START_REF] Sun | Apatite concentrate, a potential new source of rare earth elements[END_REF][START_REF] Hammache | Recovery of light rare earth elements by leaching and extraction from phosphate mining waste (Fluorapatite and Carbonate-Fluorapatite)[END_REF]. Apatite is an important host mineral for REEs in igneous and metamorphic rocks, with trivalent rare earth cations substituting calcium ions in the apatite lattice structure (with an REEs concentration that can exceed 1g per kg of ore) [START_REF] Dorozhkin | Ecological principles of wet-process phosphoric acid technology[END_REF].

Furthermore, the huge amount of apatite ores on Earth (the world phosphate rock production is estimated to be more than 250 million tons per year [START_REF] Wu | Recovery of rare earth elements from phosphate rock by hydrometallurgical processes -A critical review[END_REF]) makes this material a promising alternative source for extraction of REEs [START_REF] Stone | Processing of rare earth phosphate concentrates: A comparative study of pre-leaching with perchloric, hydrochloric, nitric and phosphoric acids and deportment of minor/major elements[END_REF][START_REF] Alemrajabi | Recovery of rare earth elements from nitrophosphoric acid solutions[END_REF]. It is noteworthy, however, that extraction of REEs from apatite has not been extensively studied compared to other main minerals such as monazite, bastnasite and xenotime [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF].

REEs are commonly subdivided into three categories: light (LREEs; La-Sm), medium (MREEs; Eu-Dy) and heavy (HREEs; Ho-Lu and Y) [START_REF] Park | A biosorption-based approach for selective extraction of rare earth elements from coal byproducts[END_REF]. They are known to be difficult to separate from each other, due to their similar chemical and physical properties. Nevertheless, several processing routes have been developed to recover rare earths such as precipitation, filtration, adsorption, ion exchange and solvent extraction [START_REF] Kumar | Solid-liquid extraction of heavy rare-earths from phosphoric acid solutions using Tulsion CH-96 and T-PAR resins[END_REF][START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF][START_REF] Anastopoulos | Adsorption of rare earth metals: A review of recent literature[END_REF], the latter being currently considered as the most commerciallyrelevant technology [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF][START_REF] Park | A biosorption-based approach for selective extraction of rare earth elements from coal byproducts[END_REF][START_REF] Arunraj | Cellulose and Saccharomyces cerevisiae Embark to Recover Europium from Phosphor Powder[END_REF]. Separation processes based on ion-exchange and solvent extraction techniques have been shown to allow separation between REEs [START_REF] Reddy | Liquid-Liquid Extraction Processes for the Separation and Purification of Rare Earths[END_REF]. With controlled experimental conditions, fair separations between LREEs and HREEs have been reported [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF][START_REF] Radhika | Liquid-liquid extraction and separation possibilities of heavy and light rare-earths from phosphoric acid solutions with acidic organophosphorus reagents[END_REF][START_REF] Wu | Simultaneous recovery of rare earths and uranium from wet process phosphoric acid using solvent extraction with D2EHPA[END_REF][START_REF] Orabi | Extraction of rare earth elements from Abu-Tartour wet process phosphoric acid using synthesized salicylaldehyde azine[END_REF].

The aim of this work was to recover REEs from a sterile waste product of the phosphate industry exploiting phosphate ores of "Djebel Onk" in Tébessa eastern region of Algeria. The solid residue was first leached with three different inorganic acids (nitric, phosphoric and sulfuric acids) at different concentrations and leaching times. The leachates were further treated with two organophosphorous extractants (di-(2-ethylhexyl) phosphoric acid and trioctylphosphine oxide) at various concentrations in chloroform in order to assess the feasibility of extracting the various REEs.

Materials and methods

Samples and reagents

Sulfuric (H2SO4), nitric (HNO3) and phosphoric (H3PO4) acids (Reagent grade; Fluka) were used for apatite-ore leaching. Chloroform (Analytical grade; Fluka) was used as diluent for extractants.

Organophosphorus extractants, di-(2-ethylhexyl) phosphoric acid (D2EHPA) and trioctylphosphine oxide (TOPO), were obtained from Sigma-Aldrich and used without further purification. The chemical structures of D2EHPA and TOPO are shown in Figure 1. REE nitrate standards (Sigma-Aldrich) were used for ICP-OES calibration. Deionized water was used for the preparation of all aqueous solutions. Samples of apatite ore from Djebel Onk (Tébessa, Algeria) were provided by the Somiphos company.

The flowsheet followed by the Somiphos company in its phosphate plant in Tébessa is shown in Figure 2. Among the various sterile wastes (i.e. products with a too low phosphate concentration for a profitable commercial exploitation) generated in the Somiphos' phosphate plant, sample T1 was selected in this study because it exhibited the highest REEs content (about 0.1 wt. %). TriOctylPhosphine Oxide (TOPO)

Characterization techniques

X-Ray Diffraction (XRD)

The mineralogical analysis of the phosphate ore residue T1 was carried out by X-ray diffraction (XRD).

XRD data were collected using an X-ray diffractometer BRUKER-binary V3 (Raw) using Cu K1 radiation (λ = 1.5406 Å), running at 40kV and 40mA, with detection in the 2θ range 10-90°.

X-Ray fluorescence (XRF)

The chemical composition of the phosphate ore residue was determined by X-ray fluorescence (XRF)

with wavelength dispersive analysis (WD-XRF) by means of a PANalytical PW2400 Sequential WDXRF Spectrometer (X-ray tube anode material: Rh; power: 3 kW).

Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES)

Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) was used to determine the concentration of REEs in aqueous phases. Analyses were performed in emission mode with a 700 series Varian Vista Pro ICP-OES spectrometer with axial torch. The various standards used for ICP-OES and analysis conditions are given in Table 1.

Table 1. REE standards and wavelengths used for ICP-OES analyses.

REEs standards properties

Eu(NO3)3 Gd(NO3)3 Y(NO3)3 Yb(NO3)3 Ce(NO3)3 La(NO3)3 MW (g/

Leaching procedure

The phosphate ore waste product T1 (Figure 2) was leached according to the protocol schematically shown in Figure 3. Briefly, 20 g of solid were soaked in 250 mL (S/L ratio = 80 mg / mL) of an acid aqueous solution at room temperature (T = 25 ± 1 °C). HNO3, H3PO4 and H2SO4 were used at various concentrations ranging from 0.5 to 3 N. The system was stirred vigorously at 750 rpm for times ranging from 0.5 to 24 h. Eventually, the solid residues were separated from the leachates by means of a filter paper.

Figure 3. Leaching of the phosphate ore waste product.

