Sabrine Trabelsi
email: trabelsi4sabrine@gmail.com

Anne Morel
email: anne.morel@ensam.eu

Guenael Germain
email: guenael.germain@ensam.eu

Zoubeir Bouaziz

Tool wear and cutting forces under cryogenic machining of titanium alloy (Ti17)

Keywords: Titanium alloy, Cryogenic assistance, Tool wear, Cutting force, High pressure water jet assistance

Titanium alloy is well known for its difficulty to machine, owing to the important "tool wear" phenomenon. Machining assistance is an interesting solution to lengthen the tool lifetime. In this study, we focused on the effect of cryogenic assistance-during machining of Ti17-on the tool wear and cutting forces for different combinations of cutting speed, feed rate and depth of cut. Compared to conventional lubrication, cryogenic support lengthens the tool life for all tested conditions and has no significant influence on cutting force. A comparison of the cryogenic effect and high-pressure water jet assistance is also presented.

Introduction

Titanium alloys have high strength, high chemical reactivity and a low thermal conductivity, causing a high temperature at the tool/chip interface. The high temperature accelerates the tool wear which results in a short tool life [START_REF] Arrazola | MaChinability of titanium alloys (Ti6Al4V and Ti555.3)[END_REF]. To overcome this problem, effective cooling of the interface tool/chip is recommended. The cryogenic support allows a significant cooling by nitrogen liquid, (-196 • C) which makes it possible to improve the tool life when machining titanium alloys, thus avoiding the degradations of the tool among which can be mentioned abrasion, adhesion and diffusion, which are intensified when temperature increases [START_REF] Venugopal | Growth of tool wear in turning of Ti-6Al-4V alloy under cryogenic cooling[END_REF]. Wang and Rajurkar studied the effect of the cryogenic assistance on tool lifetime and surface roughness when machining hard-to-machine materials with different tool inserts [START_REF] Wang | Cryogenic machining of hard-tocut materials[END_REF].

They carried out machining of:

-reaction bonded silicon nitride (RBSN) with three different polycrystalline cubic boron nitride tools (CBN50 of Sandvik and VC734 and VC722 of Valenite); -titanium alloy Ti6Al4V, tantalum and Inconel 718 with H13A tungsten carbide tool from Sandvik.

They found that the tool life is lengthened and the surface roughness is improved with cryogenic assistance for all combinations of tool inserts / materials studied. For the titanium alloy Ti6Al4V, which was machined at 1 mm depth of cut, with a feed rate of 0.2 mm/rev and a cutting speed of 2.2 m/s, the flank wear Vb was equal to 1.1 mm in conventional machining and dropped to 0.22 mm with cryogenic support after 46 mm of machining. Surprisingly, no significant change for the three force components was observed.

Dhananchezian and Pradeep Kurmar compared the influence of cryogenic support to that of conventional lubrication when machining titanium alloy Ti6Al4V at a depth of cut of 1 mm, a feed rate of 0.159 mm/rev and a different cutting speed of 27, 63, and 97 m/min. A modified tool projecting cryogenic liquid on the cutting face and on the primary and secondary flank faces was used. It was noticed that the temperature decreases at the speed of 97 m/min from 504 • C to 192 • C. After 5 min of machining at a speed of 63 m/min, the flank wear was 536 and 370 μm in conventional lubrication and cryogenic support, respectively [START_REF] Dhananchezian | Cryogenic turning of the Ti-6Al-4V alloy with modified cutting tool inserts[END_REF].

The literature contains other works dealing with the application of the cryogenic support on the rake face or the flank face or the rake and flank face simultaneously, and the optimal position of the nozzle during the machining of Ti-6Al-4V alloy. For a depth of cut of 1.27 mm, a feed rate of 0.254 mm/rev and a cutting speed of 1 , 1.5 , 2 , and 2.5 m/s, respectively, it was found that the best injection position of the cryogen liquid is obtained with an injection nozzle between the chip and the rake face of the tool. This assistance increases the cutting and the thrust force and reduces the feed force because it lowers the friction coefficient at the tool-chip interface. In addition, the shear angle increases and the shear band thickness decreases [START_REF] Shane | Friction and cutting forces in cryogenic machining of Ti-6Al-4V[END_REF]. This article aims at investigating the effect of cryogenic support on the Ti17 titanium alloy for two operating conditions, namely roughing and finishing tests, and its impact on the tool lifetime, cutting force and surface roughness. The results of the cryogenic support are then compared to those of conventional lubrication and high-pressure water jet support. A particular attention is drawn to the degradation modes of the tool.

Experimental setup

The material used is the titanium alloy Ti17 (also called Ti-5Al-2Sn-2Zr-4Mo-4Cr). The chemical composition and the mechanical properties are presented in Tables 1 and2. The Ti17 is a mixed alloy of α and β phases (Fig. 1). Its transus temperature is 880 • C. Above this temperature, only the phase β exists. It is mostly used in aeronautic field for its mechanical properties such as resistance to high temperatures, which makes it very difficult to machine. The machining tests were carried on a lathe-turning machine "LEADWELL LTC25iL" (2500 rev/min and a maximum power of 24 kilowatts). A three-component force sensor (9275B) was placed on the tool to acquire the three force components. A charge amplifier (Kistler 5019B) was used to convert the electrical charge yield by the piezoelectric sensor into proportional voltage. The analog signals output are amplified by a charge amplifier (Kistler 5019B). Thereafter, they are passed to an analog/digital converter. The evolution of the effort over time is provided by the Catman Easy software. A Seco JetStream PCLNR 2525M12 tool was used with CNMG120412-23 H13A insert showing a geometry defined by a rake angle of 7 • , a flank angle of 6 • , an edge radius of 30μm and a nose radius of 1.2 mm. The nitrogen jet is provided by two nozzles of 1.7 mm in diameter that project the liquid on the rake face of the tool (Fig. 2). A tank of 180 liters provides the nitrogen liquid supply at a pressure of 12 bars. The cryogenic fluid is supplied to the tool with insulated pipes and a phase separator fitted next to the tool.

The change of cutting parameters (feed rate, depth of cut and cutting speed) results in different tool degradation modes as well as a change of the tool life. An experimental campaign was conducted with a cutting speed of 50 and 90 m/min, a feed rate of 0.1 and 0.3 mm/rev, and a depth of cut of 1.5 and 3 mm. The combination of these parameters was determined by a complete experimental design made by 2 3 experiments to study the effect of each parameter on the tool wear, its life and the cutting force. Table 3 summarizes the test data.

For each test, the analysis focused on:

-the evolution of the tool flank wear and crater; -the tool degradation modes; -the chemical elements present on the tool insert; -the surface roughness (Ra and Rt criterion); -the three cutting force components.

3 Results and discussions

Tool Life

Figure 3 shows the evolution of the flank wear for the first seven tests of the experimental design. Test N • 8 (ap 3 mmf 0.3 mm/rev-Vc 90 m/min) has been removed because the edge collapses after 10 seconds of machining. For ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min (Test N • 1), in conventional lubrication, there is an increase of the flank wear, then occurs a steady state between 12 and 17 min at a flank wear of 0.13 mm, followed by a gradual wear increase again. Under cryogenic conditions, on the contrary, wear evolves constantly. For ap 3 mm-f 0.1 mm/rev-Vc 50 m/min (test N • 2), at first, the curves obtained in both lubrication and cryogenic assistance evolve in very similar ways. From 10 min of machining, the tool wear in lubrication increases more rapidly to reach 0.2 mm after 15 min of machining, whereas in cryogenic conditions it continues to increase gradually up to 0.2 mm for 29 min of machining.

For ap 1.5 mm-f 0.3 mm/rev-Vc 50 m/min (Test N • 3), up to 3 min of machining, the evolution of the flank wear with conventional lubrication and cryogenic assistance are very close, before diverging strongly. For ap 3 mm-f 0.3 mm/rev-Vc 50 m/min (Test N • 4), from the beginning of machining, the flank wear is slightly greater with the nitrogen liquid. However, after 1.1 min, the wear in lubrication becomes much more important.

We can therefore conclude that if the machining condition becomes more severe, the divergence between the two curves begins at a lower machining time. For the cutting speed of 90 m/min, the evolution of the two curves becomes very close with almost the same slopes. The following table (Table 4) shows the lifetimes for each cutting condition and the gain in tool life using the cryogenic assistance compared to the conventional lubrication.

