Marie-Aude Vitrani

Cécile Poquet

Guillaume Morel

Applying virtual fixtures to the distal end of a minimally invasive surgery instrument

The comanipulation paradigm, in which a user and a robot simultaneously hold a tool, allows for gesture guidance. In particular, virtual fixtures, which are geometrical constraints imposed to the tool by the robot, have received a great interest in the domain of surgical applications. So far, this concept has been implemented in the context of open surgery. This paper explores the application of virtual fixtures for minimally invasive surgery, where the tool is inserted in the patient through a fulcrum. Here, a key issue is to return to the surgeon forces that are virtually applied at the instrument distal tip, while the robot is physically attached to the instrument proximal handle.

To this aim, two approaches are investigated. A first approach consists in applying a full wrench at the proximal end of the instrument that is equal to the wrench constituted by a pure force applied to the instrument's distal tip. A second approach consists in applying a pure force to the instrument proximal end, thanks to a lever model about the fulcrum.

The two approaches are compared through experiments during which naive subjects blindly perform virtual object palpation and robot guided movements. During experiments, indicators involving motion and force analysis are computed. The user capacity to distinguish between several virtual objects is evaluated as well. Although drastically different, the two approaches provide assistance with a similar level of efficiency.

I. INTRODUCTION A. Virtual Fixtures and Comanipulation

Virtual fixtures are geometrical constraints actively imposed by a robot to its end-effector [START_REF] Abbott | Haptic virtual fixtures for robot-assisted manipulation[END_REF]. They have been conceived in the context of telemanipulation, where they were applied to a motorized master arm. In this case, they constitute an additional haptic feedback provided to the user, thus easing the slave telemanipulator control [START_REF] Abbott | Virtual fixture architectures for telemanipulation[END_REF]. In the present paper, virtual fixtures are considered in the context of comanipulation.

Comanipulation is a paradigm in which a robot and a subject simultaneously hold a tool and perform a task. The two most basic functions that a comanipulator can exhibit are a free mode, where the tool movements are not constrained at all, and the locked mode, where the robot prevents the tool from any movements [START_REF] Poquet | A novel comanipulation device for assisting needle placement in ultrasound guided prostate biopsies[END_REF]. In between, the robot can apply a partial constraint. A first approach consists in imposing a given geometrical equality constrain to the tool [START_REF] Moore | Cobot implementation of virtual paths and 3d virtual surfaces[END_REF]. For example the robot can impose that a given point T of the tool remains still, while the tool orientation around T is freely Authors are with (1) Sorbonne Universités UPMC Univ. Paris 06, UMR 7222, ISIR, Paris, France, (2) INSERM, U1150, Agathe-ISIR, F-75005, Paris France, (3) CNRS, UMR 7222, ISIR, F-75005, Paris, France. Email: vitrani@isir.upmc.fr.

This work was partly supported by the project PROSBOT funded by ANR, TECSAN 2011 program, under reference ANR-11-TECS-0017 and by french state funds managed by the ANR within the Investissements d'Avenir programme (Labex CAMI) under reference ANR-11-LABX-0004. Figure 1. Comanipulating an instrument through a fulcrum: left -the 6-DOFs robot Apollo assists a urologist who manipulates an endorectal ultrasound probe to perform prostate biopsies [START_REF] Poquet | An endorectal ultrasound probe comanipulator with hybrid actuation combining brakes and motors[END_REF]; right -the same concept applied to endoscopic surgery set by the user. In a second approach, virtual fixtures can be conceived as inequality constraints, thus separating the space into free regions and forbidden regions. The reader interested in more details on these approaches and their implementation can consult a recent review on virtual fixtures in [START_REF] Bowyer | Active constraints/virtual fixtures: A survey[END_REF].

B. Application to assistance to surgery

The concepts of comanipulation and virtual fixtures have received an increasing interest in the particular context of surgical robotics [START_REF] Morel | Comanipulation[END_REF]. Pioneer examples include PADyC, proposed in 2001 for cardiac surgery applications [START_REF] Schneider | A six degree of freedom passive arm with dynamic constraints (padyc) for cardiac surgery application: Preliminary experiments[END_REF] and the steady hand robot aimed at assisting eye surgery [START_REF] Li | A constrained optimization approach to virtual fixtures[END_REF].

Meanwhile, in the Operating Rooms, the comanipulation concept was successfully applied to orthopedic surgery, with a particular focus on assistance to bone milling, following the work on Acrobot and active constraints [START_REF] Jakopec | The hands-on orthopaedic robot acrobot: Early clinical trials of total knee replacement surgery[END_REF]- [START_REF] Cobb | Accuracy provides enduring functional improvement in arthroplasty:18 months results of robotic assisted unicompartmental knee replacement[END_REF]. For this application, virtual fixtures are used to delimit forbidden regions, where the milling instrument shall not penetrate, in order to preserve bony tissue. As a result, the surgeon is assisted in sculpting a region whose geometry has been defined during a planning procedure, with more safety and more precision. In this scenario, a preoperative procedure is to be performed at the beginning of the operation to register the bone and the robot. Comanipulation and virtual fixtures for bone surgery are now available for clinical practice, e.g. with the Makoplasty system whose efficiency in increasing the gesture precision has been proven though clinical cases [START_REF] Nawabi | Haptically guided robotic technology in total hip arthroplasty: a cadaveric investigation[END_REF]. The gesture precision is even increased when a visual feedback is used in combination with a force feedback [START_REF] Francoise | A comanipulation device for orthopedic surgery that generates geometrical constraints with real-time registration on moving bones[END_REF].

C. Keyhole surgery: the fulcrum

In this paper we focus on applying comanipulation and virtual fixtures in the context of so-called keyhole surgery, as illustrated in Fig. 1. Elongated instruments are introduced into the patient's body through natural orifices or small incisions. The instrument possesses only 4 Degrees of Freedom (DOFs): three independent rotations around the insertion point and one translation along the instrument longitudinal axis. A kinematic constraint is thus formed and challenges the surgeons' sensorimotor system. Combined with the lack of depth perception due to the indirect visual 2D feedback, this degrades the manipulation skills increases the duration of the learning process [START_REF] Huang | Learning kinematic constraints in laparoscopic surgery[END_REF].

In order to assist surgeons' manipulation through a fulcrum, a number of robotic devices have been developed, with different kinematic designs. In some cases, such as [START_REF] Guthart | The intuitive telesurgery system : overview and application[END_REF], a 4 DOF robot exhibiting a remote center of motion (RCM) is used. This implies the robot base body to be carefully placed in the workspace prior to instrument manipulation, in such a way that its RCM coincides with patient's entry point. In other cases, a conventional 6-DOFs robot is used. This allows placing the robot base independently from the insertion point location. Such a 6-DOFs robot can be fully actuated, as in [START_REF] Konietschke | The dlr mirosurge -a robotic system for surgery[END_REF]. In this case, one has to solve for the kinematic constraint in real time, using either a knowledge on the fulcrum location, as proposed in [START_REF] Ortmaier | Cartesian control issues for minimally invasive robot surgery[END_REF]- [START_REF] Pham | Analysis of a moving remote center of motion for robotics-assisted minimally invasive surgery[END_REF], or an additional sensor to estimate this location, as proposed in [START_REF] Krupa | Achieving high precision laparoscopic manipulation through adaptive force control[END_REF]. The robot can also be partially actuated, as in [START_REF] Low | A review of master-slave robotic systems for surgery[END_REF]. Here, a first combination of 3 active DOFs is used to position the wrist center; 2 passive DOFs in the wrist allows free orientation of the instrument axis while the last DOF, corresponding to the instrument rotation around its axis, is motorized. Such a combination allows to respecting the kinematic constraint independently from the location of the fulcrum with respect to the robot base, while using four actuators only.