The leachate composition was determined by ICP-OES after appropriate dilution. The leaching efficiency of REEs (Eleach) was determined by the following equation:

𝐸 𝑙𝑒𝑎𝑐ℎ = 𝑚 𝑙𝑒𝑎𝑐ℎ 𝑚 0,𝑇1 × 100 (1)
where 𝑚 𝑙𝑒𝑎𝑐ℎ is the mass of the REE in the leachate and 𝑚 0,𝑇1 is the initial mass of the REE in the waste product T1.

Liquid / liquid extraction

After acidic leaching, solvent extraction was performed at room temperature. Two organophosphorous extractants were used, TOPO and D2EHPA (Figure 1), at various concentrations in chloroform.

Chloroform is only weakly polar and therefore has a relatively low affinity for TOPO and D2EHPA

(the P=O bond in TOPO and P=O, C-O-P and P-O-H bonds in D2EHPA bring them a polar character), which is beneficial for extraction. Indeed, diluent should not have a too high affinity towards the extractant because strong interactions between the extractant and the diluent would result in a lower concentration of "free" extractant available for reaction with metal at the liquid-liquid interface [START_REF] Kuipa | Diluent effect on the solvent extraction rate of copper[END_REF].

For instance, Smelov et al. reported a decrease in the extraction efficiency of zinc when increasing the solvent ability to solvate D2EHPA [START_REF] Smelov | The Extraction of Zinc by Di-2ethylhexylphosphoric Acid from Nitric and Perchloric Acid Solutions[END_REF].

Solvent extraction was carried out by stirring equal volumes (5.0 mL) of aqueous organic phase and aqueous leachate (O/A volume ratio = 1) for 10 min using a mechanical stirrer (100 rpm), and by further separating the aqueous phase from the organic phase with a separating funnel. The concentrations of REEs in the aqueous phase before and after extraction were determined by ICP-OES.

The distribution coefficient (DREE), extraction efficiency (Eextr) and separation factor between two REEs i and j (SFi/j) were obtained from the following equations [START_REF] Wu | Simultaneous recovery of rare earths and uranium from wet process phosphoric acid using solvent extraction with D2EHPA[END_REF]:

𝐷 𝑅𝐸𝐸 = [𝑅𝐸𝐸] 0,𝑙𝑒𝑎𝑐ℎ -[𝑅𝐸𝐸] 𝑙𝑒𝑎𝑐ℎ 𝑉 𝑙𝑒𝑎𝑐ℎ 𝑉 𝑜𝑟𝑔 [𝑅𝐸𝐸] 𝑙𝑒𝑎𝑐ℎ (2)
𝐸 𝑒𝑥𝑡𝑟 = 100 (1 - [𝑅𝐸𝐸] 𝑙𝑒𝑎𝑐ℎ [𝑅𝐸𝐸] 0,𝑙𝑒𝑎𝑐ℎ ) (3)
𝑆𝐹 𝑖/𝑗 = 𝐷 𝑅𝐸𝐸 𝑖 𝐷 𝑅𝐸𝐸 𝑗 (4)
where [REE]0,leach and [REE] leach are the REE concentration in the leachate before and after extraction, respectively, and Vleach and Vorg are the volumes of the aqueous leachate and organic phase, respectively.

Results and discussion

Characterization of the phosphate ore waste product

The XRD analysis (Figure 4) identified carbonate-fluorapatite as the main crystalline phase of the phosphate ore residue T1. Quartz was also found to be present in substantial amount, as already reported elsewhere [START_REF] Nettour | Determination of physicochemical parameters of Djebel Onk phosphate flotation (Algeria)[END_REF]. The REE content of the phosphate ore residue determined from XRF is shown in Table 2 (the full XRF results are provided in the Supporting Information).

Leaching

Efficiency of the different acids

Three inorganic acids, HNO3, H2SO4 and H3PO4, were used for leaching the phosphate ore residue.

The expected reactions between fluorapatite and these acids can be represented as follows [START_REF] Wu | Recovery of rare earth elements from phosphate rock by hydrometallurgical processes -A critical review[END_REF][START_REF] Habashi | Recovery of the Lanthanides From Phosphate Rock[END_REF][START_REF] Sluis | A Clean Technology Phosphoric Acid Process[END_REF]: and H3PO4 and concluded that the dissolution of REEs in H3PO4 was lower compared to the other three acids [START_REF] Stone | Processing of rare earth phosphate concentrates: A comparative study of pre-leaching with perchloric, hydrochloric, nitric and phosphoric acids and deportment of minor/major elements[END_REF]. H2SO4 allowed partial leaching of REEs from the phosphate ore residue. However, the leaching efficiency with H2SO4 was found significantly lower than with HNO3, which is in line with reported literature [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF][START_REF] Hammache | Recovery of light rare earth elements by leaching and extraction from phosphate mining waste (Fluorapatite and Carbonate-Fluorapatite)[END_REF][START_REF] Walawalkar | Process investigation of the acid leaching of rare earth elements from phosphogypsum using HCl, HNO3, and H2SO4[END_REF][START_REF] Ismail | Leaching of Some Lanthanides from Phosphogypsum Fertilizers by Mineral Acids[END_REF][START_REF] Preston | The recovery of rare earth oxides from a phosphoric acid by-product. Part 1: Leaching of rare earth values and recovery of a mixed rare earth oxide by solvent extraction[END_REF][START_REF] Ogata | Selective recovery of heavy rare earth elements from apatite with an adsorbent bearing immobilized tridentate amido ligands[END_REF]. The lower performance obtained with H2SO4 results from the precipitation of gypsum (see reaction II) which tends to incorporate REEs. For instance, Ogata et al.

Ca10(PO4)6F2 +
reported that, at high H2SO4 concentrations (up to 6 M), most of the REEs contained in apatite samples were lost due to co-precipitation with the formed gypsum [START_REF] Ogata | Selective recovery of heavy rare earth elements from apatite with an adsorbent bearing immobilized tridentate amido ligands[END_REF]. We report in Figure 5b the leaching efficiency after 3-hour leaching in the various acids (concentration: 3 N). When leaching was carried out with HNO3, Eu was almost completely released from the phosphate ore residue while a moderate efficiency (∼ 50 -75 %) was obtained for La, Eu, Gd and Y. It is noteworthy that leaching efficiency was very weak for Yb (less than 5 %), whatever the acid used. It can thus be concluded that there is no correlation between the leaching efficiency and the category of REEs, i.e. LREEs, MREEs and HREEs.

Impact of nitric acid concentration

HNO3 was considered for the subsequent parts of this study as it was shown to yield the best results (section 3.2.1). Figure 6 shows the leaching efficiency in HNO3 solutions of various concentrations ranging from 0.5 to 3 N for a leaching time of 0.5 h. The leaching of the phosphate ore residue increased with increasing nitric acid concentration, in good agreement with the literature [START_REF] Wu | Recovery of rare earth elements from phosphate rock by hydrometallurgical processes -A critical review[END_REF]. It should be stressed, however, that increasing too much the acid concentration would be detrimental for REEs extraction by cation-exchanger extractant such as D2EHPA [START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF]. Eu was more efficiently leached than the other REEs, whatever the acid concentration, and was completely released from the solid from a nitric acid concentration of 2 N. The acid concentration did not impact the overall sequence of leaching efficiency.