Gain = tool lif e(cryogenic)tool lif e(lubrication) tool lif e(lubrication) * 100

The tool end-of-life criterion is defined by a flank wear of Vb=0.2 mm. It is worth noting that the cryogenic cooling lengthens the tool life regardless of the cutting parameters, but its efficiency differs depending on the used parameters. Indeed, the tool life decreases if the feed, the depth of cut or the cutting speed increases. A complementary study was conducted to better understand the effect of each parameter on the tool life (Fig. 4). In order to take into account the specific nature of the different controlling parameters, it was chosen to represent their effects for a factor increase of 1 mm for the depth of cut, 0.1 mm/rev for the feed rate and 10 m / min for the cutting speed. As a result, the standardized effects are given by: Standardized effect (eap)=( Eap /1.5)/N (ap varies in the range of 1.5 to 3.0 mm, so 1.5 x 1 mm) Standardized effect (ef)=( Ef /2)/N (f varies in the range of 0.1 to 0.3 mm/rev, so 2 x 0.1 mm/rev) Standardized effect (eVc)=( EVc /4)/N (Vc varies in the range of 50 to 90 m/min, so 4 x 10 m/min) With N=|Eap /1.5|+|Ef /2|+|EVc /4| Eap, Ef and EVc are respectively the effect of depth of cut, the effect of feed rate and the effect of cutting speed.

The feed rate shows to be the most influential parameter on the tool life in both cryogenic and conventional lubrication. The second affecting parameter is the cutting speed and the last is the depth of cut. However, this depth of cut is the first responsible criterion causing the greatest difference between the two techniques, considering the tool life. When the cutting speed increases, the heat generation becomes Berhingam et al. carried out the same kind of study on a Ti-6Al-4V alloy regarding the influence of the depth of cut and the feed rate at a cutting speed of 85 m /min. It was noted that the feed rate is the most influential parameter on the tool life at a constant cutting speed. The authors explain this phenomenon by a temperature (and a wear) increase due to a higher heat generation when the feed rate increases [START_REF] Bermingham | New observations on tool life, cutting forces and chip morphology in cryogenic machining Ti-6Al-4V[END_REF].

It is clear that the cryogenic assistance increases the tool life for all the combinations of cutting parameters. For a cutting speed of 50 m/min, the gain in the tool life with a cryogenic machining increases if the depth of cut increases. On the other hand, it decreases with the increase of the feed rate. There is no doubt the cryogenic assistance effectively cools the tool for high depth of cut but it cannot compensate, in a similar way, for the heating of the tool due to the increase of the feed rate.

For the cutting speed of 90 m/min, the gain due to the cryogenic support increases if the feed rate or the depth of cut increases. However, at this cutting speed, tool lifetime is very short, because the generated temperatures are very important. Therefore, the cutting speed and the feed rate must be adequately chosen to machine the Ti17 alloy.

The following pictures (Fig. 5) show the rake and the flank faces and their associated wears after 1 minute of machining with the cryogenic assistance for the various machining configurations. For low feed rates, the flank wear is regular and crater wear is not visible. In contrast, for a high feed rate, the wear is much greater on the flank face and on the rake face where a crater wear is clearly visible. In addition, for this feed, a notch wear can also be noticed. When the feed rate increases, the thickness of the chip increases and the force gets higher. The heat generation is more important because it leads to decreasing the tool hardness and accelerating the wear phenomenon [START_REF] Venugopal | Growth of tool wear in turning of Ti-6Al-4V alloy under cryogenic cooling[END_REF].

After 1 min of machining at f 0.1 mm/rev-ap 1.5 mm, the crater wear is not visible at the end of life of the tool. After about 30 min of machining, a built up edge (BUE) is formed and the crater wear is significant (Fig. 6). For the depth of cut of 3 mm, the crater wear is observable at one minute.

The crater wear is formed in the direction of chip evacuation after the titanium builds up on the cutting face, and then it is removed by peeling. At a feed rate of 0.3 mm/rev, from 1 minute of machining, a notch is formed and the crater is localized at the primary cutting edge (Figs. 7 and8).

Besides the adhesive wear and the abrasion, characteristic of the conventional machining, the wear mode is a creep deformation of the cutting edge, accelerating its collapse especially for greater feed rates [START_REF] Ayed | Degradation modes and tool wear mechanisms in finish and rough machining of Ti17 Titanium alloy under high-pressure water jet assistance[END_REF]. This degradation mode is not observed in cryogenic machining assistance as temperature decreases.

Cutting forces

The cutting forces in machining with the cryogenic assistance are compared to those of conventional lubrication (Fig. 9).

For all the configurations, the cutting forces in conventional lubrication are slightly lower than those obtained with cryogenic support except for the case of ap 1.5 mmf 0.3 mm/rev and Vc 90 m/min. This last tendency can be explained by the rapid wear of the tool when increasing the cutting speed and the feed rate at the same time. This difference is not significant. The cutting force does not seem to be modified by the cryogenic assistance. The thrust force decreased for all the configurations except for (ap 1.5 mm-f 0.3 mm/rev-Vc 50 m/min) where the increase is 2.6 % only. The feed force also declined for all the configurations except ap 1.5 mm-f 0.1 mm/rev-Vc 90 m/min where the increase is 10 %. For a better understanding of the evolution of the cutting forces when machining with LN2, friction tests were conducted using an open system tribometer where a pin rubs on the outer surface of a cylindrical part (made of the work material to be machined) in rotation (Fig. 10). Tests were achieved in conventional lubrication and under cryogenic cooling for three different cutting speeds.

In these tests, a carbide pin similar to the grade of the cutting tool rubs at relevant contact pressure and high sliding speed against the work piece Ti17. During the test, normal and tangential forces are measured to determine the friction coefficient by an inverse method. The normal force is set at 200 N.

During the contact between the pin and the work piece, the tangential force is due to friction between the two materials and the plastic deformation of the contact area (Fig. 11).

A numerical simulation of the test was therefore carried out in order to decouple the friction between the two materials and the effect due to the plastic deformation [START_REF] Ayed | Approches expérimentales et numériques de l'usinage assisté jet d'eau haute pression : étude des mécanismes d'usure et contribution à la modélisation multi-physiques de la coupe-Thèse[END_REF]. The coefficients obtained are shown in the following figure (Fig. 12). The friction test is performed at 3 sliding velocities (Vs=50, 75, 100 m/min).

The friction coefficient μ in cryogenic assistance is lower than that in lubrication. For both conditions, the friction coefficient decreases if the cutting speed increases. At a cutting speed of 50 m/min, the friction coefficient decreases from 0.5 in cryogenic condition to 0.36 in conventional lubrication, corresponding to 28 % decrease, whereas with the speed of 100 m/min it decreases from 0.4 to 0.27, that is to say 32.5 %. Thus, the friction coefficient decreases more strongly when the cutting velocity increases. This decrease in friction coefficient should result in decreasing the cutting force. We can also speculate that the decrease in the friction coefficient is compensated by the increase in the hardness of the work piece material due to the surface cooling by the cryogenic fluid [START_REF] Shane | Friction and cutting forces in cryogenic machining of Ti-6Al-4V[END_REF]. A complementary study will be performed to confirm or deny this hypothesis.

Chip morphology

For every machining test, the chip was collected and observed. Micrographs were performed to highlight the shear bands. It is noted that the chip is continuous and spiral for a feed rate of 0.1 mm/rev, and then it becomes fragmented when the feed rate increases at 0.3 mm/rev. The color of the chip is darker in conventional lubrication whereas it remains unchanged in cryogenic assistance. This is explained by the occurrence of an oxide layer due to the temperature rise in the first condition. From the micrographs of the chips, the following geometrical parameters of the chips have been identified: φ: the shear angle; Dc: The distance between two segments of the chip; F seg : segmentation frequency; D min ; D max (Fig. 13).

F seg = V c D c
The obtained results are summarized in Table 5. For the three cutting conditions, the segmentation frequency has increased and the shear angle has decreased with the application of LN2. The cryogenic assistance decreases the thermal softening and increases the flow stress compared to the conventional lubrication. If the rise of the cutting speed increases the thermal softening and the primary shear angle, then it is logical to expect that the cryogenic cooling decreases the shear angle compared to the conventional lubrication. Microscopic observation of the shear bands shows that their thickness has decreased. For ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min, the shear band thickness decreased from 2.09 μm in conventional lubrication to 1.08 μm in cryogenic support; roughly corresponding to 48 % drop. This decrease in thickness can be explained by the higher location of the shear zone due to the reduction of temperature at the tool/chip interface and the reduction of the frictional force between the cutting face and the chip [START_REF] Shane | Friction and cutting forces in cryogenic machining of Ti-6Al-4V[END_REF].