D. Force control for manipulation involving a fulcrum

Little literature is available on force control through a fulcrum. Most of it proposes to integrate a force sensor at the distal end of the instrument and to implement a distal force closed loop controller (see e.g. [START_REF] Ortmaier | Cartesian control issues for minimally invasive robot surgery[END_REF]). This question is treated independently from the robot kinematics and fulcrum constraint. The aim here is, in a context of force feedback teleoperated systems, to control the instrument-organ interaction despite disturbance forces applied at the fulcrum.

In the context of comanipulation, the question of force control is not limited to the distal interaction. Rather, it is required to deal with simultaneous distal (instrument-organs) and proximal (instrument-surgeon-robot) interactions, while minimizing the forces applied to the fulcrum. This question is treated in [START_REF] Zemiti | A force controlled laparoscopic surgical robot without distal force sensing[END_REF], where a 4 DOFs comanipulation robot exhibiting a RCM is presented for the implementation of a force feedback loop, when forces are applied both at the distal and proximal ends of an endoscopic surgery instrument. This configuration is shown to raise specific kinematic stability problems, formally studied in [START_REF] Zemiti | On the force control of kinematically defective manipulators interacting with an unknown environment[END_REF].

Meanwhile, to our knowledge, there is no literature dealing with the control of the wrench applied by a 6-DOFs robot to the handle of an instrument in order to produce virtual

D V F R U Patient User Robot Instrument Virtual Object F f F r F u F v M r M u M f z i y i x i z 0 y 0 x 0 O 0 Figure 2.
Wrenches applied to a comanipulated key-hole surgery instrument. Point D denotes the distal end (physical tip) of the instrument inserted into the patient through the fulcrum point F. The user and the robot hold the proximal part (handle) of the instrument at point U and point R, respectively. Point V is where a force F v is to be emulated in order to simulate the interaction with a virtual object fixture to its distal end, the instrument being comanipulated through a fulcrum. Such a configuration is illustrated in Fig. 1, for two different applications: prostate biopsies, where the comanipulted instrument is an endorectal utrasound probe insterted through the anus and endoscopic surgery, where the robot and the surgeon comanipulate an elongated instrument through a trocar. In these applications, the use of a 6-DOFs robot rather than an RCM allows avoiding to precisely register the robot base with respect to the patient anatomy thus easing the installation. However, it has the disadvantage, compared to 4 DOFs robot with RCM appropriately registered, to possibly apply undesired forces at the fulcrum.

The present paper deals with the force control of such a comanipulated system. More precisely, the main question under investigation is how to apply a wrench, with a 6-DOFs robot, to the handle of an instrument inserted through a fulcrum, in such a way that a user holding the handle feels that a given force is distally applied. This question is specific to assistance to key-hole surgery since, in open surgery, there is no interaction with a fulcrum that may affect the forces applied to the instrument and thus the surgeon's felt forces. Meanwhile, a secondary question concerns the minimization of the forces applied to the fulcrum during such an operation.

The paper is organized as follows. Two strategies for computing the distal wrench are proposed in Sec. II. They are then compared through experiments. Section III describes the experimental methods (setup, virtual fixtures, protocol and indicators). Section IV provides the results, that are further discussed in Sec. V.

II. TWO CONTROL STRATEGIES A. Problem formulation

Our aim in this paper is to evaluate how to generate distal virtual fixtures for a minimally invasive instrument comanipulated at its proximal end.

As depicted in Fig. 2, the instrument is modeled as a straight line joining the proximal (handle) end U to the distal end D (tip). A frame F I = (U, x I , y I , z I ), with z I = (1/ -→ DU ) -→ DU is attached to the instrument. Three wrenches are applied to the instrument during a comanipulated experiment. Firstly, the user applies a wrench denoted:

{W u } = F u M u U , (1)
where F u is a vector force and M u is a vector moment applied at proximal point U.

Secondly, the wrench applied by the patient to the instrument through the fulcrum F is noted:

{W f } = F f M f F , (2)
where F f is a vector force and M f is a vector moment applied at the insertion point F.

Notice that if a 4 DOFs joint model is assumed for the fulcrum, leaving free only three rotations around a fixed point F and one translation along z I , then the twist representing the velocity of the instrument with respect to a fixed frame, writes, at Point F:

{T I } = ω = ω x x I + ω y y I + ω z z I v z z I F . (3)
Reciprocally, if friction is neglected, then the joint does not dissipate any mechanical power for all the possible velocities of the instrument. This allows to establish [START_REF] Angeles | Fundamentals of Robotics Mechanical Systems[END_REF] that the wrench transmissible through the fulcrum writes:

{W f } = F f = F f x x I + F f y y I M f = 0 F . (4)
The third wrench applied to the instrument is produced by the comanipulator. In this paper, the robot is supposed to be able of applying a controlled wrench:

{W r } = F r M r R , (5)
where F r is a vector force and M r is a vector moment applied at a given proximal point R.

The robot shall be programmed to apply virtual fixtures. The virtual fixture generator, by itself, does not fit in the scope of the paper. A conventional approach is supposed to be used: considering the position and orientation of the instrument, the virtual fixture generator shall produce a virtual force that can be either repulsive (forbidden region) or attractive (guide), see examples in Sec. III. In a conventionnal configuration, this vector force F v should be applied at a distal point V , inside the patient, whose location is also provided by the virtual fixture generator. However, in the configuration on minimally invasive surgery, the robot shall apply a wrench {W r } at a proximal point W in such a way that the user feels that the virtual wrench {W v }:

{W v } = F v 0 V (6)
Figure 3. The problem under consideration in this paper: how to compute a proximal wrench {W r } to be applied by the robot that will be felt by the user as if a wrench {W v } was distally applied has been distally applied.

How to compute {W r } from {W v } is the central question of this paper, as depicted in Fig. 3. It is important to notice that, from a mechanical point of view, the answer to this question is not unique due to the presence of internal forces. In other words, given a solution {W r1 } that provides a satisfactory behavior for the robot control, any other solution {W r2 } that writes:

{W r2 } = {W r1 } + {W f 1 } , (7)
where {W f 1 } corresponds to a wrench verifying Eq. ( 4) can result in the same user (felt) wrench. Indeed, the difference between {W r2 } and {W r1 } can be totally compensated by the fulcrum wrench without changing the user wrench. Combining Eq. ( 7) with Eq. ( 4), the condition for two robot wrench solutions to be equivalent writes:

∃φ x ∈ R, ∃φ y ∈ R / {W r2 } -{W r1 } = φ x x I + φ y y I 0 F . (8)
This formulation raises a question on the forces φ x and φ y exerted at the fulcrum. Indeed, in the context of minimally invasive surgery, it is desired that these forces are minimized. However, because {W u } is unknown, and may also include components that are transmissible through the fulcrum (thus affecting {W f }), it is impossible to a priori compute the solution for {W r } that will minimize {W f }.