Figure 6. Leaching efficiency for various HNO3 concentrations (leaching time: 0.5 h).

Leaching time

Extraction of REEs

Based on the results reported in section 3.2, extraction of REEs was carried out after the leaching of the phosphate ore residue with HNO3 3 N for 24 h at room temperature. Figure 8 shows the extraction efficiency of the various REEs by TOPO in chloroform. TOPO is a neutral solvation extractant. In highly concentrated nitric systems as those considered in this study, REEs are coordinated around the phosphoryl group of TOPO (the electron donor character of the oxygen atom of the phosphoryl group is strengthened by the three long alkyl chains), yielding an extractable neutral amino complex. The overall reaction can be represented as [START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF][START_REF] Reddy | Liquid-Liquid Extraction Processes for the Separation and Purification of Rare Earths[END_REF]:

REE 3+ + 3NO 3 -+ 3TOPO ̅̅̅̅̅̅̅̅ = REE(NO 3 ) 3 (TOPO) 3 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ (IV)
where TOPO ̅̅̅̅̅̅̅̅ and REE(NO 3 ) 3 (TOPO) 3 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ denote TOPO and the complex in the organic phase, respectively.

As expected from reaction IV, the extraction efficiency was found to increase with the concentration of TOPO and a virtually total extraction of Eu, Gd, Y and Yb was achieved with 0.3 M of extractant.

These results are of great practical interest for valorizing waste products of the phosphate industry as Y and Eu have been designated as critical REEs that are expected to be in short supply in the coming years [START_REF] Al-Thyabat | In-line extraction of REE from Dihydrate (DH) and HemiDihydrate (HDH) wet processes[END_REF]. La and Ce were much less extracted, with performance not exceeding 38 and 55 %, respectively. Qualitatively similar results were reported for tributylphosphate, another neutral solvation extractant with which only REEs lighter than Sm were effectively extracted from nitric systems [START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF].

It is noteworthy that much lower extraction efficiencies were reported for both LREEs and HREEs (∼ 10 and 20 %, respectively) when TOPO diluted in kerosene was used to extract REEs from apatite ores leached with sulfuric acid [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF]. It confirms the major impact of (i) the nature of the acid used in the leaching step and (ii) the type of diluent, on the liquid/liquid extraction. Figure 9 shows the separation factors (computed from Equation 4) between the three categories of REEs (HREEs, MREEs and LREEs) as a function of the TOPO concentration. The selectivity between HREEs and LREEs was found to increase with the TOPO concentration (Figure 9a). It reached values in the range 150 -750 for 0.3 M, thus offering excellent capabilities for selective separation of HREEs and LREEs. It can be noted, however, that much smaller selectivities (not exceeding 6) were obtained when using lower TOPO concentrations (0.05 and 0.2 M). The selectivity between HREEs and MREEs was very low, irrespective of the TOPO concentration (Figure 9b), while the selectivity between MREEs and LREEs increased with the TOPO concentration and exceeded 100 for the highest TOPO concentration (Figure 9c). Finally, as shown in Figure 9d, TOPO was unable to separate selectively REEs belonging to the same category (HREEs, MREEs or LREEs). Figure 10 shows the extraction efficiency of the various REEs by D2EHPA in chloroform. Similarly to TOPO, the REEs extraction efficiency was found to increase with increasing the D2EHPA concentration in the organic phase. It is worth mentioning, however, that increasing the extractant concentration leads to an increase in the organic-phase viscosity, and thus a too high extractant concentration may result in difficulty of phase separation [START_REF] Wu | Simultaneous recovery of rare earths and uranium from wet process phosphoric acid using solvent extraction with D2EHPA[END_REF].

From the results shown in Figure 10 it can be concluded that the extraction efficiency of D2EHPA increased with decreasing the ionic radius of REEs [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF]. Similar results were reported elsewhere [START_REF] Battsengel | Recovery of light and heavy rare earth elements from apatite ore using sulphuric acid leaching, solvent extraction and precipitation[END_REF][START_REF] Kumar | Solid-liquid extraction of heavy rare-earths from phosphoric acid solutions using Tulsion CH-96 and T-PAR resins[END_REF][START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF][START_REF] Radhika | Liquid-liquid extraction and separation possibilities of heavy and light rare-earths from phosphoric acid solutions with acidic organophosphorus reagents[END_REF]. It can be understood thanks to the HSAB theory [START_REF] Pearson | Hard and Soft Acids and Bases[END_REF] since D2EHPA can be considered as a hard (Lewis) base due to its chemical structure with localized partial charges. The hardness of REEs (Lewis acids) increases as their ionic radius decreases, which results in stronger interactions with D2EHPA and thus better extraction efficiency.

Extraction efficiencies were typically lower with D2EHPA than with TOPO with a maximum efficiency of 88 % for Yb (the hardest acid among the various REEs under consideration) and less than 3 and 4 % for La and Ce, respectively. The lower performance of D2EHPA is partly due to the high acidity of the nitric-phosphoric acid solution obtained by leaching fluorapatite with nitric acid (reaction I). Indeed, D2EHPA belongs to the category of cation-exchanger extractants whose action can be represented in the following general and simplified form (organophosphoric acids tend to form dimers in low polar media) [START_REF] Krea | Liquid-liquid extraction of uranium and lanthanides from phosphoric acid using a synergistic DOPPA-TOPO mixture[END_REF]:

REE 3+ + 𝑛HL ̅̅̅̅ = REE(HL) 𝑛-3 L 3 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ + 3H + (V)
where HL ̅̅̅̅ and REE(HL) 𝑛-3 L 3 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ denote D2EHPA and the metal-extractant complex in the organic phase, respectively.

D2EHPA therefore mainly operates by ion exchange (proton vs. metal), which is thermodynamically less favorable in a strongly acidic medium as shown by reaction V [START_REF] Xie | A critical review on solvent extraction of rare earths from aqueous solutions[END_REF][START_REF] Reddy | Solid-Liquid extraction of terbium from phosphoric[END_REF]. That is also why much higher concentrations of D2EHPA were required (up to 1.8 M) compared to TOPO (not above 0.3 M).

Conclusion

In this study, the feasibility of extracting REEs contained in an industrial waste product from phosphate ores of "Djebel Onk" (Tébessa, Algeria) was investigated. The phosphate ore residue, mainly composed of carbonate-fluorapatite and quartz, was first leached by considering three inorganic acids (HNO3, H2SO4 and H3PO4) at room temperature. The best results were obtained with HNO3 3 N. After

Figure 1 .