Comparison of the effect of the cryogenic support to that of the HP water Jet

In order to go further in the analysis of the cryogenic assistance effect, two machining conditions similar to those of Ayed et al., namely the finishing test (ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min) and the roughing test (ap 3 mm-f 0.3 mm/rev-Vc 50 m/min), were performed on our material. Ayed compared the effect of High-pressure water jet support at 100 and 250 bars to the conventional lubrication for these two operating conditions [START_REF] Ayed | Degradation modes and tool wear mechanisms in finish and rough machining of Ti17 Titanium alloy under high-pressure water jet assistance[END_REF].

Roughing tests

The flank wear in machining with HPWJ assistance 100 bars and with HPWJ assistance 250 bars evolve in a similar way, but they evolve slower than the conventional lubrication and the cryogenic machining. The cryogenic assistance lengthens the tool life from 1.1 min in conventional lubrication to 1.75 min, which induces a gain of 59 %. However, it is less effective than HP water jet, which ensures a lifetime of 4.17 min at 100 bars and 4.75 min at 250 bars, which corresponds to a gain of 279 and 331 %, respectively (Fig. 14). The tool chemical analysis shows titanium adhesion to the rake and flank faces of the insert. At 2 min, a titanium oxide layer formation can be observed on the rake face, just next to the tip, and adherent titanium is observed on the remainder of the tool (Fig. 15). This shows that the tip of the tool was not cooled, because for a feed rate of 0.3 mm/rev, the contact length tool/chip increases. The nitrogen liquid is therefore unable to reach the tip of the tool to provide a suitable cooling, whereas the mechanical action of water jet allows the fragmentation of the chip and, therefore, a reduction in the contact length between the chip and the tool, which cools the cutting edge more effectively.

Titanium adhesion was also noticed on the flank face after one minute of machining. A micro-crack, which leads to a rupture of the edge, was also visible (Fig. 16).

The temperature increases with both the depth of cut and feed rate. When it is high, diffusion and adhesion are the two most dominant mechanisms. At this temperature, titanium is very reactive with many chemical elements, especially cobalt which is the binder of the cutting inserts. This chemical affinity leads to a dissolution of cobalt in the titanium, which induces loosening of the tungsten carbide grains of the insert [START_REF] Hua | Acobalt diffusion based model for predicting crater wear of carbide tools in machining titanium alloys[END_REF][START_REF] Zhang | Investigation on diffusion wear during high-speed machining Ti-6Al-4V alloy with straight tungsten carbide tools[END_REF]. The cooling must hence be significant to the tip to prevent the edge rapid wear.

Finishing tests

For the condition (ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min), the lifetime of the tool insert is 35 and 23 min in cryogenic and conventional lubrication, respectively, that is to say a gain of 52 %. With the HP water jet assistance at 100 bars, the tool life is 33 min (43 %). However, it decreases to 23.8 min (3.8 %) with a pressure jet of 250 bars. In this configuration, the feed rate is small (unlike the rough configuration), and the cryogenic cooling is more effective as the contact length tool/chip is low (Fig. 17).

The gain is slightly more significant in cryogenic conditions than with the high-pressure water jet assistance. On the other hand, the HP water jet mechanical action allows the fragmentation of the chip, which is not the case for the cryogenic assistance. For better understanding of the evolution of wear in cryogenic assistance, microscopic observations and chemical analyzes were performed on the tool insert. It was noticed that up to 15 min of machining the wear is uniform, the titanium clusters are adherent on both the rake and the flank faces (Fig. 18).

Up to 30 min of machining, there is no deep crater but chemical analysis reveals the existence of titanium deposits, which are removed in 33 min accentuating the crater formed in the direction of the flow of the chip by adhesive wear (Fig. 19). The streaks on the flank face show the abrasive wear which results from tearing of welded titanium clusters. An SEM analysis of chemical elements for the first cutting condition (ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min) shows the existence of titanium on the flank face. This layer welded to the flank face is torn, causing tool wear. It is the adhesive wear (Fig. 20).

In finishing, the surface roughness is as important as the tool life in insuring the desired quality. To this end, the roughness of the part was raised (Fig. 21).

Unlike in conventional lubrication, the surface roughness with the cryogenic assistance does not increase linearly but remains constant between 0.4 and 0.5 μm up to 30 min. It increases with increasing Vb. In conventional lubrica- tion, the surface roughness starts from a lower value (0.3 μm), but increases linearly until 0.7 μm after 20 min (value obtained in cryogenic conditions at 33 min).

With high-pressure water jet assistance, the roughness fluctuates in larger intervals compared to the case of cryogenic assistance. The work-piece surface shows scratches due to recycling fragments of chips, slipping between the cutting tool and the workpiece [START_REF] Ayed | Tool wear analysis and improvement of cutting conditions using the high-pressure water-jet assistance when machining the Ti17 titanium alloy[END_REF].

Conclusion

The research was conducted to study the effect of cryogenic assistance when machining titanium alloy Ti17 for different machining setups. The results can be grouped as follows:

• The cryogenic support increased the life of the tool relative to the conditional lubrication for all the tested combinations. • For the cutting speed of 50 m/min, the lifetime increases sharply with cryogenic assistance. However, for a cutting speed of 90 m/min, the tool life falls sharply for both roughing and finishing tests. The gain with the cryogenic support becomes low. • Cutting efforts are similar in cryogenic machining and conventional machining, while the friction coefficient is lower with cryogenic assistance. This seems to be due to the material hardening at low temperature. • The comparative study between the HP water jet support at 100 and 250 bars led by Ayed and the cryogenic support showed that the cryogenic assistance is marginally more effective for a finishing operation (ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min). However, in the roughing test (ap 3 mm-f 0.3 mm/rev-Vc 50 m/min), HP water jet assistance is more effective; mainly because of the mechanical action of the water jet that provides cooling to the tip of the tool.

Fig. 1

 1 Fig. 1 SEM observation of the microstructure of the titanium alloy Ti17

Fig. 2 Fig. 3

 23 Fig. 2 Experimental setup

Fig. 4 Fig. 6

 46 Fig. 4 Standardized effects of cutting parameters

Fig. 7 Fig. 8 Fig. 9

 789 Fig. 7 Microscopic observations of the tool wear at 1 min of machining with cryogenic assistance (Vc 50 m/min-ap 1.5 mm-f 0.3 mm/rev)

Fig. 12 Fig. 10

 1210 Fig. 12 Friction coefficient evolution

Fig. 11 Fig. 13

 1113 Fig.11Contact between the pin and the work-piece[START_REF] Klinkova | Characterization of friction properties at the workmaterial/cutting tool interface during the machining of randomly structured carbon fibers reinforced polymer with carbide tools under dry conditions[END_REF]

Fig. 14

 14 Fig. 14 Evolution of the flank wear (ap 1.5 mm-f 0.1 mm/rev) for various machining assistance

Fig. 15

 15 Fig. 15 Microscopic observation of the rake face of the tool at a 1 min and b 2 min of machining (ap 3 mm-f 0.3 mm/rev-Vc 50 m/min)

Fig. 16

 16 Fig. 16 Flank face microscopic observation of the tool at a 1 min and b 2 min of machining (ap 3 mm-f 0.3 mm/rev-Vc 50 m/min)

Fig. 17 Fig. 18

 1718 Fig. 17Flank wear evolution (ap 1.5 mm-f 0.1 mm/rev-Vc 50 m/min)

Fig. 19

 19 Fig. 19 Tool wear with cryogenic assistance at a 30 min, b 33 min at ap1.5 mm-f 0.1 mm/rev-Vc 50 m/min

Table 1

 1 Chemical composition of Ti17 (%)

	Ti	Al	Mo	Cr	Zr	Sn
	82.5	5.16	4.08	4.06	2.01	2.06

Table 2

 2 Mechanical properties of the material

	Ultimalte Tensile strength (MPa)	1110
	σ p02 %	1020
	E (GPa)	114
	Elongation (%)	5

Table 3

 3

	Tests performed on experimental design	Test N •	ap (mm)	f (mm/rev)	Vc (m/min)
		1	1 . 5	0 . 1	5 0
		2	3	0 . 1	5 0
		3	1 . 5	0 . 3	5 0
		4	3	0 . 3	5 0
		5	1 . 5	0 . 1	9 0
		6	3	0 . 1	9 0
		7	1 . 5	0 . 3	9 0
		8	3	0 . 3	9 0

