Xi Wang

Marc Christie

Eric Marchand

TT-SLAM: Dense Monocular SLAM for Planar Environments

This paper proposes a novel visual SLAM method with dense planar reconstruction using a monocular camera: TT-SLAM. The method exploits planar template-based trackers (TT) to compute camera poses and reconstructs a multiplanar scene representation. Multiple homographies are estimated simultaneously by clustering a set of template trackers supported by superpixelized regions. Compared to RANSACbased multiple homographies method [1], data association and keyframe selection issues are handled by the continuous nature of template trackers. A non-linear optimization process is applied to all the homographies to improve the precision in pose estimation. Experiments show that the proposed method outperforms RANSAC-based multiple homographies method [1] as well as other dense method SLAM techniques such as LSD-SLAM or DPPTAM, and competes with keypointbased techniques like ORB-SLAM while providing dense planar reconstructions of the environment.

I. INTRODUCTION

Research on SLAM techniques (Simultaneous Localization And Mapping) has drawn a big amount of attention in the robotics community and led to implementations in various use cases: indoor and outdoor, in the urban and in the wild. Sparse SLAM methods either rely on direct alignment of pixel-level information or minimization of re-projection errors on extracted keypoints and similar low-level image features [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF], [START_REF] Engel | Lsd-slam: Large-scale direct monocular slam[END_REF], [START_REF] Engel | Direct sparse odometry[END_REF].

However, more high-level geometric features such as lines and planes can be exploited and integrated into visual SLAM systems as they provide a more semantic abstraction and are more robust over point-based image features.

Planes, for example, are ubiquitous geometric feature in man-made environments and objects, and enjoy worthwhile characteristics in visual tracking and SLAM tasks. Planar models only require a small set of parameters but can reconstruct complex scenes in a dense fashion. Planar models are also easy to estimate and track using homographies that express relations between image and world spaces. Henceforth, many tracking algorithms are based on single homography transforms: SLAM [START_REF] Pirchheim | Homography-based planar mapping and tracking for mobile phones[END_REF], object visual tracking [START_REF] Dame | Second-order optimization of mutual information for real-time image registration[END_REF] or robotic visual servoing [START_REF] Marchand | Feature tracking for visual servoing purposes[END_REF].

While the single homography constraint can be easily exploited in tracking tasks on scenes with a dominant plane, this assumption severely limits applications to more general environments.

A number of contributions have therefore explored the use of multiple plane representations. Wang et al. [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF] proposed a ransac-based relative camera pose estimation under multiple Author are with Univ Rennes, Inria, CNRS, Irisa, France. Email:{xi.wang}@inria.fr {marc.christie, eric.marchand}@irisa.fr planar structures with the help of superpixels. Inspired by this work, this paper proposes a multiple planar SLAM framework using template-based trackers and superpixels to estimate camera trajectories and reconstruct a dense partial mapping from monocular image sequences (see Fig. 1).

Our contributions are: (1) a novel method of initializing template trackers with the help of superpixels, (2) a mean shift clustering system to handle planar segmentation and pose estimation, and (3) a non-linear optimization refiner for improving precision and robustness by merging template tracker estimations.

II. RELATED WORK

A range of related work can be found under the topic of estimating camera pose and mapping in planar worlds. Some rely on the single homography assumption in which the workspace is usually one-dominant-planar scenes [START_REF] Benhimane | Homography-based 2d visual tracking and servoing[END_REF]. Pirchheim and Reitmayr [START_REF] Pirchheim | Homography-based planar mapping and tracking for mobile phones[END_REF] designed and developed a mobile augmented reality SLAM system for single planar environments. Combining the process with IMUs (Inertial Measurement Unit) also helps in improving the precision and eliminating ambiguities during homography decomposition [START_REF] Guan | Visual odometry using a homography formulation with decoupled rotation and translation estimation using minimal solutions[END_REF], [START_REF] Saurer | Homography based visual odometry with known vertical direction and weak manhattan world assumption[END_REF].

Another class of approaches addresses worlds through the Manhattan assumption: all three dimensional planes in the environment are perpendicular to each other. Such an assumption is well suited in standard indoor and urban scenarios and simplifies the model, improving performance and precision in specific use-cases [START_REF] Saurer | Homography based visual odometry with known vertical direction and weak manhattan world assumption[END_REF], [START_REF] Flint | Manhattan scene understanding using monocular, stereo, and 3d features[END_REF], [START_REF] Yang | Pop-up slam: Semantic monocular plane slam for low-texture environments[END_REF].