 1 Figure 1. Chemical structures of the organophosphorus extractants.

Figure 2 .

 2 Figure 2. Different steps for the treatment of phosphate ores by the Somiphos company in Djebel Onk (Tébessa, Algeria). T2 -T4 are commercialized products whereas T1, T5 and T6 are waste products.

Figure 4 .

 4 Figure 4. Comparison of the experimental XRD data (phosphate ore residue T1) with the ASTM XRD data reference 98-003-4653 (carbonate-fluorapatite: C1.483Ca9.35F1.98O23.329 P4.72).

  Figure 5a shows the REEs concentrations in the leachate after 3-hour leaching in 3N HNO3, H3PO4 and H2SO4 solutions. H3PO4 has proven ineffective for leaching REEs. It is in qualitative agreement with Stone et al. who investigated the leachability of REEs from fluorapatite using HClO4, HCl, HNO3

Figure 5 .

 5 Figure 5. REEs concentrations in the leachate (a) and leaching efficiency (b) for various acids (acid concentration: 3 N; leaching time: 3 h).

Figure 7

 7 Figure 7 reports the impact of the leaching time on REEs release. All experiments were carried out in HNO3 3 N at room temperature. Eu was totally released from the solid after 0.5 h. On the other hand, only ∼ 50-70 % of La, Ce, Gd and Y were released under these operating conditions. Walawlakar et al. reported similar leaching efficiencies for La, Ce and Y contained in phosphogypsum samples leached with HNO3 3 N in only 20 min but by working at temperatures in the range 50 -80°C [42].

Figure 7 .

 7 Figure 7. Leaching efficiency for various leaching times (leaching agent: 3N HNO3).

Figure 8 .

 8 Figure 8. REEs extraction efficiency as a function of TOPO concentration.

Figure 9 .

 9 Figure 9. Separation factors between REEs as a function of TOPO concentration. (a) selectivity between HREEs and LREEs; (b) selectivity between HREEs and MREEs; (c) selectivity between MREEs and LREEs; (d) selectivity among REEs belonging to the same category.

Figure 10 .

 10 Figure 10. REEs extraction efficiency as a function of D2EHPA concentration.

Figure 11 .

 11 Figure 11. Separation factors between REEs as a function of D2EHPA concentration. (a) selectivity between HREEs and LREEs; (b) selectivity between HREEs and MREEs; (c) selectivity between MREEs and LREEs; (d) selectivity among REEs belonging to the same category.

  24 h, it was indeed possible to recover almost 100 % of all REEs from the solid residue (La, Ce, Eu, Gd and Y) with the exception of Yb for which leaching efficiency did not exceed 10 %. Liquid / liquid extraction was further applied with various concentrations of organophosphorous extractants (TOPO and D2EHPA) in chloroform at room temperature. TOPO at 0.3 M enabled a virtually total extraction of Eu, Gd, Y and Yb while La and Ce were much less extracted (38 and 55 %, respectively). TOPO at 0.3 M also showed excellent selectivities between HREEs (Y, Yb) and LREEs (La, Ce) and between MREEs (Eu, Gd) and LREEs with separation factors up to ∼ 750 and 100, respectively. However, it failed to selectively separate HREEs from MREEs. D2EHPA exhibited lower extraction efficiencies (max. 88 % for Yb) than TOPO but it has proven to be more efficient in terms of selectivity, thus potentially allowing the separation of REEs into three fractions corresponding to LREEs, MREEs and HREEs. Overall, the selectivity between REEs belonging to different categories increased with the TOPO concentration whereas the opposite was observed with D2HEPA. None of these organophosphorous extractants was able to yield a satisfying separation between REEs belonging to the same category (HREEs, MREEs or LREEs).

Table 2 .

 2 REE content of the phosphate ore residue.

	Peak List
	98-003-4653
	10	20	30	40	50	60	70	80	90
					Position [°2Theta] (Copper (Cu))
	Element	La		Ce	Eu	Gd		Y	Yb
	wt. %	0.0280		0.0140	0.0004	0.0078	0.0363	0.0049

Acknowledgements

The authors warmly thank the Algerian Ministry of Higher Education and Scientific Research (MESRS) for Abderraouf Soukeur's Ph.D. scholarship (N°: 484/PNE/France/2019-2020) through the National Exceptional Program (PNE). The authors are also grateful to Fatiha Halouat for ICP analyses and to Mokhtar Lakhal, Rebai Houam and Bessam Amara, from the Somiphos phosphate mining company, for their cooperation in carrying out this work.

acid medium using bifunctional phosphinic acid resin, tulsion CH-96, Solvent Extr. Ion Exch. 27 (2009) 695-711. https://doi.org/10.1080/07366290903270031.


Katy Blanc
email: kblanc@i3s.unice.fr

Diane Lingrand
email: lingrand@i3s.unice.fr

Frederic Precioso
email: precioso@i3s.unice.fr

SINGLETS: MULTI-RESOLUTION MOTION SINGULARITIES FOR SOCCER VIDEO ABSTRACTION

The burst of video production appeals for new browsing frameworks. Chiefly in sports, TV companies have years of recorded match archives to exploit and sports fans are looking for replay, summary or collection of events.

In this work, we design a new multi-resolution motion feature for video abstraction. This descriptor is based on optical flow singularities tracked along the video. We use these singlets in order to detect zooms, slow-motions and salient moments in soccer games and finally to produce an automatic summarization of a game.

We produce a database for soccer video summarization composed of 4 soccer matches from HDTV games for the FIFA world cup 2014 annotated with goals, fouls, corners and salient moments to make a summary. We correctly detect 88.2% of saliant moments using this database. To highlight the generalization of our approach, we test our system on the final game of the handball world championship 2015 without any retraining, refining or adaptation.

Introduction

In the world of digitization we live in, big quantities of numerical data are stored and available. This is particularly common for image and video databases since a simple clip in high definition of 30s contains 750 frames (with 25fps) and therefore more than a billion pixels. The amount of stored videos keeps increasing every hour. For instance, last IPhone and Samsung smart phones take short videos instead of static pictures, that they called respectively "live photos" and "motion photos". "Live photo" is perfectly chosen name since even a very brief motion recording gives life to a simple picture. Besides every Facebook user can now have a video profile on his main own page instead of a classic profile picture. The number of Youtube videos increased to such an extent that Google Research just released a dataset called YouTube-8M that contains half a million hours of videos [START_REF] Abu-El-Haija | Youtube-8m: A large-scale video classification benchmark[END_REF]. To face this always increasing amount of videos, algorithms must analyze and recognize the content of these elements to be able to extract knowledge, statistics and ev-erything that a user could look for. With over a decade of extensive research, there has been a tremendous development in the domain of video content mining [START_REF] Lavee | Understanding video events: a survey of methods for automatic interpretation of semantic occurrences in video[END_REF][START_REF] Vijayakumar | A study on video data mining[END_REF].