Table 4 Tool

 4

	life for different
	cutting parameters	Tool life (min)
	Condition	Conv. lubrication	Cryogenic	Gain (%)
	ap 1.5-f 0.1-Vc 50	23	35	52
	ap 3-f 0.1-Vc 50	15	29	93
	ap 1.5-f 0.3-Vc 50	3.21	4.1	27
	ap 3-f 0.3-Vc 50	1.1	1.75	59
	ap 1.5-f 0.1-Vc 90	1.09	1.2	10
	ap 3-f 0.1-Vc 90	0.13	0.17	30.7
	ap 1.5-f 0.3-Vc 90	0.1	0.12	20
	ap 3-f 0.3-V c90	0.02	0.033	65

Table 5

 5 Geometrical parameters of the chip

	Vc	f	ap	condition	φ	Dc(μm)	f seg (KHz)	D min (μm)	D max (μm)	Fc(N)
	50	0.1	1.5	Cryo	36.58	109.22	7.62	142.415	224.94	436
				Lub C	76.3	153	5.44	88	150.6	429
	50	0.3	3	Cryo	31.1	169.6	4.91	197.1	350.5	1893
				Lub C	51.5	277.5	3	367	731.7	1846
	90	0.1	1.5	Cryo	36.4	68.1	22	72.9	127.7	429
				Lub C	38.5	110.6	13.56	122.8	264.9	420


Ronan Fablet
email: rfablet@irisa.fr

Patrick Bouthemy
email: bouthemy@irisa.fr

Non-parametric motion activity analysis for statistical retrieval with partial query

Keywords: motion information, statistical models, video indexing, video retrieval with query by example, partial query, motion-based image segmentation, motion classification

We present an original approach for motion-based video retrieval involving partial query. More precisely, we propose a unified statistical framework allowing us to simultaneously extract entities of interest in video shots and supply the associated content-based characterization, which can be used to satisfy partial queries. It relies on the analysis of motion activity in video sequences based on a non-parametric probabilistic modeling of motion information. Areas comprising relevant types of motion activity are extracted from a Markovian regionlevel labeling applied to the adjacency graph of an initial block-based partition of the image. As a consequence, given a set of videos, we are able to construct a structured base of samples of entities of interest represented by their associated statistical models of motion activity. The retrieval operations is then formulated as a Bayesian inference issue using the MAP criterion. We report different results of extraction of entities of interest in video sequences and examples of retrieval operations performed on a base composed of one hundred video samples.

Introduction

Retrieving multimedia documents through large databases is of growing importance in various application fields such as audio-visual archives, multimedia editing, meteorology, traffic surveillance. In particular, to cope with the increasing amount of video data, it is required to define appropriate automatic or semiautomatic schemes for video characterization based on their content, and to associate some measure of content similarity to these description schemes [START_REF] Aigrain | Content-based representation and retrieval of visual media : A state-of-the-art review[END_REF][START_REF] Brunelli | A survey on the automatic indexing of video data[END_REF].

As far as visual documents are concerned, retrieval schemes can be divided into three main categories: retrieval with textual query, retrieval with query by sketch, retrieval with query by example. Textual query simply consists in using natural language to express a query [START_REF] Wactlar | Intelligent access to digital video: The informedia project[END_REF]. It implies to assign a list of key-words to a video, as currently done for audio-visual archives in a manual manner. However, manual annotating cannot cope with the tremendous amount of video data to be analyzed. Automatic semantic characterization of visual content can be performed from the transcription of audio stream as in Informedia project [START_REF] Wactlar | Intelligent access to digital video: The informedia project[END_REF]. Nevertheless, the correspondence between the audio stream and the visual content is not always guaranteed, and visual information represents also an important cue not to be neglected for video retrieval. Besides, methods for semantic characterization of visual content have also been proposed [START_REF] Naphade | Probabilistic multimedia objects (Multijects) : a novel approach to video indexing and retrieval in multimedia systems[END_REF][START_REF] Vasconcelos | Statistical models of video structure for content analysis and characterization[END_REF]. For instance, in [START_REF] Vasconcelos | Statistical models of video structure for content analysis and characterization[END_REF], movies are classified into romance and action films, and in [START_REF] Naphade | Probabilistic multimedia objects (Multijects) : a novel approach to video indexing and retrieval in multimedia systems[END_REF], features are proposed to detect explosions or waterfalls in video sequences. However, the achieved characterization reveals rough or dedicated, and automatic annotating of videos still remains beyond reach for non-specific video bases.

The second category of approaches for video retrieval relies on querying by sketch. To introduce more flexibility in the retrieval process, a sketch drawn by the user to express his/her query can be considered [START_REF] Del Bimbo | Symbolic description and visual querying of image sequences using spatiotemporal logic[END_REF][START_REF] Chang | VideoQ-an Automatic content-based video search system using visual cues[END_REF]. For instance in [START_REF] Chang | VideoQ-an Automatic content-based video search system using visual cues[END_REF], the user can draw a sketch representing the global shape of the object of interest and can specify its direction of displacement by an arrow. Thus, for queries such "retrieve cars going to the right" or "retrieve skiers moving to the left of the image", this scheme is efficient. However, this approach does not allow to formulate a wide range of queries. For instance, how to sketch a query such as "retrieve rugby game samples".

The third class of approaches handles video queries formulated as searching for similar examples as given video samples [START_REF] Adjeroh | A distance measure for video sequences[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Jain | Query by video clip[END_REF][START_REF] Mohan | Video sequence matching[END_REF][START_REF] Vinod | Activity based video shot retrieval and ranking[END_REF]. It benefits from the large research efforts devoted to the automatic extraction of numerical content-based descriptors related to color, texture or motion information. These lowlevel features are stored to compare videos using some feature-based similarity measure. The main limitation of video retrieval with query by example lies in the requirement for the user to be able to provide the system with an initial video query representative of the kind of samples he/she looks for. However, methods relying on query by example currently appears more suited to deal with the variety of contents present in video bases.

As far as retrieval with query by example is concerned, the proposed solutions mainly consider global queries [START_REF] Adjeroh | A distance measure for video sequences[END_REF][START_REF] Deng | Content-based search of video using color, texture and motion[END_REF][START_REF] Fablet | Motion-based feature extraction and ascendant hierarchical classification for video indexing and retrieval[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Jain | Query by video clip[END_REF][START_REF] Mohan | Video sequence matching[END_REF][START_REF] Vinod | Activity based video shot retrieval and ranking[END_REF]. These schemes rely on a global characterization of video content. Nevertheless, the content of the submitted video query is seldomly of interest as a whole w.r.t. user point of view. Furthermore, it seems important to offer the opportunity to the user to focus on specific areas of the video. Therefore, handling partial queries appears necessary. This reveals complex since it requires to automatically extract and characterize entities of interest (w.r.t. user expectations) from each sample of the considered video base.

In this paper, we propose an original approach to tackle this issue while focusing on dynamic content analysis. We have designed a unified statistical framework for the extraction and the characterization of entities of interest in video shots. It relies on a nonparametric probabilistic modeling of motion content in terms of motion activity. In addition, our method provides a complete scheme for video retrieval using partial query embedded in a statistical framework. The remainder of this paper is organized as follows. Section 2 outlines the general ideas underlying our work. Section 3 presents the local motion-related measurements we exploit for non-parametric motion activity modeling. In Section 4, the statistical modeling of motion information and the issue of estimating these models is addressed. Section 5 is concerned with image segmentation w.r.t motion activity with a view to automatically extracting entities of interest. Section 6 deals with motion-based video retrieval with partial query. Experiments are reported in Section 7, and Section 8 contains concluding remarks.

Problem statement

As stressed previously, handling partial queries primary implies to extract entities likely to be of interest for the user. Even if a simple block-based analysis at different scales could supply a first answer to these requirements, some segmentation of the scene, if available, appears more appropriate. The complexity of the segmentation task lies in the variety of situations to cope with in non-dedicated video bases. In a wide range of contexts, the searched entities of interest are nevertheless closely related to specific dynamic content. Hence, motion information represents an important cue for content-based video indexing and retrieval. As far as motion content is concerned, we have obviously to face different kinds of partial video queries. For instance, as illustrated in Figure 1(a-b), the user might be interested in a given moving element in the scene. Such a situation can be tackled using usual motion detection or segmentation techniques [START_REF] Fablet | Moving object detection in color image sequences using region-level graph labeling[END_REF][START_REF] Gelgon | A region-level motion-based graph representation and labeling for tracking a spatial image region[END_REF][START_REF] Irani | Detecting and tracking multiple moving objects using temporal integration[END_REF][START_REF] Mitiche | Computation and analysis of image motion: a synopsis of current problems and methods[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF] provided the scene is not too complex to process. Other cases have also to be considered such as areas of interest composed of different entities. In Figure 1(c-d), we display an example of rugby video sequence within which one might focus on a particular area of the playing field where the game actually lies. Our goal is to define an appropriate method able to handle these different kinds of situations. Furthermore, in addition to the extraction of entities of interest in video shots, we aim at performing within the same framework the associated characterization w.r.t. motion content with a view to straightforwardly tackling video retrieval with partial query.