A number of approaches rely on planar scene SLAM and visual tracking systems by exploiting the depth information of RGB-D cameras. Kaess [START_REF] Kaess | Simultaneous localization and mapping with infinite planes[END_REF] proposes a quaternion formulation for 3D planes to improve convergence speed during optimization. Hsiao et al. [START_REF] Hsiao | Keyframe-based dense planar slam[END_REF] extended the previous work to a real-time keyframe-based RGBD planar SLAM: It does keyframe-based local odometry with help of geometric and photometric information for fast pose estimating. Then all the keyframes data are handled by a factor graph map using incremental smoothing and mapping technique (iSAM).

Approaches driven by deep learning neural networks also gained popularity and showed improved performances in many computer vision tasks. Pop-Up SLAM [START_REF] Yang | Pop-up slam: Semantic monocular plane slam for low-texture environments[END_REF] demonstrates good performance for planar scene especially when the environment is texture-less. Yang and Scherer [START_REF] Yang | Monocular object and plane slam in structured environments[END_REF] proposed to add 3D object detection by bounding boxes as another constraint for Manhattan structured environments.

The use of superpixels in SLAM techniques has raised interest in the community. A superpixel is a group of pixels sharing spatial and chromatic similarities, usually generated by clustering or segmentation methods: classic works include SLIC [START_REF] Achanta | Slic superpixels compared to state-of-the-art superpixel methods[END_REF], SEEDS [START_REF] Van Den Bergh | Seeds: Superpixels extracted via energy-driven sampling[END_REF] and graph-segmentation superpixel [START_REF] Felzenszwalb | Efficient graph-based image segmentation[END_REF]. In the computer vision and robotic visionary domain, the technique is exploited as it provides a rough planar estimation.

More specifically, Concha and Civera propose to integrate superpixel techniques in sparse [START_REF] Concha | Using superpixels in monocular slam[END_REF] and dense [START_REF]Dense Piecewise Planar Tracking and Mapping from a Monocular Sequence[END_REF] SLAM systems to enhance mapping results. The idea consists of a Monte Carlo ranking to find the correspondence and initial 3D pose of superpixel-represented planes. The paper proposes an optimization framework to refine the plane poses with already known camera pose estimated separately from a PTAM system. Later, in DPPTAM [START_REF]Dense Piecewise Planar Tracking and Mapping from a Monocular Sequence[END_REF], superpixels are used in a semi-dense tracking system. Similar to [START_REF] Concha | Using superpixels in monocular slam[END_REF], plane estimation is handled in a decoupled fashion to camera pose which is found by semi-dense SLAM system. Ransac and SVD on three dimensional points is used for estimating the plane equation. A dense mapping optimization technique is therefore designed with superpixels information too.

Recently, [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF] proposed a coupled estimation of multiple planes and camera pose based on multiple homographies. A dedicated RANSAC is applied on keypoints and ambiguities in plane estimation are eliminated via multiple homographies in order to simultaneously achieve sparse tracking and dense mapping.

Template-based trackers is a well-known technique in robotics to track and estimate planar image patches by registering different primitive geometric models w.r.t various metrics: e.g., sum of square difference (SSD), zero-mean normalized cross-correlation (ZNCC), and mutual information (MI). Planar trackers usually estimate a homography transform between a template patch and query image via optimization method. Many applications are derived from template-based trackers including augmented reality [START_REF] Marchand | Pose estimation for augmented reality: a hands-on survey[END_REF], robot control [START_REF] Spindler | Vision-based robot control with visp[END_REF], etc. Compared with RANSAC methods (e.g., [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF]), using template trackers to continuously extract homographies has the following advantages: 1) it solves well the data association problem when multiple planes are present in the scene; 2) it provides continuous observation of the tracking results, therefore the system has more flexibility to deal with the keyframe selection problem; 3) RANSAC method tends to require higher computational cost when dealing with multiple planes, as template trackers are much lighter and deterministic in terms of results.

Combining the advantage of template tracker and the work of multiple homographies pose estimation [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF], we present a novel method of multiple planar vSLAM. It supports: 1) a novel method of tracking camera pose and mapping multiple planar environments simultaneously in a dense fashion; 2) a method of generating, clustering and utilizing template trackers with support of superpixel images for vSLAM applications; 3) a mean of applying homography-based nonlinear optimization on template trackers as a refiner for achieving better pose estimation and mapping quality.