In this article, we present a new motion descriptor based on extracting singularities in the motion domain in Section 3, that is detecting specific motion patterns in the optical flow. In Section 3.2, we build a unified description of optical flow that allows us to describe different aspects of video semantics. We call this descriptor singlet which corresponds to motion singularities at different resolutions tracked along a video. As a good context of video abstraction, we focus on the application of our new motion features for sport analysis, more specifically soccer matches. In the experiment section, our flow description is detailed for zoom detection, extraction of salient moments and slowmotion detection. We then propose an automatic method of production of video skimming. Finally, we evaluate the singlets' efficiency in various contexts: soccer games from the World cup 2014 and the final game of handball world championship 2015.

Related Works

We classify the contributions regarding video analysis along two axes: retrieval and abstraction [START_REF] Hu | A survey on visual content-based video indexing and retrieval[END_REF].

On the one hand, video retrieval is a very active research field aiming at providing tools to retrieve videos from content. The current state of the art methods for video content representation start by detecting keypoints. Most of the time, these keypoints are then tracked along the video, and finally described by combining a description of both static and dynamic visual information (shape, appearance...). Among these contributions, let us cite the seminal work on Space-Time Interest Points (STIP) [START_REF] Laptev | On space-time interest points[END_REF] which proposed to combine Histograms-on-Oriented-Gradients (HOG) with Histograms-on-Optical-Flow (HOF). In [START_REF] Raptis | Proceedings, Part I, chapter Tracklet Descriptors for Action Modeling and Video Analysis[END_REF], the tracklets are also defined from HOG and HOF and classified using dynamic time warping. Improved dense trajectories (iDT) adds SURF and MBH (derivative of HOF) to the description, keeping a combination of keypoint displacements [START_REF] Wang | Action Recognition by Dense Trajectories[END_REF]. However all these standard motion descriptors usually do not hold complex motion information. Recently, deep learning convolution networks for video description, such as the C3D network [START_REF] Tran | Learning spatiotemporal features with 3d convolutional networks[END_REF], have been considered, but for now they only achieves complementary results compared to iDT.

Abstraction consists in segmenting the video stream into consistent content units and generating a brief overview of the video from these units. Truong et al. [START_REF] Truong | Video abstraction: A systematic review and classification[END_REF] lists and compares techniques providing video abstraction by distinguishing video summarization, made of static video keyframes, from video skimming, made of dynamic video shots. Four types of video are much analyzed: meetings, movies, broadcast news and sports [START_REF] Xiong | Semantic retrieval of video[END_REF]. The growing mass of available video data is well illustrated in the sports domain: TV channels have broadcast matches in soccer competitions for years. Nowadays, the amount of sport broadcast has drastically increased with the legalization of sports betting. The algorithms to enhance these broadcasts are eagerly awaited and related research works have emerged.

In video abstraction and in particular in soccer video abstraction, people do not use the state of the art representation, iDT, which is made for retrieval and is not suitable for motion abstraction. From a single match, there is already a big amount of information to extract in order to summarize the match: number of passes or goals, players' statistics... For example, by focusing on play-break session can filter video information [START_REF] Ekin | Generic play-break event detection for summarization and hierarchical sports video analysis[END_REF]. To detect the play-break moments, Xu et al. [START_REF] Xu | Algorithms and system for segmentation and structure analysis in soccer video[END_REF] used heuristic rules based on view classification (long, medium and close-up views) while Xie et al. [START_REF] Xie | Structure analysis of soccer video with hidden markov models[END_REF] used a stochastic structured model by HMM. Also in a stochastic approach, Leonardi et al. [START_REF] Leonardi | Semantic indexing of soccer audio-visual sequences: a multimodal approach based on controlled markov chains[END_REF] proposed controlled Markov chains to detect goals.

In general, the first approach in soccer video analysis is to segment shots and extract features. These low-level features are extracted from the frames and are often associated with hand-crafted features, like line marks, ball tracking or the color of the players jersey. Gong et al. [START_REF] Gong | Automatic parsing of tv soccer programs[END_REF] use these features to classify events like shots or corner kicks.

A soccer match is quite long and contains few interesting actions, which is why detecting salient moments is the most active research side in the soccer video domain. Other hand-crafted features like the overall excitement computed from shot length, motion and audio activity are used to characterize game extracts in [START_REF] Hanjalic | Generic approach to highlights extraction from a sport video[END_REF]. These features are found by building mid-level representation of the shots that can be learned to recognize events: Duan et al. [START_REF] Duan | A mid-level representation framework for semantic sports video analysis[END_REF] used shot lengths and texture maps to train a SVM while Wu et al. [START_REF] Wu | Events recognition by semantic inference for sports video[END_REF] used global motion estimation to train a neural network. Sadlier et al. [START_REF] Sadlier | Event detection in field sports video using audio-visual features and a support vector machine[END_REF] focused on audio features, and low-level features to train a SVM and they claims their techniques to be generic while only focusing on "field sports" and thus benefiting from knowing the ground color (grass), field line marks and others shared characteristics. Yow et al. [START_REF] Yow | Analysis and presentation of soccer highlights from digital video[END_REF] built a panoramic representation of a shot and then select important shots using heuristics. Assfalg et al. [START_REF] Assfalg | Semantic annotation of soccer videos: automatic highlights identification[END_REF] and Tabii et al. [START_REF] Tabii | A new method for soccer video summarizing based on shot detection, classification and finite state machine[END_REF] used finite state machines, respectively one based on ball motion, players positions and jerseys and the other one based on play field segmentation, shot detection and classification, however this method requires good handmade rules. Ye et al. [START_REF] Ye | Exciting event detection in broadcast soccer video with mid-level description and incremental learning[END_REF] chose an incremental learning SVM on a mid-level description containing the features of successive moments like view labels, line mark positions and shot descriptors to select highlights. After using an artificial neural network in order to detect the appearance of logos and score and using Hough and k-means to detect goal mouths, Zawbaa et al. [START_REF] Zawbaa | Event detection based approach for soccer video summarization using machine learning[END_REF] classified goals, attack and other events with an SVM from the detection of goal mouth position. In recent work, Raventos et al. [START_REF] Raventos | Automatic summarization of soccer highlights using audio-visual descriptors[END_REF] ranked shots and their associated keyframe using face and skin detection, whistle detector and user specifications.

All these methods use at best an energy function to measure the motion activity whereas the motion in a soccer game is probably the most important information. We now present our adaptive and generic representation to describe the motion and show how this representation allows us to build a video abstraction.