In the next, among the infinite number of possible solutions described by Eq. ( 8), we select two remarkable solutions. The first one, called exact wrench computation, consists in computing {W r } equal to {W v }. Namely, with this approach, the robot applies at point R the wrench (a force and a moment) that a pure virtual force F v exerted at point V would apply at point R. The second solution consists in applying a pure force at point R (no moment) with the robot. This solution, which refers to a force-lever model, is chosen mainly because it simplifies the robot design. Indeed, a robot with only 3 actuated joints serially mounted with a passive spherical wrist centered at point R can implement this strategy (see details in Sec. II-D).

B. Exact Wrench Computation (EWC)

The most immediate way to emulate {W v } with the robot is to apply with the robot a wrench {W r } that is equal to the wrench {W v }. This corresponds to the conventional wrench moment displacement formula:

{W r } = F v 0 V = F v -→ RV × F v R = F v -l V z I × F v R (9)
where l V > 0 is defined by l V z I = -→ V R.

C. Lever Model Computation (LMC)

Another possible approach consists in using the lever principle, i.e. balancing the distal pure force F v with a proximal pure force F r . With this approach, the robot is controlled to apply a wrench with a null moment at point R ( M r = 0). It shall balance the pure force F v applied at point V , given the particular kinematic constraint imposed by the fulcrum.

One shall compute {W r } (with a null moment at point R) that is mechanically equivalent to {W v } for all the movements permitted by the fulcrum. In other words, assuming that the kinematic constraint is depicted by Eq. ( 3), {W r } shall develop the same mechanical power as

{W v }, ∀{ω x , ω y , ω z , v z } ∈ R 4 .
Denoting:

{W r } = F rx x I + F ry y I + F rz z I 0 R , (10)
it is straightforward to show that the mechanical power developed by {W r } is:

P r = {T I } {W r } = ω x x I + ω y y I + ω z z I v z z I + -→ RF × ω R F rx x I + F ry y I + F rz z I 0 R = l F ω y F rx -l F ω x F ry + v z F rz (11)
where stands for the screw scalar product and l V > l F > 0 is defined by: l F z I = -→ FR. Similarly, denoting:

{W v } = F vx x I + F vy y I + F vz z I 0 V , (12)
the mechanical power developed by {W v } writes:

P v = {T I } {W v } = -(l V -l F ) ω y F vx + (l V -l F ) ω x F vy + v z F vz (13)
The wrenches {W r } and {W v } are equivalent iff:

∀ ω x , ω y , ω z , v z P r = P v , (14)
which is equivalent to:

     F rz = F vz F rx = -l V -l F l F F vx F ry = -l V -l F l F F vy (15)
Thus, denoting the lever factor:

α = l V -l F l F > 0 , (16)
the wrench to be applied by the robot for a given force F v virtually applied at point V writes:

{W r } = F r = -αF vx x I -αF vy y I + F vz z I M r = 0 R . (17)

D. Differences between the EWC and LMC approaches

Two ways of computing {W r } from a given F v virtually applied at point V are given by Eqs. ( 9) and [START_REF] Konietschke | The dlr mirosurge -a robotic system for surgery[END_REF]. In theory, they are mechanically equivalent providing that the kinematic constraint imposed by the patient entry point to the instrument verifies Eq. ( 3). Indeed, it is straightforward to verify that their difference satisfies the necessary condition given by Eq. ( 8). From a perceptual point of view, the user may not feel any difference although the values of the force/moment components drastically differ: force components along x I and y I have opposite signs in both Equations while the moment components in Eq. ( 9) are zeroed in Eq. [START_REF] Konietschke | The dlr mirosurge -a robotic system for surgery[END_REF].

In practice, the two computation strategies significantly differ by several aspects. In the next, we list them and explain how they were taken into account to design an experimental set-up allowing for practically investigating these open questions.

i) A first aspect concerns the forces applied by the instrument at the fulcrum. As mentioned earlier, it is impossible to a priori determine which strategy will minimize the forces applied at the fulcrum due to the possible contribution of the unknown user wrench to {W f }. To evaluate this question, an experimental apparatus allowing to independently measuring forces and moments at the fulcrum will be used in Sec. III.

ii) The second aspect that distinguishes the two possible approaches for simulating a distal force F v is that, for the LMC approach, it is assumed that deformations induced by tissue elasticity are null, while the EWC approach does not rely on any particular model for the patient-instrument relative kinematics. In practice though, deformations do occur. This could lead to a lack of precision when applying LMC while EWC is still valid. Again, theoretically predicting the effect of this approximation on the quality of force perception for the user is difficult. Rather, an experimental approach will be used in Sec. III to study this question using an apparatus that includes deformations at the fulcrum.

iii) The third difference between the two strategies concerns the data required to compute the robot wrench. For EWC, only the geometry of the robot is to be known, as well as the desired location of V long the instrument axis. Meanwhile, for LMC, α has to be computed from Eq. ( 16) which, in practice, requires to know where point F stands. In other words, a registration between the robot and the patient is required, which reduces the interest of using a 6-DOFs robot rather than a 4 DOFs RCM robot. In practice, if we want to avoid registration, an arbitrarily constant value α can be used instead of α, corresponding to an average lever ratio, typically 1. This strategy will be experimentally evaluated in Sec. III.

iv) The fourth factor that distinguishes the two strategies has a significant impact in practice. While EWC strategy requires 6 actuated DOFs, only 3 actuated DOFs can be sufficient for LMC. Indeed, consider a 6-DOF robot consisting in 3 actuated DOFs serially mounted with a passive (unactuated) 3 DOFs wrist realizing a ball joint at point R. With such a robot, the three first actuators are used to produce a desired F r while the passive spherical wrist ensures that M r = 0. Clearly, in the perspective of transferring the technology to a clinical application, being able of exploiting a robot with only three actuators instead of six brings a significant advantage in terms of robot complexity, weight, inertia and cost. For this reason, such a particular robot kinematic configuration, with 3 actuators only, will be used to implement LMC in the next section.

III. EXPERIMENTAL METHODS

Experiments have been conducted in order to compare the efficiency of the two proposed approaches.

A. Experimental setup overview

The comanipulator used for the experiments is a 6 active DOFs haptic device which main specifications are listed Table I (model: Virtuose 6D -provider: Haption [START_REF] Haption | [END_REF]). Its kinematics comprises 3 first pivot joints that position a point R and a 3 joint wrist realizing a ball joint around R. Depending on the strategy to be experimented, the wrist joints will be actuated or not. Thanks to a fine mechanical design involving low friction cable transmissions, low inertia fiber carbon links, and gravity compensation springs, the Virtuose 6D robot allows to control {W r } in open loop with a high precision.