III. OVERVIEW

We propose TT-SLAM as a novel visual SLAM technique which relies on template trackers (TT) for planar environments. It comprehends the following modules (see overview in Fig. 2): (a) generation and tracking of template trackers: we add template trackers on regions of superpixelizd images and track them in the sequence of images; (b) clustering of decomposed planes: we rely on a mean shift clustering algorithm to group similar decomposed planes from homographies to extract a multi-planar structure; (c) nonlinear refiner: we apply a non-linear optimization framework on template trackers to refine camera pose and multiple planes simultaneously on both the single incoming image and whole the image sequence (Bundle Adjustment-like). All the modules are presented in details in the following sections.

IV. MULTIPLE TEMPLATE TRACKERS

The main idea of our work is to rely on multiple template trackers to both estimate a camera pose and a dense planar mapping of a 3D scene.

Planar template tracker is a technique which tracks a planar image region on a sequence of frames. The technique outputs a homography transform H from a reference region in the first image to the current one. In a planar scene, the homography transform 2 H 1 2 SL(3) is used to describe the transformation of a three-dimensional plane from one image I 1 to another I 2 . When the camera is intrinsically calibrated, i.e. the intrinsic matrix K is known, all pixels from I 1 and I 2 can be presented as normalized three dimensional coordinates denoted as: p 1 and p 2 2 R 3 . The homography matrix is therefore a constraint between those points within the planar region: In subfig.c, tracking and clustering template trackers is performed (different colors represent different found planes in 3D, see subfig.d). Finally, passing through the refiner module, our method is able to recover camera trajectories together with a dense planar environment which conserves well plane perpendicularity without applying any Manhattan assumption.

p 2 = 2 H 1 p 1
This transform is actually composed of a rotation matrix 2 R 1 2 SO(3), a translation vector 2 t 1 2 R 3 and a normal vector in the first frame I 1 : n 1 = (a, b, c) > 2 R 3 (Eq. 1). The three dimensional plane associated is then formulated as p > n 1 = d, where p 2 R 3 are three dimensional points on the plane and d is the perpendicular distance to the origin:

2 H 1 = 2 R 1 + 2 t 1 d n 1 > (1)
Different methods have been proposed to compute a homography matrix between images, some rely on keypoints [START_REF] Kanazawa | Detection of planar regions with uncalibrated stereo using distribution of feature points[END_REF] and others exploit pixel-level information [START_REF] Agarwal | A survey of planar homography estimation techniques[END_REF]. For most template tracking problems, it is regarded as a differential image alignment problem at a pixel level.

The objective of differential image alignment is to estimate a displacement ⇢ of an image template I ⇤ in multiple frames. It can be treated as a frame-to-frame tracking process, where the I ⇤ is usually a Region-of-Interest (RoI) extracted from the reference frame. One then requires a similarity measure f to represent the distance between the reference image and the warped image. With the above definitions, one can describe the differential image alignment problem under an optimization problem:

b ⇢ t = arg max ⇢ f (I ⇤ , w (I, ⇢)) (2)
where we aim at finding the displacement b ⇢ t which maximizes the similarity under a given measure f . For the purpose of clarity, the warping function w is an abused notation to define a general transformation of the image I parameterized by ⇢. In the context of planar homography estimation, we search on ⇢ 2 sl(3) which has 8 parameters. In order to accelerate the searching process, the inverse compositional formulation technique is proposed by precomputing derivatives of the reference image (see more details in [START_REF] Baker | Lucas-kanade 20 years on: A unifying framework[END_REF], [START_REF] Dame | Second-order optimization of mutual information for real-time image registration[END_REF]).