Video movement analysis

Our method of motion content analysis is inspired by the work of Kihl et al. [START_REF] Kihl | Multivariate orthogonal polynomials to extract singular points[END_REF] which extracts singularities from motion in the domain of fluid mechanics. A singularity is a vanishing point akin to root for polynomials. It can be seen like keypoints in optical flow. Optical flows are projected to polynomial bivariable function space to detect these vanishing points from their polynomial approximations. Starting from the definition of these singularities, we design a new local motion video content descriptor.

Polynomial projection of optical flow and singularities

The two horizontal and vertical components of the optical flow U and V at each pixels (x 1 , x 2 ) are computed using the method of Gunnar Farneback [START_REF] Farnebäck | Two-frame motion estimation based on polynomial expansion[END_REF]. U and V are projected onto Legendre basis to get the best approximation in the polynomial optical flow space. Then they are expressed in a canonical basis.

P U (x, y) = K k=0 L l=0 u k,l .x k .y l ; P V (x, y) = K k=0 L l=0 v k,l .x k .y l (1) with K + L ≤ degree.
Similarly to the work of Kihl et al. [START_REF] Kihl | Multivariate orthogonal polynomials to extract singular points[END_REF], we restrict approximations to degree 1.

U V A x 1 x 2 + b = a 11 x 1 + a 12 x 2 + b 1 a 21 x 1 + a 22 x 2 + b 2 (2)
Indeed, according to A and b, the singularities of the optical flow appears at the position

(x 1 x 2 ) T = -A -1 b.
The type of a singularity depends on tr(A) and ∆(A).

∆(A) = (tr(A)) 2 -4 det(A) (3)
We present the different configurations in figure 1.

Figure 1. Classification of singularities based on the value of A (illustration from [START_REF] Kihl | Multivariate orthogonal polynomials to extract singular points[END_REF]).

Singularities are detected using a sliding window at different scales (from 0.1h to 0.5h by steps of 0.1h where h is the smallest dimension of the video, usually the height). This makes the singularity to be multi-resolution compliant. Multiple singularities are detected at different scales at the same position. These multiple singularities have not been merged, as for SIFT features, since they could be of different types or intensity and carry different information.

By definition, a singularity corresponds to vanishing points. Thus no singularity will be detected in a pure translation. A singularity is not detected in situations where A is not invertible. Moreover the highest the determinant is, the more significant singularities are preserved: a threshold on det(A) permits to filter the noisy singularities and to keep informative ones. No thresholding on det(A) implies to keep every singularities, even the ones with very small motion which are most probably produced by pixel noise.

Thereafter, we globally or locally extract these singularities, according to what we focus on.

Spatio-temporal representation

As introduced above, singularities can be tracked along a video to describe a time lapse.

For T frames, T -1 optical flows are computed. On each of these optical flows, we extract the singularities. In order to build chains of singularities, called singlets, they are matched in reverse time. Based on the hypothesis that a singularity has a small displacement between two frames and to reduce computational cost, we match only singularities in a near neighborhood. Thus, for each singularity sing s in the optical flow f t , the singularity candidates in the optical flow f t-1 are restricted to a near neighborhood V (sing s ). Two singularities are considered in the same neighborhood if their sliding windows have a suitable overlap ratio (figure 3.2) as defined directly below:

V (sing s ) = sing; area(W (sing) ∩ W (sing s )) area(W (sing) ∪ W (sing s )) > α
(4) where W (sing s ) is the sliding window of sing s . To match singularities during time, the best candidate within a close neighborhood is selected as the one which minimizes the singularity distance described below:

d(   A x y   ,   A x y   ) = ||A-A || F +λ|| x y - x y || 2 (5)
where λ is a weight balancing the distance between the positions and the similarity between singularity coefficients values. In each affine optical flow f t , a singularity sing s is described by 6 coefficients, 4 in A and 2 in b, and the distance matching deals with these information.

• Since b contains information about the singularity center location within its windows W (sing s ), we convert this center in a pixel position (x, y).

• Since A contains information about the singularity type (fig 1), matching the coefficients of A leads to match singularities of the same type or at least with close vector field aspects.

The entire algorithm to extract singularities and match them as a singlet is described in algorithm 2. An example of singlet is presented in figure 3.

Collecting singlets along a video and analyzing their shapes, positions or their lengths provide robust description of optical flow within this time lapse. Besides, in the next section, we detail our application of singlets description on soccer videos in order to sum up sport matches. Facing the lack of benchmark from TV in the domain of sport video analysis, we have recorded our own videos from HDTV broadcasting. We manually annotated zooms and slow motions from 4 soccer matches of the FIFA World CUP 2014 (Germany vs Portugal, Nigeria vs Argentine, France vs Honduras, Switzerland vs France) and the Qatar Handball World Cup 2015 final. Each video has been scaled to 25 fps.

In order to evaluate our salient moment detection, we have extracted the ground-truth for the 4 selected matches (Germany vs Portugal, Nigeria vs Argentine, France vs Honduras, Switzerland vs France) from lists of salient moments extracted on the official FIFA website [START_REF]fifa world cup brazil: matches description[END_REF]. As can be seen from these ground truths, the description of each salient event is linked to a given minute of the match and describes roughly the action. We manually annotated the salient moments from the FIFA description with the number of starting and ending frames to obtain a frame level decision.

We improved the annotation of this benchmark to make it compliant with a computer vision groundwork. First, we have completed this list of salient moments by adding all corners and kick-off to fill missing actions. Secondly, we have merged the salient moments which are listed twice: for instance, a goal from a kick-off listed as first an action of kick-off and an action of goal. We call the ground-truth with this completed list of salient moments: Extended groundtruth. In table 1, we report the amount of salient moment in each games and in each database.

In this database, there are more than 7 hours, precisely 696002 frames. For reproducible research sake, all our metadata and our code will be available on our website1 .

Zoom detection

In a soccer match from TV channel, zooms, and in particular zoom(s)-in(s), are effective indicators of highlights and salient moments of the match, since they represent a natural reaction of the cameraman to an action salience.

To evaluate, we use a video of the half soccer game, i.e. more than 128500 frames. We only annotated persistent zooms which are important in intensity and in time. There are exactly 5659 positive optical flows and 122841 negative optical flows. To compare each methods, we use ROC curves (figure 4 and5) which well illustrate performances, even in the case of unbalanced classes.

The two singularities star node and improper node (figure 1) represent zooms. Two conditions are required for these detection: a strong determinant det(A) and a low ∆(A) (cf eq. 3). det(A) corresponds to the intensity of the optical flow. In figure 4, we evaluate the influence of a threshold on det(A) over zoom detection performance: no threshold on det(A) implies that every global motion is a zoom candidate, even slight ones and as one could guess, that option gives poor results; with a threshold on det(A), results are quite stable. Since projections are all computed from optical flows and in order to get a detection with time consistency closer to human perception, we add a chronological window to average these ∆(A) during time. After grid search on the window size from 5 to 100, best results are obtained with a time history of 30 frames, that almost corresponds to a second. We obtain best results with a chronological average, a threshold of 0.2 on det(A) and a threshold of 4 on ∆(A) (figure 4).