Motion detection or segmentation techniques have been exploited to detect and track entities of interest in the context of video indexing [START_REF] Chang | VideoQ-an Automatic content-based video search system using visual cues[END_REF][START_REF] Courtney | Automatic video indexing via object motion analysis[END_REF][START_REF] Gelgon | Determining a structured spatiotemporal representation of video content for efficient visualization and indexing[END_REF]. Motion segmentation [START_REF] Gelgon | A region-level motion-based graph representation and labeling for tracking a spatial image region[END_REF][START_REF] Mitiche | Computation and analysis of image motion: a synopsis of current problems and methods[END_REF] is usually expressed as the explicit partitioning of the image into homogeneous regions involving 2D parametric motion models. However, they remain highly computationally expensive and not reliable enough to deal with large video corpus. Besides, in case of complex dynamic scenes such as articulated motions, a single object may be divided into several different regions. Grouping them into a meaningful entity remains a difficult issue. On the other hand, motion detection schemes [START_REF] Fablet | Moving object detection in color image sequences using region-level graph labeling[END_REF][START_REF] Irani | Detecting and tracking multiple moving objects using temporal integration[END_REF][START_REF] Mitiche | Computation and analysis of image motion: a synopsis of current problems and methods[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF] first require in case of a mobile camera the estimation of the dominant image motion assumed to be due to camera motion and aims at separating moving objects from the background, but no further characterization of the associated areas is straightforwardly available. In both cases, the motion-based description of extracted objects is generally their trajectories and the retrieval process relies on trajectory matching [START_REF] Dagtas | Models for motion-based video indexing and retrieval[END_REF].

For retrieval issues, the description of motion information is as important as the extraction of the entities of interest. In addition, characterizing scene motion by object trajectories might appear insufficient and inappropriate. Besides, schemes have been recently proposed for global motion characterization based either on local motion-related measures [START_REF] Fablet | Motion-based feature extraction and ascendant hierarchical classification for video indexing and retrieval[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Nelson | Qualitative recognition of motion using temporal texture[END_REF] or on dense optic flow fields [START_REF] Deng | Content-based search of video using color, texture and motion[END_REF][START_REF] Fablet | Statistical motion-based object indexing using optic flow field[END_REF][START_REF] Jain | Query by video clip[END_REF][START_REF] Vinod | Activity based video shot retrieval and ranking[END_REF]. In this paper, we adapt this kind of approaches to deliver a relevant motion characterization in a more flexible way compared to descriptions based on 2D parametric motion models. Motion activity will be described using the probabilistic framework we have introduced in [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]. To solve for the extraction of entities of interest, we resort to a Markovian region-level labeling approach applied to the adjacency graph resulting from an ini- tial spatial partition of the image into blocks. This is achieved by exploiting the statistical similarity measure derived from our probabilistic modeling framework. This means that the latter allows us to produce both the desired motion segmentation and the appropriate motion classification.

To cope with retrieval using partial query, we use the proposed motion activity segmentation scheme to build a base of entities of interest extracted within representatives key-frames of the elementary shots of the processed video set. We store each extracted entity and its associated statistical motion activity model. Given a query (video sample), we similarly extract entities of interest in the submitted example. The user selects one of these entities as the partial query. Since our motion characterization relies on a probabilistic framework, we can formulate the motion-based retrieval process as a Bayesian inference issue [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Vasconcelos | A probabilistic architecture for content-based image retrieval[END_REF].

Local motion-related measurements

To characterize motion content within a given region, our approach relies on the analysis of the distribution of local motion-related measurements. Two kinds of local motion-related quantities can be exploited. On one hand, one can consider dense optic flow fields [START_REF] Deng | Content-based search of video using color, texture and motion[END_REF][START_REF] Fablet | Statistical motion-based object indexing using optic flow field[END_REF][START_REF] Jain | Query by video clip[END_REF][START_REF] Vinod | Activity based video shot retrieval and ranking[END_REF]. In our context, the computation of such fields reveals time consuming and situations likely to be encountered are too complex to get accu-rate and reliable estimation. As a consequence, we prefer to consider local motion-related quantities directly derived from the spatio-temporal derivatives of the intensity function [START_REF] Fablet | Motion-based feature extraction and ascendant hierarchical classification for video indexing and retrieval[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Nelson | Qualitative recognition of motion using temporal texture[END_REF].

Since our goal is to characterize the actual dynamic content of the scene, we have first to cancel camera motion. To this end, we estimate the dominant image motion between two successive images, and we assume that it is due to camera motion. To cancel camera motion, we then warp the preceding and next images of the selected key-frame in the shot onto the key-frame and process these three images.

Dominant motion estimation:

To model the global transformation between two successive images, we consider a 2D affine motion model (a 2D quadratic model could also be considered). The velocity w Θ (p), at pixel p, related to the affine motion model parameterized by Θ is given by:

w Θ (p) = a 1 + a 2 x + a 3 y a 4 + a 5 x + a 6 y (1)
with p = (x, y) and Θ = [a 1 a 2 a 3 a 4 a 5 a 6 ]. The six affine motion parameters are computed with the robust gradient-based incremental estimation method described in [START_REF] Odobez | Robust multiresolution estimation of parametric motion models[END_REF]. It comes to solve:

Θ = arg min Θ p∈S ρ (DF D(p, Θ)) (2)
where DF D(p, Θ) = I(p + w Θ (p), t + 1) -I(p, t), and I(•, t) and I(•, t + 1) are the image intensity functions at times t and t + 1, and S the support of the estimation, i.e. the image grid. ρ is a hard-redescending M-estimator. In practice, we consider the Tukey's biweight function. This function ρ and its derivative ψ depend on a parameter C and are defined as follows:

ρ(x, C) =      x 6 6 - C 2 x 4 2 + C 4 x 2 2 if |x| < C C 6 6 otherwise (3) ψ(x, C) = x(x 2 -C 2 ) 2 if |x| < C 0 otherwise (4)
The use of a robust estimator ensures the dominant image motion estimation not to be sensitive to secondary motions due to mobile objects in the scene. The minimization is performed by means of an iterative reweighted least-square technique embedded in a multiresolution framework. More precisely, we op-erate with an incremental strategy. The initial value Θ 0 is set to zero. A succession of refinements ∆Θ k are then computed and cumulated using first order approximations r p of the residual DF D(p, Θ k ), where Θ k denotes the sum of increments computed before iteration k and ∆Θ k the increment to be estimated at iteration k according to:

∆Θ k = arg min ∆Θ k p∈S ρ(r p ) (5)
where r p is expressed as:

r p = I(p + w c Θ k (p), t + 1) -I(p, t) + ∇I(p + w c Θ k (p), t + 1) • w ∆Θ k (p) (6)
with ∇I denoting the spatial intensity gradient. The estimate Θ k+1 at iteration k + 1 is updated as follows:

Θ k+1 = Θ k + ∆Θ k (7)
Increments are estimated and cumulated until the stopping criterion on the norm of ∆Θ k is satisfied.

Local motion-related quantity:

We now process the image sequence generated by compensating for the estimated dominant image motion. To evaluate the residual motion in the compensated image sequence, the following local motionrelated quantity is considered:

v obs (p) = s∈F (p) ∇I * (s) • |I * t (s)| max   η 2 , s∈F (p) ∇I * (s) 2   (8)
where I * (s) is the intensity function at point s in the warped image, F (p) a 3 × 3 window centered on p, η 2 a predetermined constant related to the noise level in uniform areas (typically, η = 5), and I * t the temporal derivative of the intensity function I * . I * t (p) is approximated by a simple finite difference. Whereas the normal flow measure

I * t (p)
∇I * (p) turns out to be very sensitive to noise attached to the computation of spatio-temporal derivatives of the intensity function, the considered motion-related measurement forms a more reliable quantity, still simply computed from the intensity function and its derivatives. This quantity has already been successively used for motion detection issues [START_REF] Fablet | Moving object detection in color image sequences using region-level graph labeling[END_REF][START_REF] Irani | Detecting and tracking multiple moving objects using temporal integration[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF], and for motion-based video indexing and retrieval [START_REF] Fablet | Motion-based feature extraction and ascendant hierarchical classification for video indexing and retrieval[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF].