A rod with a handle is connected to the robot last body in order to emulate a surgical tool. To emulate the patient, a dedicated apparatus has been designed and fabricated. The rod is connected to an intermediate mechanical part through a cylindrical joint. This intermediate part is connected to a fixed drum through four springs as it can be seen on Fig. 4. The springs stiffness has been experimentally tuned in such a way that the obtained behavior is similar to those of an incision point or a natural orifice of a patient. Namely, it is not a perfect link, as the fulcrum point F can be displaced to simulate tissue deformations, while friction appears through the cylindrical link. In order to be able of measuring {W f }, the drum is mounted on a force sensor.

As we want to assess the efficiency of the virtual fixtures for the two proposed control laws, the space that is behind the drum is hidden by a screen. Therefore, the users are not able to directly visualize the tool tip position. A global view of the setup is given in Fig. 5.

B. Virtual Fixtures used for the experiments

In order to cover a large range of surgical scenarios, where virtual fixtures correspond to either repulsive regions in the aim of increasing safety (e.g. [START_REF] Jakopec | The hands-on orthopaedic robot acrobot: Early clinical trials of total knee replacement surgery[END_REF]) or attractive paths to guide an instrument (e.g. [START_REF] Schneider | A six degree of freedom passive arm with dynamic constraints (padyc) for cardiac surgery application: Preliminary experiments[END_REF]), three types of virtual fixtures have been implemented for the experiments.

• Repulsive spherical region A virtual spherical object, centered at a fixed point C, with a radius r is designed. The projection C of C on the instrument main axis, namely the line (DU), is first computed. Then, Point V where the force should be applied in case of intersection between the instrument and the sphere is set to:

V = D if --→ UC > -→ CD C otherwise (18)
When V belongs to the sphere, then an intersection is detected and a force is applied. The force is radial and proportional to the radial depth of V into the sphere, which writes:

F v =      k s r- -→ CV -→ CV -→ CV if r ≥ -→ CV > 0 0 otherwise ( 19
)
where k s is the stiffness of the sphere. This is illustrated in Fig. 6.

• Repulsive plane A virtual plane Π is defined, thanks to a point P ∈ Π and a normal vector n, pointing from the forbidden region to the 6. Computation of the virtual force F v to simulate the interaction between the instrument and a virtual sphere authorized region. The virtual plane applies no forces when the instrument distal tip D is the authorized region and a repulsive force when D is in the forbidden region. Point V is set to the instrument tip D. Its projection on Π, denoted V , is first computed. The force is normal to the plane and proportional to the penetration of V beyond Π, which writes:

F v = k p --→ V V if --→ VV . n > 0 0 otherwise , (20)
where k p is the stiffness of the plane.

• Attractive line A virtual line (∆) is defined thanks to a point P ∈ (∆) and a unit direction vector u. The role of the virtual fixture is to help the user keeping the instrument distal tip D on (∆). To this aim, Point V is set to the instrument tip D. Its projection on (∆), denoted V , is first computed. The force then simply writes:

F v = k l --→ VV , (21)
where k l is a stiffness.

C. Experimental protocol

Fourteen naive subjects have been enrolled in the study, aged 13 to 60. The subjects were not paid for the experiment. None of them have declared suffering from a sensorimotor deficiency. They had to perform 3 different exercises. Firstly, a Ball Sorting Out (BSO) exercise during which 4 virtual spheres with different sizes were simulated by the robot while the subjects were asked to blindly palpate them and to sort them out from the smallest one to the largest one. These balls have the same stiffness, that was tuned to provide an easy contact detection while experimentally preserving stability (k s = 200 N/m). The ball radius are log-distributed: R = {1.5, 2.4, 3.75, 6} cm. There is only one virtual ball at a time in the workspace. The balls are directly facing the entry point. Whatever the ball size, its most proximal point is always located at a given place, as illustrated in Fig. 7. Therefore, in order to evaluate the ball size, the subjects must palpate laterally. The balls are presented to the subject in a random order, then the subjects can switch to a previously presented ball, as many times as they want. Once they think they have sorted out the balls, they stop the exercise and name the ball from the smallest to the largest.

Secondly, a Plane Sorting out (PSO) exercise during which 4 planes with identical geometry but different stiffnesses were simulated by the robot while the subjects were asked to blindly palpate them and to sort them out from the softest one to the hardest one. The plane stiffness values were tuned to respect stability constraint and to range from a "soft feeling" to a "hard feeling". They are log-distributed: k p = {200, 340, 580, 1000} N/m. The virtual plane presents no geometrical particularity with the other elements of the experiments. Note that theoretically, palpating only one point of the plane could be enough for a subject to infer the stiffness. However, all the subjects decided to palpate the plane at several locations and to push against the plane. The PSO exercise unfolds as the BSO exercise. It stops when the subjects name the plane from the softest to the stiffest.

Thirdly, a Line Following (LF) exercise during which the subjects were asked to draw a straight line with the instrument tip "following the robot indication". In this exercise, an initial configuration is given to the tool by the operator. The subject must then make the tip of the tool following a straight line at his/her own pace, back and forth (3 times). The line direction is unknown, and the subject can use only the force feedback to follow the minimum force path. The line stiffness was tuned to k l = 300N/m so as to respect experimental stability conditions.

For the three exercises, the following general instructions are given to the subjects: the general context of the study (key hole surgery) is explained to the subjects, with particular emphasis on the prostate biopsy procedure. This is aimed at making them aware that during the exercises, forces applied at the fulcrum should be minimized. They are explicitly asked to pay attention to this objective during all the exercises. The subjects do not know anything more about the goal of the experience. They are asked to do each exercise twice: one trial for each controller, chosen in a random order for the three exercise, thus avoiding an influence of the learning effect on the statistical results. However, the subjects are not aware that two different controllers are being used. They are simply asked to repeat twice each exercise. Notice also that the subjects do not see the instrument tip, which is hidden behind the screen. They see only the proximal part of the instrument, the insertion apparatus and the robot. This way their perception of virtual objects is only obtained through the kinesthetic feedback.

D. Indicators

In order to assess the differences between EWC and LMC, several physical variables are recorded during the experiments. Among them, those that are representative of the gesture quality (forces at the fulcrum, positioning precision, movements smoothness) and the perception quality (duration and adequacy of the sorting out exercises) are used as performance indicators. Namely, the selected indicators are:

• for all the exercises:

the task completion time t total , which is the time needed by the subject to perform the exercise. the Spectral Arc Length (SAL) of the trajectories of point R as defined in [START_REF] Balasubramanian | A robust and sensitive metric for quantifying movement smoothness[END_REF]. SAL is the opposite of the length along the spectral curve of a movement. Not only it is an image of the complexity of the movement Fourier magnitude spectrum, but it is also dimensionless and independent of the movement magnitude and duration. Its value is negative; the closer it is to zero, the simpler the movement Fourier spectrum is and thus the smoother the movement is. the maximal force F max applied by the tool on the fulcrum. the mean force F mean applied by the tool on the fulcrum.