Usually zooming are detected by the Global Motion Estimation (GME) method [START_REF] Ye | Exciting event detection in broadcast soccer video with mid-level description and incremental learning[END_REF]. For this method, we used the RGMC [START_REF] Safdarnejad | Robust global motion compensation in presence of predominant foreground[END_REF] method to compute the homography h t that models the camera motion for each frame t.

x = m 0 x + m 1 y + m 2 y = m 3 x + m 4 y + m 5
According to [START_REF] Qian | Global Motion Estimation and Its Applications[END_REF], a zoom is then detected if m 0 and m 4 are equals. We set then a threshold on their difference. The best threshold value found for GME method is 0.0004.

In [START_REF] Duan | A unified framework for semantic shot classification in sports video[END_REF], Duan quantified motion vectors to produce two histograms, on angles and on magnitudes. A zoom is detected if there is enough vectors with small norms and enough vector angles between the following angles We compare our method with the best parameter setting with reference approaches but we can see by looking at figures 4 and 5 jointly that our method is not very sensitive to the parameter setting since most of the settings provide better results than reference approaches.

In the table 2, we compute the accuracy of each method with the best corresponding threshold. Since our database is unbalanced with 5% of positives samples, the precision values are weak but are still a good indicator of recognition rate to check if the classifier does not always answer negative classes.

Our zoom detection method has three advantages. The main advantage of our method is that zooms are detected even if the zoom direction is not in the image center. As can be seen in figure 6, the optical flow center (represented as the light blue dot on the third row) is very far from the zoom center which is still detected. To the best of our knowledge, such a result can only be achieved with our approach. Moreover, we can also localize the zoom center which is an indicator of where the action happens. Finally, the last advantage is to easily differentiate zoom-in and zoom-out. In the case of those singularities, star node and improper node, the eigenvalues of A are equals. Thus we simply have to check the sign of one of the eigenvalues to differentiate zoom-in and zoom-out. This method is very efficient to detect zoom anywhere in the video.

Therefore, extracting global singularity on the whole op-

Global excitement

We made the hypothesis that a salient moment of team sports is when several players are in conflict to get the ball or when players are running towards the goal (attack). In that cases, there are local singularities around moving zones and these singularities will have a temporal consistency.

We detect singularities in each optical flow within a sliding window and compute a spatial histogram on their positions. Our purpose is to detect regions where there is an global excitement. Each image is splitted by a 3x3 histogram, 9 uniform bins (see figure 7).

In order to stabilize spatial histograms through time, we sum spatial histograms within a temporal window of size 10 frames. We discard video regions where there is a scoreboard and sum up the remaining bins. We choose this indicator to select moments for a summary and sort them according to their intensity based on the aforementioned hypothesis. These histograms are particularly interesting when they are extracted from the farthest view in a match. Figure 7. Left: a shot with all detected singularities. Each colored square corresponds to one singularity, with the color of their type (figure 1). Right: their corresponding space-time histogram expressed with the given heat scale representing the amount of singularity.

Other clues indicate that an important action just happened such as replays (slow motions).

Slow motion detection

When a fast action deserves to be detailed, producers usually use slow motions, often from an other point of view to see all details. Thus we can detect the match salient moments in spotting slow replay. Most of the proposed solutions for this detection problem use the video production habits that consist usually in putting a logo before and after each replay. Pan et al. [START_REF] Pan | Detection of slowmotion replay segments in sports video for highlights generation[END_REF] used a HMM algorithm to detect slow motion from differences between frames and an HMM to model states before and after the slow motion like editing effects for shot transition. Zawbaa et al. [START_REF] Zawbaa | Event detection based approach for soccer video summarization using machine learning[END_REF] filter each frame of the video with the logo dominant color and a trained SVM predicts if the logo appears or not. This type of method has the drawback of both requiring a training set of logo appearance and totally ignoring that the motion is very slow.

To detect slow motion, we focus on the slowness intensity of motion. Our method is based on a simple assumption that is: in a slow replay, a motion will be consistent during time. A singlet describes a typical motion evolution until it totally change its type. Therefore the length of singlets tells us how long a motion last. Thus several long singlets implies that the shot is a slow motion.

We compute the length of each singlet and store their length in a histogram of 100 bins. The histogram is then considered as the feature vector for detecting video slowness. To detect slow motion in video, we train a SVM with a radial basis kernel function after whitening and a PCA on our slow motion feature vector. To train an SVM, we use a database of 82 videos containing 41 slow motion and 41 non slow motion video parts extracted from three of the soccer matches. In our experiment, we set the parameters as α = 0.4 for the neighborhood selection (cf eq 4), λ = 0.02 for the matching distance (cf eq 5) and C = 29 and γ = 4.10 3 for the SVM training.

The test sets is composed by the rest of slow motion and non slow motion samples in each soccer matches, being 33 slow motion segments and 33 non slow motion segments. In order to evaluate the power of generalization of our descriptor, we add 5 slow motions and 5 non slow motions part extracted from the handball game.

Table 3 presents our recognition results on each slow motions dataset. As you can see, we obtain high accuracy for soccer slow motions classification. With the same feature extraction framework and without retraining the SVM, we obtain a slow motion detection at high precision score for the handball dataset. Since our framework was trained on soccer matches and since we do not change any parame-ters, regarding the results on the handball game, it is indeed generic in spite of an over detection effect.

In the next part, we describe how singlets are useful through these detections to extract salient moments of a match and make a summary.

Salient moment detection and match summarization

Singularities and singlets represents motion regions. Globaly extracted, singularity represents camera motion: we use star node and improper node to spot zooms in section 4.2. Locally extracted, they represents players and ball mouvements: we use the amount of singularities to characterize global excitement. Singlet identifies singularity's evolution during time: we use their length to notice slow motions by their nature.

From the singlets' descriptions, we compute a summarization. We select best moments by a combination of several zoom-in and zoom-out, followed by a peak in the space time histogram of singularities and then a replay of the action with a slow motion.

In order to combine different clues of the salient moments, we build a frieze for each different values. In figure 8, you can see on the left a soccer video frame and on the right its actual singlets space-time histogram. Underneath, from top to bottom, there are 5 friezes. The first frieze corresponds to extracted zooms: red for zoom-in and blue for zoom out. The second frieze shows the quantity of zoom changes within a second according a heat scale. The next frieze shows the amount of large vectors also using a heat scale. We use this light indicator to contrast close-up view from large field view. The forth frieze indicates SVM classification for slow motions in close up views: red for slow motion and blue for non slow motion. Finally the last frieze indicates the amount of singularities: the global excitement indicator.