As stressed previously, our approach relies on a statistical modeling of the distribution of the local motion-related measurements. It can be regarded as an extension of texture modeling for grey level images. In our approach, local motion quantities play a role similar to grey levels for texture analysis not withstanding the continuous nature of the exploited motion information. Since the proposed Gibbsian modeling framework is based on cooccurrence measurements, it in fact requires to use motion-related observations defined over a finite set. Besides, to ensure feasible comparison of motion content between different videos, we introduce in practice a quantization of the continuous motion measurements within a predefined bounded interval. Another reason to fix a limit beyond which these local motion measurements are no more regarded as usable is due to the fact that gradientbased motion measurements known to be valid for rather small motion magnitude. Typically, sampling within [0, 4] on 16 levels proves accurate enough in our previous work [START_REF] Fablet | Motion-based feature extraction and ascendant hierarchical classification for video indexing and retrieval[END_REF][START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]. We had also investigated logarithmic quantization but it did not prove relevant in our experiments. Let Λ be the discretized range of values for {v obs (p)}.

Statistical modeling of motion activity

Temporal Gibbs models of motion activity

To characterize motion activity in an area of interest within the key-frame of a given video shot, we exploit the probabilistic framework presented in [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF] which involves non parametric statistical models of motion activity. We briefly outline the scheme developed for characterizing global motion content within video shots (further details can be found in [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]) and specify it to the case of a given spatial area.

Let {x k } be the sequence of quantized motionrelated quantities for the processed shot and k 0 the frame number of the selected key-frame. Let R denote the spatial region of interest in the image k 0 and {x R k } the restriction of sequence {x k } on the spatial support of region R. We assume that the pair

x R = {x R k0 , x R k0+1 }
is the realization of a first-order Markov chain:

P M (x R ) = P M (x R k0 ) p∈R P M (x R k0+1 (p)|x R k0 (p)) (9)
where M refers to the motion activity model. P M (x R k0 ) designates the a priori distribution of X R k0 . We will consider in practice a uniform law for P M (x R k0 ). In this causal modeling framework, we evaluate only temporal interactions, i.e., cooccurrence of two given values at the same grid point at two successive instants. The advantages are two-fold. First, it permits to handle certain kinds of temporal non-stationarity. Second, it enables an exact computation of the conditional likelihood P M (x R ). This is crucial since it allows us to achieve model estimation in an easy way and to define an appropriate statistical similarity measure based on the Kullback-Leibler divergence [START_REF] Basseville | Distance measures for signal processing and pattern recognition[END_REF].

In addition, we consider an equivalent Gibbsian formulation of

P M (x R k0+1 (p)|x R k0 (p)) which comes to the introduction of potentials Ψ M x R k0+1 (p), x R k0 (p)
defining the model M such as:

P M x R k0+1 (p)|x R k0 (p) = exp Ψ M x R k0+1 (p), x R k0 (p) with ∀ν ∈ Λ, ν∈Λ exp [Ψ M (ν, ν )] = 1 (10)
Besides, this Gibbsian setting establishes a correspondence with cooccurrence distributions [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Gimel'farb | Texture modeling by multiple pairwise pixel interactions[END_REF][START_REF] Zhu | Filters, random fields and maximum entropy (FRAME) : towards a unified theory for texture modeling[END_REF]. In fact, the conditional likelihood P M (x R ) can be expressed according to an exponential formulation involving a dot product :

P M (x R ) = P M (x R k0 ) • exp Ψ M • Γ R ( 11
)
where

Γ R = {Γ R (ν, ν )} (ν,ν )∈Λ 2 is the cooccurrence distribution defined by: Γ R (ν, ν ) = p∈R δ(ν -x R k0+1 (p)) • δ(ν -x R k0 (p)) ( 12
)
where δ is the Kronecker symbol. Ψ M • Γ R is the dot product between the cooccurrence distribution Γ R and the potentials Ψ M :

Ψ M • Γ R = (ν,ν )∈Λ 2 Ψ M (ν, ν ) • Γ R (ν, ν ) (13)
The modeling scheme can be considered as nonparametric in two ways. On one hand, the statistical model M does not refer to a 2D parametric motion model. Whereas the latter aims at representing the global transformation occurring between successive frames, our approach copes with the description of motion information in terms of motion activity. On the other hand, from a statistical point of view, our approach is also non-parametric in the sense that the distribution {P M (ν|ν )} (ν,ν )∈Λ 2 is not assumed to follow a known parametric law (Gaussian,. . . ).

As far as video indexing and retrieval is concerned, the availability of the exponential formulation ( 11) is interesting for several reasons. First, it makes feasible and simple the computation of the conditional likelihood P M (x R ) for any sequence x and region R. Second, for indexing issues, the storage of the motionrelated quantities x R is not needed. In fact, all motion information are entirely captured by the cooccurrence distribution Γ R and then by the activity model M.

Maximum likelihood estimation

Given a sequence of motion-related measurements x R within a region R, we aim at identifying the model M R , specified by its potentials Ψ c M R , best fitting x R . To this end, we consider the Maximum Likelihood (ML) criterion:

M R = arg max M P M (x R ) = arg max M LL M (x R ) with LL M (x) = ln P M (x R ) (14)
In fact, the considered temporal Gibbsian modeling framework consists in a product of |R| independent first-order Markov chains defined at each point of the region R.

These Markov chains are characterized by their common transition ma-

trix {P c M R (ν|ν )} (ν,ν )∈Λ 2 .
Therefore, the ML model estimate M R is readily determined from the empirical estimation of the transition probability

P c M R (x R k0+1 (r)|x R k0 (r)) as follows: Ψ c M R (ν, ν ) = ln {x R k0+1 (p) = ν, x R k0 (p) = ν } {x R k0 (p) = ν } ( 15
)
Using cooccurrence notation, it comes to:

Ψ c M R (ν, ν ) = ln     Γ R (ν, ν ) ϑ∈Λ Γ R (ϑ, ν )     (16)

Parzen-Rosenblatt estimation

In Section 5, we will exploit the motion activity modeling framework described above to characterize the dynamic content in a given image block. The use of the ML criterion can become irrelevant if the number of available samples is too small. To overcome this problem occurring for small regions, we consider a regularized solution to the model estimation issue by using a Parzen-Rosenblatt (PR) window estimator [START_REF] Parzen | On estimation of probability density function and mode[END_REF].

For given sequence x and area R, it comes to substitute in relation ( 16) a regularized version Γ R for the cooccurrence distribution Γ R . To get Γ R , Γ R is convolved with a Gaussian kernel of variance σ 2 :

Γ R (ν, ν ) = (γ,γ )∈Λ 2 η (γ -ν) η (γ -ν ) • Γ R (γ, γ ) (17)
where η (γν) is the weight of the Gaussian PR window given by:

η (γ -ν) = exp -(γ -ν) 2 /2σ 2 υ∈Λ exp -(υ -ν) 2 /2σ 2 (18)
Therefore, we infer the expression of potentials Ψ f M R of the PR model estimate M R as follows:

Ψ f M R (ν, ν ) = ln     Γ R (ν, ν ) ϑ∈Λ Γ R (ϑ, ν )     (19)
In addition, we can perform model complexity reduction in order to supply an informative representations of the motion activity while remaining parsimonious [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]. After PR estimation, we select relevant potentials of estimated model M R by evaluating likelihood ratios as described in [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF].

Segmentation based on motion activity

Given a video shot, we aim at extracting areas of interest in the representative key-frame of the shot in an automatic way. Here, meaningful entities are supposed to correspond to areas comprising pertinent motion activity. To this end, we exploit the statistical motion activity modeling introduced in the previous section. A prominent advantage of such an approach is to provide within the same framework the extraction and the characterization of particular areas which will then be used to perform video retrieval with partial query.

In the sequel, we assume that a primary partition of the image is available. In practice, we consider a block-based partition (it could also be a texture-based or color-based segmentation). The goal is to build meaningful clusters from this initial set of blocks w.r.t. motion content. Hence, we first define a similarity measure related to motion activity (subsection 5.1). Secondly, this similarity measure is used to achieve the labeling of the block-based partition (subsection 5.2).

As previously defined, k 0 is the frame number of the representative key-frame of the shot. Considering three images in the shot, i.e. the one preceding the keyframe, the key-frame and the one following the keyframe, we determine the pair {x k0 , x k0+1 } of maps of motion-related measurements as described in Section 3. Let us consider a partition of the image defined by the set of N bl blocks {B i } i∈{0,...,N bl } . We further assume that motion activity within each block B i is characterized by means of the associated statistical model M Bi issued from the cooccurrence distribution Γ Bi as explained in Section 4. Let us stress that we perform this estimation using the PR estimator (relation ( 19)).