• for the BSO and PSO exercises only, a score is computed to quantify the adequacy of the answers. Namely, when the subject sorts out the spheres or the planes without any errors, a score σ = 2 is given; when all the spheres or planes are correctly sorted out except for one inversion between two consecutive items, a score σ = 1 is given; when there are more errors than one single inversion, a score σ = 0 is given. 8 gives, for illustration purposes, example trajectories of points T and R during each of the three exercises.

In order to evaluate the influence of the control method on the performance indicators, statistical tests are used to determine whether a difference experimentally observed between two groups of measured values is statistically significant or not. As usually admitted in the human motion analysis literature, tests resulting in a p-value smaller than 0.05 is considered to be statistically significant. Note that due to some technical issues, the recorded sensory data was corrupted for two subjects during the BSO and PSO exercises and for one subject during the LF exercise. Therefore, only twelve (resp. thirteen) data sets have been included for the statistical analysis of the BSO and PSO (resp. LF) exercises.

Table II analyzes the accuracy of the subjects' answers for the sorting out exercises. For both exercises, the measured average score is higher with LMC than with EWC. However, the observed difference between the score means is not statistically significant (p > 0.05). Not that the score σ being non-continuous, a Wilcoxon signed rank test has been used to compute the p-values.

Figure 9 shows the indicators for trajectory smoothness, fulcrum force (mean and max) and experiment duration averaged across subjects, for the three exercises. For all the four indicators, a slight difference between LMC and EWC can be observed, in either way. However, results seem globally similar. This similarity is confirmed in Table III. In this table, p-values computed from paired t-tests are used to compare EWC and LMC. All the slight differences observed have no statistical significance since none of the p-values is below 0.05.

For the Line Following exercise, the results for the precision (maximum error d max and mean error d mean ) are given in Fig. 10. Here, it can be observed that EWC clearly outperforms LMC. This is confirmed through the statistical test made between EWC and LMC since p-values equal 0.0004 for d max and 0.0001 for d mean .

Finally, subjects were asked, at the end of the session, whether they had felt a difference between the two repetitions of each exercise. The answers fell in three categories:

• one subject felt more comfortable with LMC but wasn't able to explain precisely what was different from the EWC command; • two subjects felt that EWC provided "more help" than LMC, only for the LF exercise. However, they were not able to differentiate both commands in BSO and PSO exercises; • ten subjects didn't notice any difference between two repetitions of any exercise. This indicates that, from the user point of view, there is not much difference between the two controllers.

V. DISCUSSION Most indicator comparisons between EWC and LMC exhibit no statistically significant difference. From a mathematical point of view, these results shall not be interpreted as a proof for both controllers to perform equally. Rather, these results indicate that the average difference of performance between the two controllers, if any, is too small to be observed through these experiments, given the inter-subject variability. In other words, there is a high probability that the actual difference for these indicators is, indeed, small. This is confirmed by the fact that most users did not notice a difference between the two controllers.

It is worth noticing that the forces applied at the fulcrum are, in average, rather low for all the sorting out exercises, under both conditions. Meanwhile, much larger forces were exerted on the virtual objects while large movements were produced by the users, see typical examples in Fig. 8. This result was surprising to the authors as, from Eq. ( 8), large differences in fulcrum forces were expected. We interpret the relative smallness of fulcrum forces as resulting from the fact that subjects were explicitly asked to avoid exerting large forces at the fulcrum. They were trying to precisely maintain point F still. A typical motor behavior for precisely controlling the position of a point under disturbances is to increase the impedance at this point along the direction of the disturbance force. In these experiments, disturbance forces to be rejected to lie in the ( x i , y i ) plane. It may thus be hypothesized that the subjects selected a motor behavior leading to a high impedance at point F in the ( x i , y i ) plane. If the subjects' impedance was high at point F, then this would also explain why they essentially did not feel any difference between the two controllers, while actually applying wrenches to balance the fulcrum-compatible robot wrenches.

As for the LF exercise, the precision of the tip trajectory control is higher with EWC than with LMC, with statistical significance, see Fig. 10. For this exercise, subjects' attention is brought to the tip, that shall precisely follow a straight line. Therefore, it can be hypothesized that subjects tend to increase the impedance at the instrument tip. This may be conflicting with the high impedance requirement at point F. As a result, it can be observed that the fulcrum forces are larger, in average, during LF exercise than during sorting out exercises (see Fig. 9). Note that when following a line, the distal virtual force should be minimized by the subject, while when palpating, eventually large virtual forces should be applied to distinguish between stiffness and sizes. In that sense, the fact that the fulcrum forces are larger for the LF exercise is not a scale effect due to higher distal virtual forces, but rather a consequence of a poorer control at the fulcrum level.

The hypothesis that the fulcrum forces control is degraded during the LF exercise may explain why EWC performs better than LMC. Indeed, remind that EWC control is the exact solution of the problem, independently from any entry point model. therefore, whatever the fulcrum displacement, EWC provides a feedback that exactly corresponds to a pure distal force. Rather, LMC is based on two hypotheses: first, the impedance at F shall be high (infinite) and second, the coefficient α shall be close to 1. These conditions are poorly verified during the LF experiments, which may explain the difference between the two modes in terms of tip precision, which depends on how well a subject can interpret the emulated distal force.

Further investigation is certainly needed to evaluate the precision performance for tip guidance. First, remind that the experiments are here performed blindly, while the subject doesn't know in advance the trajectory to follow. In a real surgical configuration, not only the instrument tip is controlled under visual guidance, but also the geometrical constraint is a priori known by the user. Performing LF experiments under these more realistic conditions would probably tend to lower the difference of performance between the two controllers, since the visual feedback would equally contribute to an increased precision in both conditions.

VI. CONCLUSION

Comanipulation and virtual fixtures offer a demonstrated interest for assistance to surgery. Meanwhile, little attention has been paid so far to the emulation of distal force from proximal comanipulation.

In this paper, this question is demonstrated to admit an infinite number of solutions, due to the fulcrum constraint. Experimental results comparing two selected approaches do not lead to a clear difference between them. From a practical point of view, this similarity may advantageously lead to select LMC rather than EWC. Indeed, contrarily to EWC, LMC can be implemented with a three actuators arm combined to a passive spherical wrist. An example of such a device is given in [START_REF] Poquet | An endorectal ultrasound probe comanipulator with hybrid actuation combining brakes and motors[END_REF].

As the paper concerns the generation of a proximal force to emulate a distal force, the experiments were designed in such a way that the subjects focus on the haptic feedback produced by the robot. For this reason, no visual feedback was used. This is a limitation in the perspective of exploiting the results for assistance to surgery, where both a visual feedback and a haptic feedback will be simultaneously available. A further investigation is to be performed considering now the combination of visual feedback and force feedback. A base for this future work can be found in [START_REF] Francoise | Assistance to bone milling: A tool mounted visual display improves the efficiency of robotic guidance[END_REF], where in comparison to unimodal tests, the combination of both information is shown to lead to increased performances, in the context of surgery.

  and 0.003 kg.m2

Figure 4 .