A match summarization is the concatenation of detected salient moments. A salient moment is detected if within 30 seconds time frame there are:

• at least two zoom direction changes, and

• an activity peaks higher than 1500 (at least 1500 singularities) in a farthest view, and

• a slow motion replay in a close up view.

Therefore, we extract a list of main moments of the match with these rules. On these 4 matches, our method obtains the results referred in table 4.

Unfortunately, the authors of summarization methods for soccer games do not provide any source code nor any binary executable to reproduce their results on our database and the re-implementation implies either human user specifications, not provided thresholds or logo database collection. This makes the comparison impossible for video summarization. We can summarize a soccer match by extracting zooms, by detecting slow motion and salient moments without any hypothesis on the player movements, just in analyzing global video motion. To compute the summary, the shots that contains the detected activity peaks are aggregated.

Since we do not use either soccer characteristics or producing specificities (e.g. logos), our approach is generic. In order to confirm this, we have set all parameters of our method for soccer and train the SVM on soccer video training set. We have then extracted salient moments on a extract of an handball match without any retraining, refining or adaptation. The extract is a part the HDTV video of the final of the 2015 world championship, Qatar against France (figure 9). We detect on that extract one salient moment, followed by one slower replay, out of the three which are indeed in this extract ground-truth. Please notice that the handball field is purple, and that the players are moving differently with zone restriction rules really different from soccer games.

Discussion

In this article, we focus on detecting salient moments as zooms, slow motion replays and global excitement of play- ers. However our description gives other information within the projection coefficients that could lead to a semantic description of a game.

For instance, the simple degree 0 on polynomial basis (cf eq.1) can provide interesting information in the process of semantic description: u 0,0 and v 0,0 gives the translation on the vertical and the horizontal axis. These coefficients from the projection of the global optical flow, as computed for zoom detection 4.2, characterize the camera translation and then they determine the presence of an attack phase or a counterattack phase.

These projections can be done from any bivariable function to any degree of polynomial bivariable function. We are currently studying these coefficients to provide other clues on a soccer match.

In the open code, we provide the possibility to set the degree of polynomial projection, so these other motion features can be easily computed.

Conclusion

We have presented in this article a new robust multi-scale video descriptor: the singlets. They correspond to the tracking of singularities in the polynomial projections of optical flow along the temporal dimension of the video.

This descriptor proves its informativeness in detecting zooms (in and out), slow motions and salient moments during sport events without any ad-hoc elements (no logo, no particular ground color), thus allowing to build relevant sport summary.

On future works, we will evaluate the potential of singlets for a retrieval task as a motion descriptor itself or as a complementary description to a shape and color description.

Figure 2 .

 2 Figure 2. Two successive optical flows: Searching a match for the singularity s c t within the singularities in the previous optical flow. Regarding the overlap ratio, s sp t-1 and s c t-1 are candidates while s sn t-1 is not. The match is the closest singularity regarding localization and type: s sp t-1 . Singularity types sp, sn and c respectively correspond to spiral, star node and center.

Figure 3 .

 3 Figure 3. Singlets: illustration of matching of singularities extracted from real optical flow on three consecutive frames in a soccer match. It is a spiral singularity (red, as in figure 1) as can be seen from the flow. Match FIFA Extended ground-truth ground-truth Germany vs Portugal 30 27 Nigeria vs Argentine 51 35 France vs Honduras 54 32 Switzerland vs France 40 26

Figure 4 .

 4 Figure 4. ROC curves of our method for different thresholds on det(A). Best result is obtained when there is a threshold of 0.2 on det(A) and an averaged ∆(A) on 30 frames.

Figure 5 .

 5 Figure 5. ROC curves for each methos for zoom detection: our method vs Duan method vs GME method.

Figure 6 .

 6 Figure 6. A zoom detected in a soccer match. From left to right: 3 consecutive frames. From top to bottom: original frames (ball highlighted by a red square), original optical flows and polynomial optical flow approximations. In the last rows, the singularity center is represented by a small target and it is centered on the soccer ball that you can see in the first row.

Figure 8 .

 8 Figure 8. Top left: random frame of a soccer match. Top right: its space time histogram. Bottom: 5 friezes that describe a salient moment detection criteria (from top to bottom: zoom-in/out, zoom changes count, saturation, slow motion detection and activity score).

Figure 9 .

 9 Figure 9. Frame of the extract of handball game.

  sing s in flow n do foreach singularity of flow n-1 within V(sing s ) do find the one with the best distance between their As and the singularities positions; end if the bestdistance is under 2 then if the bestMatch is at the end of a singlets then add sing s in this singlets; else create a singlets with the both singularities.; if no match has been found within flow n

	foreach frame in the shot do
	get the frame f n ;
	if previous frame exists then
	compute the optical flow n =(U,V) from f n-1
	and f n ;
	foreach sliding window do
	crop the optical flow within the window;
	compute the projection of each component
	U and V by doing the scalar product of
	each component with each element P i,j
	of the Legendre basis;
	change of basis to get A and b;
	detect if there is a singularity and its
	characteristics;
	end
	end
	foreach detected singularity then
	search a match in the previous flow
	until an historic of 5 flows
	end
	end
	end
	end
	Algorithm 2: Algorithm to extract singlets
	4. Experiments
	4.1. Data

Table 1 .

 1 Number of salient moments in each match according to the ground-truth of all the moments described on FIFA official webpage vs our extended ground-truth.

Table 2 .

 2 Precision, recall and accuracy for zoom detection.

	Method Precision	Recall Accuracy
	GME	3.68 %	68.4 %	19.79 %
	Duan	8.92 % 50.62 %	75.06 %
	ours	19.45 % 63.47 %	86.82 %

[15; 75] ∪ [105; 165] ∪ [195; 255] ∪ [285; 345]. Therefore, this method requires two thresholds which are not provided. The detection gives best results without filtering the magnitude histogram (i.e. no threshold on the magnitude histogram) leading us to focus on the angle histogram. The best threshold value for Duan method on the angle histogram is 42% of the pixels numbers.

Table 3 .

 3 Precision, recall and accuracy for slow motion detection on different datasets.

	Dataset	Precision	Recall Accuracy
	Train	97.06 % 80.49 %	89.41 %
	Test	76.32 % 87.88 %	79.36 %
	Test on handball	100 %	20 %	60 %

Table 4 .

 4 Precision rate of detected salient moments by our method over all the salient moments, using two different ground-truth (see paragraph 4.1).

	Match	FIFA	Extended
		ground-truth ground-truth
	Germany vs Portugal	80 %	88.9 %
	Nigeria vs Argentine	53 %	77.2 %
	France vs Honduras	53.7 %	90.7 %
	Switzerland vs France	62.5 %	96.6 %
	Mean	62.3 %	88.2 %

http://www.i3s.unice.fr/ ˜kblanc/

Acknowledgment

We are grateful to Wildmoka for fruitful discussions