Statistical similarity measure related to motion activity

Considering two regions R and R , our goal is to define a measure of content similarity between R and R w.r.t. to motion activity. Let us note M R and M R the statistical models of motion activity attached respectively to regions R and R for the sequence of motionrelated measurements resp.

x R = {x R k0 , x R k0+1 }, x R = {x R k0 , x R k0+1 }
and for the associated cooccurrence distributions resp. Γ R , Γ R .

We have built a similarity measure relying on an approximation of the Kullback-Leibler (KL) divergence [START_REF] Basseville | Distance measures for signal processing and pattern recognition[END_REF], which evaluates the similarity of two statistical distributions as the expectation of the log-ratio of these distributions. More precisely, the considered similarity measure D(M R , M R ) is a symmetrical version of the KL divergence:

D(M R , M R ) = KL(M R M R ) + KL(M R M R ) 2 (20)
where KL(M R M R ) is the KL divergence. Based on a Monte-Carlo strategy, the latter quantity is approximated as [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF]:

KL(M R M R ) ≈ 1 |R| • ln P M R (x R ) P M R (x R ) (21)
Using the exponential expression of the laws P M R (relation 11), KL(M R M R ) can be rewritten as:

KL(M R M R ) ≈ Ψ M R • Γ R -Ψ M R • Γ R |R| (22) Since M R is the ML estimate associated to the cooc- currence distribution Γ R , KL(M R M R
) is positive and equals 0 if the two statistical distributions are identical. In fact, this ratio quantifies the loss of information occurring when considering M R instead of M R to describe motion activity within area R.

Region-level graph labeling

We now present the labeling scheme of the blockbased partition of the image, {B i } i∈{0,...,N bl } , which will be exploited in the next section for image segmentation. It relies on a Markovian region-level labeling framework [START_REF] Fablet | Moving object detection in color image sequences using region-level graph labeling[END_REF][START_REF] Gelgon | A region-level motion-based graph representation and labeling for tracking a spatial image region[END_REF] applied to the adjacency graph G = (N , A) where N is the set of nodes of graph G and A the set of its arcs. Each node n i ∈ N holds for block B i with i ∈ {0, . . . , N bl }, and A represents the set of arcs between graph nodes corresponding to connected blocks (in practice, we consider a fourconnectivity neighborhood). Over this graph structure G, we define a region-level Markov random field model the sites of which are the nodes of graph G. A two-site clique neighborhood system is deduced from the set of arcs A.

Let us assume that a set of labels L relative to different motion activity models has been specified (it will be defined in the next section). We further consider that to each label l ∈ L is attached a motion activity model M l and the associated cooccurrence distribution Γ l . Let us note e = {e ni } i∈{0,...,N bl } the label field with e ni taking value in L, and o = {o ni } i∈{0,...,N bl } the observation field. In our case, at each n i , o ni refers to the motion activity characterization attached to the block B i , i.e. both model M Bi and cooccurrence distribution Γ Bi . Adopting the Maximum A Posteriori (MAP) criterion and using the equivalence between Markov and Gibbs random fields [START_REF] Geman | Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images[END_REF], the labeling scheme comes to solve for:

ê = arg min e∈L N bl U (e, o) (23)
where U (e, o) = U a (e, o) + U b (e), with U a the datadriven energy term, and U b the regularization term. Both energy terms are split in the sum of local potentials V a and V b :

           U a (e, o) = n∈N V a (e n , o n ) U b (e) = (ni,nj)∈A V b (e ni , e nj ) (24)
The regularization potential V b tends to favor identical labels for neighboring nodes:

V b (e ni , e nj ) = β • δ(e ni -e nj ) (25)
with β a parameter tuning the importance of the regularization and δ the Kronecker function. Besides, at node n i , the data-driven potential V a (e ni , o ni ) quantifies how relevant is the description of observation o ni by label e ni according to motion activity. It involves the similarity measure D, defined by the relation [START_REF] Mitiche | Computation and analysis of image motion: a synopsis of current problems and methods[END_REF], as given by:

V a (e ni , o ni ) = exp -D M en i , M Bi ( 26
)
We introduce an exponential form to get values of potential V a within the range [0, 1], which enables to set more easily the regularization parameter β.

Finally, the minimization issue ( 23) is tackled using the HCF (Highest Confidence First) algorithm [START_REF] Chou | The theory and practice of Bayesian image modeling[END_REF] since the number of nodes of the considered graph is relatively small.

Separation of entities of interest from static background

We want to come to separate the static background from entities of interest. Since we consider warped image sequences using the dominant image motion assumed to be due to the camera motion, this issue reduces to extract regions which do not conform to the dominant image motion [START_REF] Fablet | Moving object detection in color image sequences using region-level graph labeling[END_REF][START_REF] Odobez | Separation of moving regions from background in an image sequence acquired with a mobile camera[END_REF].

In a first step, we determine a binary labeling of the initial partition of the image in terms of blocks conforming or not to the dominant image motion. As the image segmentation proceeds from motion activity characterization, we have to establish a model corresponding to the static background. Even if we could a priori infer an activity model according to null motion measurements, we prefer to explicitly estimate this model from actual motion quantity distribution at points attached to the static extracted background since camera motion cannot be perfectly cancelled.

To achieve this, we exploit a by-product of the robust multiresolution estimation of the affine motion model accounting for the dominant image motion (see Section 3). More precisely, the minimization of criterion ( 5) is solved using an IRLS (Iterated Re-weighted Least Squares) technique, leading to:

∆Θ k+1 = arg min ∆Θ k+1 p 1 2 ω p r 2 p with ω p = ψ(r p ) r p ( 27
)
where ψ is defined in relation (4) and r p is given by expression [START_REF] Brunelli | A survey on the automatic indexing of video data[END_REF] where ∆Θ k is given by ∆Θ k . At the final step of the estimation of the dominant motion, the weight value ω p indicates if the point p is likely or not to belong to the part of the image undergoing the dominant image motion. By definition, ω p belongs to the interval [0, 1]. In addition, the closer ω p to 1, the more the point p conforms to the dominant image motion.

We can deduce by thresholding map ω a rough support associated to the dominant image motion. Points p satisfying ω p > µ are stated as belonging to support S d associated to the dominant image motion, and they then form the static background. Using our statistical motion activity modeling framework, we can estimate model M S d attached to S d using the PR window estimator (relation [START_REF] Gimel'farb | Texture modeling by multiple pairwise pixel interactions[END_REF]). If S d designates the comple-mentary of S d (corresponding to the outlier map), we can evaluate in the same way the associated motion activity model M S d . At this stage, we achieve a Markovian block-based labeling as described in Subsection 5.2 while considering only two labels referring to statistical models attached to regions S d and S d (i.e. label set L contains only two labels in that case). The obtained binary segmentation supplies a new estimate of the support of regions S d and S d , and their associated models M S d and M S d can be updated. Since S d includes the areas likely to be of interest for video indexing, we then extract its connected components. Let us denote by {R i } i∈{1,...,Nreg} the N reg resulting regions. For each region R i , we perform the estimation of its activity model M Ri . We then perform a second region-level labeling step applied to the original blockbased partition as explained in Subsection 5.2 with |L| = N reg + 1. We consider N reg + 1 different labels {l 0 , .., l Nreg } corresponding to the updated model M S d (label l 0 ) and to models {M Ri } i∈{1,...,Nreg} . Once convergence is reached, regions Q i formed by pixels with labels l i = l 0 are regarded as the entities of interest for the processed video shot. Besides, for each region Q i , we store its associated model M Qi as a descriptor of its dynamic content which will be used in the retrieval stage.

Retrieval with partial query

Partial query

We can now tackle retrieval with partial query by example. Considering a set of video documents, we first construct an index base composed of the set of entities and their associated activity descriptors extracted from all the stored video samples. This is achieved by segmenting each video into shots [START_REF] Bouthemy | A unified approach to shot change detection and camera motion characterization[END_REF] and by applying the motion activity segmentation scheme described in Section 5. This provides us automatically and simultaneously with the extraction of meaningful entities and the associate characterization in terms of motion activity. The addition of an entity to the base is manually validated in order to reject areas which are not relevant for indexing purpose such as logos or score captions.

Otherwise, once a video query is submitted by the user, we extract automatically from the submitted video sample local relevant entities and the user speci-fies which one is of interest to perform the retrieval of similar examples from the indexed video base.