 4 Figure 4. Close up on the mechanical device that emulates the anatomical constraint.

Figure 5 .

 5 Figure 5. Complete experimental set-up.

Figure

  Figure 6. Computation of the virtual force F v to simulate the interaction between the instrument and a virtual sphere

Figure 7 .

 7 Figure 7. Position of the different virtual balls with respect to the drum.

Figure 8 .

 8 Figure 8. Trajectories observed for different points belonging to the tool during the BSO exercise (upper left), the PSO exercise (upper right) and the line following exercise (bottom). Results are shown for one randomly selected subject for illustration purpose.

Figure 9 .

 9 Figure 9. Average value of the different indicators across the subjects, for the three exercises (gray bars: LMC; white bars: EWC). Black lines represent the standard deviation.

Figure 10 .

 10 Figure 10. Average value of the precision indicators across the subjects, for the LF exercise (gray bars: LMC; white bars: EWC). Black lines represent the standard deviation.

Table I MAIN

 I VIRTUOSE 6D SPECIFICATIONS. FRICTION AND INERTIA HAVE BEEN ESTIMATED IN AN AVERAGE POSITION, AT POINT R. THEY SHALL BE UNDERSTOOD AS ORDERS OF MAGNITUDE.

  • for LF exercise: the largest distance d max from the tool tip D to the virtual line. the mean distance d mean from the tool tip D to the virtual line.

		BSO	PSO
		EWC LMC	EWC	LMC
	Correct answers	7	9	6	10
	Answers with one inversion	1	2	3	2
	Answers with more inversions	4	1	3	0
	Mean score σ	1.25	1.67	1.25	1.83
	Std. dev. for σ	0.96	0. 65	0.87	0.39
	p-value (Wilcoxon)		0.19	0.053
	Table II
	ACCURACY OF THE SUBJECTS FOR THE SORTING OUT EXERCISES
	IV. EXPERIMENTAL RESULTS
	Figure

Table III RESULTS

 III OF THE STUDENT PAIRED-T-TEST PERFORMED TO COMPARE THE EWC AND LMC PERFORMANCE FOR THE FOUR INDICATORS USED IN FIG. 9 AND THE THREE EXERCISES.

		BSO	PSO	LF
	t total	0.055	0.234	0.591
	SAL	0.150	0.845	0.883
	F max	0.245	0.530	0.946
	F mean	0.408	0.055	0.564


Mohamed Ben Ellefi

Mohamad Motasem Nawaf

Jean-Christophe Sourisseau
email: jean-christophe.sourisseau@univ-amu.fr

Timmy Gambin
email: timmy.gambin@um.edu.mt

Filipe Castro
email: fvcastro@tamu.edu

Pierre Drap

Clustering over the Cultural Heritage Linked Open Dataset: Xlendi Shipwreck

published or not. The documents may come

Introduction

The study of the history of seafaring is the study of the relations of humans with rivers, lakes, and seas, which started in the Paleolithic. An understanding of this part of our past entails the recovery, analysis, and publication of large amounts of data, mostly through non-intrusive survey methods. The methodology proposed in this paper aims at simplifying the collection and analysis of archaeological data, and at developing relations between measurable objects and concepts. It builds upon the work of J. Richard Steffy, who in the mid-1990s developed a database of ship components. This shipbuilding information, segmented in units of knowledge, tried to encompass a wide array of western shipbuilding traditions which developed through time and space and establish relations between conception and construction traits in a manner that allowed comparisons between objects and concepts. Around a decade later Carlos Monroy transformed Steffy's database into an ontological representation in RDF-OWL, and expanded its scope to potentially include other archaeological materials [START_REF] Monroy | Synthesizing and storing maritime archaeological data for assisting in ship reconstruction[END_REF]. After establishing a preliminary ontology, completed through a number of interviews with naval and maritime archaeologists, Monroy combined the database with a multi-lingual glossary and built a series of relational links to textual evidence that aimed at contextualizing the archaeological information contained in the database. His work proposed the development of a digital library that combined a body of texts on early modem shipbuilding technology, tools to analyze and tag illustrations, a multi-lingual glossary, and a set of informatics tools to query and retrieve data [START_REF] Cobar | A digital library approach to the reconstruction of ancient sunken ships[END_REF].

Our approach extends these efforts into the collection of data, expands the analysis of measurable objects, and lays the base for the construction of extensive taxonomies of archaeological items. The applications of this theoretical approach are obvious. It simplifies the acquisition, analysis, storage, and sharing of data in a rigorous and logically supported framework. These two advantages are particularly relevant in the present political and economic world context, brought about by the so-called globalization and the general trend it entailed to reduce public spending in cultural heritage projects. The immediate future of naval and maritime archaeology depends on a paradigm change. Archeology is no longer the activity of a few elected scholars with the means and the power to define their own publication agendas. The survival of the discipline depends more than ever on the public recognition of its social value. Cost, accuracy, reliability (for instance established through the sharing of primary data), and its relationship with society's values, memories and amnesias, are already influencing the amount of resources available for research in this area. Archaeologists construct and deconstruct past narratives and have the power to impact society by making narratives available that illustrate the diversity of the human experience in a world that is less diverse and more dependent on the needs of world commerce, labor, and capital.

In the context of semantic web works toward the development of culture heritage applications, we cite recent projects that among others, provide multimedia access to distributed collections of CH resources: (i) data portals like ADS 5 , ARIADNE 6 , EUROPEANA 7 and STITCH 8 , (ii) vocabularies like the CIDOC-CRM 9 and the Getty vocabularies 10 . A different approach is adopted by [START_REF] Kharlamov | Towards analytics aware ontology based access to static and streaming data[END_REF], where authors present a framework that relies on the Ontology-Based Data Access (OBDA) paradigm to allow for virtual integration based on rewriting SPARQL queries over the EPNet ontology to SQL queries over distributed data sources. This work is centered on the Xlendi shipwreck, named after the place where it was found off the Gozo coast in Malta. The shipwreck was located by the Aurora Trust, an expert in deep-sea inspection systems, during a survey campaign in 2008. The shipwreck is located near a coastline known for its limestone cliffs that plunge into the sea and whose foundation rests on a continental shelf at an average depth of 100 m below sea level. The shipwreck itself is therefore exceptional; first due to its configuration and its state of preservation which is particularly well-suited for our experimental 3D modeling project. The examination of the first layer of amphorae also reveals a mixed cargo, consisting of items from Western Phoenicia and Tyrrhenian-style containers which are both wellmatched with the period situated between the end of the VIII and the first half of the VII centuries BC. The historical interest of this wreck, highlighted by our work, which is the first to be performed on this site, creates a real added-value in terms of innovation and the international reputation of the project [START_REF] Drap | Underwater photogrammetry and object modeling: a case study of xlendi wreck in malta[END_REF].

This paper is a continuity for a previous work published in [START_REF] Drap | Underwater photogrammetry and object modeling: a case study of xlendi wreck in malta[END_REF] where we developed tools combining photogrammetry and knowledge representation that provide new analysis of the visible part of the cargo. We have also developed an ontology that models both the photogrammetric process and the measured objects, as detailed in [START_REF] Ben Ellefi | Cultural heritage resources profiling: Ontology-based approach[END_REF]. The focus of this paper is to publish the produced CH dataset as linked open data following the semantic web best practices. Furthermore, we introduce a new GUI tool for clustering over the distribution of different artifacts in the published LOD dataset. In 2001 the UNESCO Convention for the Underwater Cultural Heritage established the necessity of making all archaeological data available to the public 11 .

The rest of the paper is organized as follow: first, section. 2 will presents the adopted photogrammetrical process during data gathering. Further, section. 3 discusses the motivation behind our conceptual model then introduces the newly published dataset with an illustrative example. Next, section. 4 presents our GUI clustering tool that provides a 3D visualization of the resources density distribution in th published dataset. Finally, we conclude and give some future direction in the last section.

Photogrammetry Survey

Data acquisition and processing using photogrammetry allow the capture of an impressive amount of underwater site features and details [START_REF] Scaradozzi | Tools and techniques for underwater archaeological sites documentation[END_REF]. In the in Xlendi shipwreck, the aim of deploying a photogrammetry framework is to perform survey and produce a complete 3D model and overall orthophoto. The acquisition system used for the photogrammetric survey was installed on the Rmora 2000 submarine made by COMEX 12 . This two-person submarine has a depth limit of 610 m with a maximum dive time of 5 hours, which provides more than enough time for the data acquisition phase of the photogrammetry survey. What is of crucial importance to us are the three high-resolution cameras that are synchronized and controlled by a computer. All three cameras are mounted on a bar located on the submarine just in front of the pilot. Continuous lighting of the seabed is provided by a Hydrargyrum medium-arc iodide lamp (HMI) powered by the submarine. The continuous light is more convenient for both the pilot and the archaeologist who can better observe the site from the submarine. The high frequency acquisition frame rate of the cameras ensures full coverage whereas the large scale of acquired images gives the eventual 3D models extreme precision (up to 0.005 mm/pixel for the orthophoto). Briefly, the deployed procedure consists of three phases, the first two are done in real-time while the third is achieved in a later step. Starting with image orientation phase, it is possible to know the exact pose of the camera at each image acquisition. On the other hand, contrary to PMVS, our developments directly use the images produced by the cameras, without any distortion correction nor rectification. We refer to [START_REF] Drap | Underwater photogrammetry and object modeling: a case study of xlendi wreck in malta[END_REF] for more details, see Figure1. Deployed in this way, the acquisition system entails zero contact with the archaeological site making it both non-destructive and extremely accurate.

The next section will introduce our method for modeling the photogrammetry data using ontologies in order to facilitate data sharing between researchers with different backgrounds, such as archaeologists and computer scientists. The ontology-based model can be particularly useful to improve and expand data analysis and to identify patterns or to generate different statistics using a simple query language that is close to natural language.

3 Xlendi As Linked Open Dataset

Ontology Conceptualization

Cultural heritage data is very heterogeneous and can have different ambiguous descriptions. Hence, the most challenging problem for metadata designers and cultural heritage experts is to provide a common conceptualization of the data. This conceptualization provides a common way of representing knowledge about some domain and a way to share a common understanding of information structure. Once we have common understanding, we can try to reason/query over this information, i.e. inference, consistency checking, etc. To develop a transversal data mining techniques and adapted systems, conceptualization must provide an intelligible description that allows a better understanding for experts manipulating the data. By organizing this information in an ontology, the conceptualization can be used to cover different terminologies and to represent a clear specification of the different meanings. In this way, the ontology model can guide the design of the knowledge bases to store the various experimental data as well as the measurement process in a knowledge manner. In the remainder of this paper, we adopt the computational meaning of ontology which can be seen as a structured system of fundamental concepts and relationships and of an agreed epistemology, i.e. clearly defined rules of evidence and reasoning, which do not privilege individual experiences or beliefs that cannot be argued against, and which at the same time include clear evaluation mechanisms for the credibility of research conclusions [START_REF] Guarino | What is an ontology?[END_REF].

In a collaborative work between archaeologists and ontology designers, we developed a common ontology that models cultural heritage artifacts in term of their typologies, photogrammetric process and spatial representation, as in [START_REF] Ben Ellefi | Cultural heritage resources profiling: Ontology-based approach[END_REF], where we presented our model for profiling archaeological amphorae. We serialized our ontology using the Web Ontology Language OWL2 13 , and we made available on14 . Following the linked data best practices [START_REF] Bizer | Linked data-the story so far[END_REF], metadata designers reuse and build on, instead of replicating, existing ontologies and vocabularies. Motivated by this observation, we linked our ontology to the CIDOC-CRM ontology [START_REF] Doerr | The cidoc conceptual reference module: an ontological approach to semantic interoperability of metadata[END_REF] and GeoSPARQL15 in order to allow more integrity cross different cultural heritage datasets using different ontologies, i.e. enabling to perform federated queries cross multiple datasets. The ontology was modeled closely linked to the Java class data structure in order to be able to manage the photogrammetric process as well as the measured items. Note that each concept or relationship in the ontology has a counterpart in Java (the opposite is not necessarily true). Finally, our ontology has been integrated in the linked open vocabularies for better terms reuse, see16 .

Xlendi LOD Dataset

We draw the reader intention that the data from Xlendi shipwreck was processed by photogrammetry in a previous work [START_REF] Drap | Underwater photogrammetry and object modeling: a case study of xlendi wreck in malta[END_REF]. The focus of this paper is to publish this dataset as linked open data following the semantic web best practices. Hence, the dataset processed by photogrammetry is stored in ABox OWL file and we made it available as open data on the datahub under the name "Xlendi Amphorae", see17 . For better understanding of the dataset, we detail in the following the two sample files "XlendiApmhoraeSample" and "PhotographSample": -The RDF file "PhotographSample" in the XlendiAmphorae dataset depicts an example of a photograph instance Photograph 13. This photograph instance is connected to a camera and a 3D transformation. The camera is described by a set of camera settings properties and enriched by a distortion specifications, which is particularly crucial for the photogrammetry measuring. The 3D transformation describes the photograph with a set of 3D points and a set of rotation matrix.

Finally, the complete set of CH artifacts, amphorae and grinding-stones, are made available in the "XlendiArtifacts" OWL file.

Xlendi Data Linking

Following semantic web best practices, we need to provide links to further candidate datasets that may contain similar instances in order to join the LOD cloud 18 . However, we provide the only available RDF data that represents am-phorae collected from the Xlendi shipwreck. Hence, we looked into DBpedia, being the most obvious target in the LOD. The only similarity that we found within this multi-domain dataset consists on the instances of the widely used concept "Camera". However, in our dataset the distinguishing criterion between different cameras is the setting (calibration, distortion, etc) not the camera type i.e. different instances refers to the camera Nikon D700 but with different setting. For this purpose, the identity link is not able to be adopted in this case ("owl:sameAs" to DBpedia camera Nikon D700 19 ), according to [START_REF] Halpin | When owl: sameas isn't the same: An analysis of identity links on the semantic web[END_REF]. Other broader links such as skos:broadMatch20 might be semantically more appropriate since they indicate a broader matching links.