Bayesian retrieval

Considering a database D comprising a set of extracted entities with their non-parametric statistical motion characterization, the retrieval process is formulated as a Bayesian inference issue based on the MAP criterion [START_REF] Fablet | Non parametric statistical analysis of scene activity for motion-based video indexing and retrieval[END_REF][START_REF] Vasconcelos | A probabilistic architecture for content-based image retrieval[END_REF]. Given a video query q and a region R q as partial query, we aim at delivering to the user examples similar to q w.r.t. dynamic content. The best match d * is given by:

d * = arg max d∈D P (d|q) = arg max d∈D P (q|d)P (d) (28)
The prior distribution P (d) allows us to express a priori knowledge on the video content relevance over the database. It could be inferred from semantical description attached to each type of video sequences or from relevance feedback by interacting with the user in the retrieval process [START_REF] Nastar | Efficient query refinement for image retrieval[END_REF]. In the current implementation of our retrieval scheme, we will set no a priori (P (d) distribution is uniform). A statistical model of motion activity M d is attached to each entity d of the database. Furthermore, a cooccurrence distribution Γ Rq relative to motion-related measurements x Rq are also attached to R q . Hence, the conditional likelihood P (q|d) is formally expressed as P M d (x Rq ) and we get:

d * = arg max d∈D P M d (x Rq ) (29)
From the exponential expression of the law P M d (relation ( 11)), we further deduce:

d * = arg max d∈D Ψ M d • Γ Rq (30)
In addition, the computation of the conditional likelihoods P M d (x Rq ) supplies us with a ranking of the elements d of the base D since we can evaluate how the different statistical models M d fits to the motionrelated measurements computed in the query area R q . In practice, we provide the user with a given number of ranked replies.

Results

Extraction of entities of interest

We have first carried out experiments for the extraction of entities of interest based on motion activity. All experiments have been performed with the values of parameters involved in the motion activity segmentation scheme given in Table 1.

In Figure 2, we show partial corresponding to the different steps of the motion activity segmentation scheme. Concerning the parameter setting (given in Table 1), it appears that the selected values of the constant η and of the regularization coefficient β have a rather weak influence on the obtained results. Similarly, threshold µ can be set in the range [0.1, 0.5] without major changes in the segmentation results. The remaining parameters, i.e., block size, number of levels and bounds of quantization of motion-related measurements, are closely related. Let us denote by N the number of quantization levels and B the size of Table 1. Parameter setting or selected options for our motion activity segmentation scheme blocks. Indeed, B has to be set in accordance to N . More precisely, we need to estimate N 2 potentials for motion activity models within blocks using 2B The considered video set involves different kinds of sport videos. Two main classes of shots can be distinguished: the first one consists of close-up of a particular area of the play field, and the second one displays global views of the scene. In the first case, the entities of interest are obviously the tracked players, whereas in the second case this is no more a single player but 1.

Motion-related measurements

Retrieval operations with partial query

We have conducted several experiments of retrieval operations with partial query. We have considered a set of one hundred video shots involving different dynamic contents. They are color image sequences downloaded from different web sites in a compressed format (MPEG, AVI, MOV). In practice, we process uncompressed grey-level sequences of about ten to twenty images. We have focused on sport shots such as rugby, football, basketball and hockey. In Figure 4, we report three examples of retrieval operations. The three best replies are given for each query. For all the processed examples, the system delivers relevant replies in terms of motion properties. To appreciate the relevance of the replies, we give for each reply d the value of the conditional likelihood P M d (x R q ). To further quantify the similarity between the retrieved entities of interest and the query, we have also determined the value of the similarity measure D computed between the statistical motion activity models estimated within the query area and those attached to the retrieved ones Let us recall that we do not need to estimate the activity model corresponding to the query in the retrieval phase; this is just performed here to enable a complementary quantitative evaluation of the results.

To evaluate the statistical diversity of the motion activity contents available in the processed base of entities of interest, we cannot supply any direct 2D absolute mapping of the elements of the base since our approach only allows to compare pairs of motion models through the similarity measure D. However, we select one "reference" model to map the base onto a 1D axis w.r.t. this model and supply such a 1D mapping for several "reference" models. We have then considered the three partial queries reported in Fig. 4 as reference models, and we have computed the distances {D(M Rq , M d )} d∈D between the motion model of the partial query R q and those of the elements d of the base D. To compute distance histograms, we need to quantize the distances {D(M Rq , M d )} d∈D . In fact, we have used the set of values {1.0exp D(M Rq , M d )} d∈D since these quantities are comprised within [0, 1]. Fig. 5 depicts histograms of these distances resulting from a linear quantization within [0, 1] using 25 levels. Plots 5.(a), 5.(b) , 5.(c) resp. refer to the distance histograms computed w.r.t. resp. the video query 1, 2 and 3 of Fig. 4. These histograms, in particular plots 5.(a) and 5.(b), show that the distribution of motion activity contents within the processed base is widespread. Besides, from these 1D mappings of the processed base, it can be envisaged that our motion modeling framework may also be exploited for motion classification since different modes seem to be discriminated in the first two plotted histograms.

Conclusion

We have presented in this paper an original approach for motion-based video retrieval able to handle partial query. It relies on an automatic and efficient extraction of entities of interest within key-frames of each video shot, which results from motion activity characterization. Motion information is expressed as non parametric statistical models which account for a large range of dynamic scene content. This statistical framework can then be straightforwardly exploited to perform the retrieval with partial query, as validated by representative real experiments.

In future work, we plan to evaluate our approach on a larger video base. An important issue will be to define a procedure to evaluate in a quantitative way our retrieval scheme (for instance, in terms of correctly classified or misclassified scenes). In particular, it will require to define a preliminary categorization of the video base, which is not so easy. Besides, we could also address the tracking of the extracted entities of interest in video shots. Then, the trajectory of the tracked entities could be also exploited for retrieval purpose. To still benefit from a Bayesian framework, this would require to propose an appropriate statistical framework to combine trajectory and motion activity characterizations.

Fig. 1 .

 1 Fig. 1. Two video samples involving different kinds of entities of interest: (a-b) tracking of a given hockey player; (c-d) focus on a particular area of a rugby playing field. The bounding polygon encompassing the area of interest is displayed in white.

Figure 2 .

 2 a contains to the key-frame of the processed shot, Figure 2.b the binary support of the dominant image motion, Figure 2.c the map of quantized motion-related measurements and Figure 2.d the extracted regions of interest w.r.t. motion activity. This scheme enabling simultaneous extraction and characterization of entities of interest within keyframes of video shots also appears efficient in terms of computational time. It indeed requires about 0.2 second of CPU time to process images of size 120 × 160 comprising 20 blocks of size 32 × 32 blocks on a Sun Creator workstation 360MHZ.

32 ×Fig. 2 .

 322 Fig. 2. Results of motion activity segmentation: (a) selected keyframe for the processed shot, (b) support of the dominant image motion in white (µ = 0.2), (c) map of motion-related measurements quantized within [0, 4] on 16 levels (visualized with greylevels within [0, 256]), (d) result of the motion activity segmentation using the PR estimator with σ = 0.5, β = 0.5 and 32 × 32 blocks. The black area holds for the region regarded as the static background and the two areas delimited by a white line are the extracted entities of interest.

Fig. 3 .

 3 Fig. 3. Examples of block-based segmentation of entities of interest within shot key-frames according to motion activity. The extracted areas are delimited in white. For these different examples, the parameters used are those given in Table1.

  the statistical diversity of the base of entities of interest]Qualitative evaluation of the statistical diversity of the base of entities of interest w.r.t. motion activity content : histograms of the similarity measures of motion activity computed between a given partial query R q and each element d of the database. In order to quantize the similarity measures D(M Rq , M d ), we consider the values 1.0 -expD(M Rq , M d ) which are within [0, 1] and a linear quantization over [0, 1] with 25 bins. We report three examples relative to every partial query introduced in Fig.4: 1D mapping w.r.t. (a) video query 1, (b) video query 2, (c) video query 3.

Fig. 5 .

 5 Fig. 5. [

  2 samples. Therefore, if we consider 32 × 32 blocks, the number of quantization levels should not be greater than 32. Setting N to 16 is a reasonable trade-off between accuracy of the representation of motion activity and computation complexity . Besides, for image sizes comprised between 120 × 160 and 352 × 288 pixels as in our video base, the use of 32 × 32 blocks proves sufficient enough to locate entities of interest in the scene. The use of the PR estimator should indeed help dealing with rather small blocks. Therefore, the choice of σ value obviously depends both on N and B. For large values of B and N , the PR regularization is not necessary, which leads to low value for σ 2 (lower than to 0.2). For 32 × 32 blocks and 16 quantization levels, it turns out that σ 2 should take a value in the range [0.2, 1.0].

rather a group of players or a particular area of the play field. We display in Figure 3