Xlendi Data Visualization

For better visualization of the stored dataset, we developed a graphical user interface tool that loads the published dataset to a 3D graphical visualization. Figure . 2 shows a view of our GUI tool demonstrating the 3D density distribution of amphorae and grinding-stones in the Xlendi shipwreck. In this way, the user can graphically depict information about different artifacts based on their 3D spatial representation. The Figure . 3.2 shows the case of Amphore A03 and its localization in the shipwreck while the corresponding information about the artifact typology is depicted in Figure . 3.2. Note that our GUI tool offers further services which are currently in a work in progress statue from which we can cite [START_REF] Drap | Ontology-based photogrammetry survey for medieval archaeology: Toward a 3d geographic information system (gis)[END_REF], where we demonstrated a prototype of implemented spatial queries using SQWRL (a SWRL21 -based query language) in our tool. For example, the operator "isCloseTo" built-ins which allows to select artifacts present in a sphere centered regarding to a specific one. In the next section we will introduce a new tool that offers a 3D clustering functionalities over the ABox part of the dataset.

Spatial clustering for Xlendi Dataset

Within the vast domain of data mining, spatial data mining is an important field of research and has always been of particular interest for archaeological community. Spatial data mining can be seen as the process of extracting potentially useful and previously unknown information from spatial datasets. One of the most fundamental tasks in spatial data mining is spatial clustering which has been steadily gaining importance over the past decade. Clustering algorithms are attractive for the class identification tasks. There are many spatial clustering methods available and each of them may give a different grouping set of a dataset. Here, we focus on density-based clustering algorithms where the idea is that objects which form a dense region should be grouped together into one cluster. These algorithms search for regions of high density in a feature space that are separated by regions of lower density. Thus, density-based methods can be used to filter out noise, and discover clusters of arbitrary shape.

In our tool, we implemented two well known clustering algorithms K-Means++ [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] and the DBSCAN [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] (i.e. as a density-based algorithm for discovering clusters in large spatial databases with noise). The main intuition behind our choice is to provide the user multiple choices to address users needs. For example, if the user knows in advance the number of clusters, K-means++ will be the more appropriate choice. Otherwise, DBSCAN clustering can be performed without knowing the number of clusters. Furthermore, we give the user the choice to select properties on which the clustering will be based, i.e. clustering Xlendi artifacts based on their typology, volume, length or height.

In the following, we detail our implementation of DBSCAN. This algorithm is mainly used to cluster point objects, which is perfectly in line with our model where any spatial object can be represented as a point (as detailed in Section.2). The main intuition is that, within each cluster, there is a typical density of points which is considerably higher than outside of the cluster. Subsequently, the density within the areas of noise is lower than the density in any other area of the clusters. Two important parameters are required for DBSCAN: a distance threshold -, and a minimum number of points -M inP ts. The parameter defines the radius of neighborhood around a point A. It's called the -neighborhood of A. The parameter M inP ts is the minimum number of neighbors within radius.

Following the main concepts defined in DBSCAN [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF], let's consider the set of amphorae in the Xlendi shipwreck as a set of n points {A 0 , .., A i , .., A n }, that DBSCAN will cluster as follow:

1. For each point A i , the algorithm computes the distance between A i and the other points. Finds all neighbor points within distance of the starting point (A i ). Each point, with a neighbor count greater than or equal to M inP ts, is marked as core point or visited. 2. For each core point, if it's not already assigned to a cluster, creates a new cluster. Finds recursively all the density points connected to it and assigns them to the same cluster as the core point. 3. Iterates through the remaining unvisited points in the data set.

Note that points not belonging to any clusters are treated as outliers or noise.

Figure . 4 depicts the setup panel within our GUI tool where user can define the setup parameters of the clustering methods. The setup panel provides access to: (i) K-Means++ setup parameters by selecting the appropriate number of clustering; (ii) DBSCAN parameters: the minimum number of neighbors (i.e. M inP ts = 2) and the threshold (i.e. = 0.004); (iii) the artifact property to cluster on. The clustering result is represented by different distribution of colors within the site, as shown in Figure 4. Furthermore, our GUI tool generates a report describing the deviation ratio of the generated clusters in term of: average, median, minimum, maximum, median absolute deviation (MAD) and root mean square (RMS). Finally, our clustering tool is integrated into our 3D geographic information system that merges photogrammetry and ontologies with an aim to the automatic production of 3D (or 2D) models through ontological queries: these 3D models are in fact at the same time a graphic image of the archaeological knowledge and the current interface through which the user can edit the dataset. Further clustering functionalities can be integrated in our GUI tool, as we cite the work on [START_REF] Drap | Ontology-based photogrammetry survey for medieval archaeology: Toward a 3d geographic information system (gis)[END_REF] where we proposed a clustering model for the Montreal Castle in Shawbak, Jordan.

Conclusion

In this paper, we introduced the Xlendi shipwreck dataset that was published as linked open data. We developed tools combining photogrammetry and knowledge managements to provide a 3D virtual survey of the cargo. The tool allows to load the LOD dataset and to visualize the spatial distribution of the different artifacts in the shipwreck. Based on this distribution, the user is able to extract different information about the artifacts dimension typologies. Different clustering methods are implemented and can be processed over the artifacts distribution aiming to be exploited according to cultural heritage tasks and users preferences.

Future directions can go towards the extension of our tool with a new interface allowing to assist CH users in building semantic queries and rules. Also, we are currently looking for potential candidate datasets that may contain similar artifacts as the Xlendi dataset in order to produce a 5-stars linked open data 22 , i.e. connecting Xlendi amphorae to the ones having similar typologies in the ADS23 .

Fig. 1 .

 1 Fig. 1. Example of obtained models for the underwater site Xlendi. An Overall orthphoto (left) and a close-up view of the generated 3D model (right)

Fig. 2 .

 2 Fig. 2. A 3D visualization of amphorae stored in the ABox by our GUI tool. (a) Amphora A03 spatial position in the Xlendi site. (b) the typology dimensions corresponding to the amphora selected in the 3D spatial site

Fig. 3 .

 3 Fig. 3. A 3D visualization of Xlendi amphora distribution by our GUI tool. (a) 3D visualization of colored clusters of amphorae. (b) A view of the clustering setup panel

W3C Consortium recommendation, see https://www.w3.org/TR/owl2-overview/

http://www.arpenteur.org/ontology/Arpenteur.owl

http://www.opengeospatial.org/standards/geosparql

http://lov.okfn.org/dataset/lov/vocabs/arp

https://datahub.ckan.io/dataset/xlendiamphorae

http://dbpedia.org/page/Nikon_D700

http://www.w3.org/2004/02/skos/core

https://www.w3.org/Submission/SWRL/

http://5stardata.info/en/

http://data.archaeologydataservice.ac.uk/query/

Acknowledgments

The authors would like to thank the iMareCulture project for partially funding this work, URL: http://imareculture.weebly.com.

//data.archaeologydataservice.ac.uk/query/ 6