Unlike common applications of template-based trackers where the regions-of-interest are usually known a priori or selected by user interaction, our system needs to automatically determine the regions-of-interest by computing adequate regions in terms of area and location consistent with a rough planar assumption. To address this problem, we rely on superpixel image decomposition. A superpixel is defined as a group of connected pixels sharing strong chromatic consistency (e.g., SLIC [START_REF] Achanta | Slic superpixels compared to state-of-the-art superpixel methods[END_REF]). We make an assumption here that each superpixel can be regarded as a potential planar region suitable for template-based trackers. During the initialization procedure, each superpixel is assigned as a RoI for a template-based tracker in order to track the regions in the following frames. Since superpixel borders are often non-planar and perturbate tracking quality, we propose to simplify the contour of superpixels by applying Teh-Chin chain approximation [START_REF] Teh | On the detection of dominant points on digital curves[END_REF] and Ramer-Douglas-Peucker algorithm [START_REF] Ramer | An iterative procedure for the polygonal approximation of plane curves[END_REF] on eroded superpixel contour. The regions are then represented as a Delaunay triangulation and considered as a tracking RoI (see Fig. 3). Though the superpixels only provide a rough a priori on region planarity, trackers which are assigned with non-planar or multi-planar regions will quickly lead to divergence during the tracking optimization process and can be removed.

By contrast with our previous work [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF] where all homographies are estimated from one given keyframe (i.e. the same reference image), new template trackers can be considered and added at any time. This reduces the risk of wrong keyframe selection, a issue identified in [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF]. A policy is therefore devised to decide when to add new template trackers by selecting superpixels which fail to superpose with an already existing template tracker, by simply measuring their ratio of region overlapping on the image surface. For every new incoming frame, we therefore compare the newly computed superpixels with current valid trackers and add new trackers on those not covered. Our ratio is defined as follows for each superpixel:

r = S tt \ S sp S sp (3)
S tt and S sp are the regions of template tracker and superpixels respectively.

V. CLUSTERING AND DECOMPOSITION

Once we obtain a set of homographies from different template trackers {H}, the next step consists in clustering homographies to obtain a simplified and better multi-planar representation. In our previous work [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF], this was achieved by a Winner-Takes-All RANSAC on detected keypoints to identity multiple planes. Here we rely on a mean shift clustering technique to decide if some trackers belong to the same plane.

Clustering is a task of grouping similar data together and classifying according to specific metrics: classic works including K-means [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF], mean shift [START_REF] Fukunaga | The estimation of the gradient of a density function, with applications in pattern recognition[END_REF], etc. Clustering is popular in computer vision and visionary robotics applications as it's able to reveal patterns from data aspect: e.g., [START_REF] Kim | Linear rgb-d slam for planar environments[END_REF] use mean shift technique for estimating undrifted rotation from vanishing points in indoor scenarios to decouple the rotation and translation in SLAM.

In our work, we expect a clustering system to separate different trackers and group similar ones as they are tracking the same three dimensional plane. As we do not know in advance the number of planes in the scene, it makes mean shift clustering an appropriate method to deal with the case as it doesn't require an initial seed number, unlike other clustering methods. Ideally, if all the trackers are initialized at the same reference frame, we may directly apply mean shift on the space of homography H 2 SL(3). However, because of the aforementioned trackers adding policy, classification cannot be performed directly on the homography space since we are dealing with trackers initialized from different reference frames. Instead, since pose estimation is a sequential tracking problem, we propose to perform the classification on the decomposed planes represented in world coordinates (see Eq. 1), and clustering them in the space of plane parameters ⇧ = {n, d} where n is the normal vector of the plane and d is the perpendicular distance to the origin.

A classical issue, however, is the ambiguity in homography decomposition. Inevitably, decomposing a single homography yields two sets of results of R, t, n which both are geometrically valid. Without extra information, at least two ambiguities exist even after applying positive depth condition, unless one element among R, t, n is known in a priori, e.g., by IMU information or known surface normal. For multiple planar homographies, we addressed the problem [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF] by proposing voting on the common direction of the translational vector. We adopt the same method in this work for not only eliminating ambiguities but also filtering low quality template trackers by measuring their translational vector to the voted common direction: if none of translational vectors is close enough to the common direction among ambiguity sets, we consider the template tracker itself may be wrongly initialized or assigned with non-planar regions.

After decomposition, we obtain a set of planes represented in world coordinates, denoted as {⇧}. Instead of clustering naively on the space of planes ⇧ = {n, d} where the euclidean distance not defined properly, a hierarchical mean shift scheme is applied by considering first the normal vectors {n}, then second the d parameter and the on-image barycenter position {d, p c } of each template trackers for grouping planes locally. We utilize the euclidean metric on both hierarchies of clustering and find the results are good enough though the space of plane normal has its own geodesic metric on the sphere group (see Fig. 4 for clustering results and correspondent depth image).

VI. NON-LINEAR MULTI-PLANE REFINER AND BA

A. Non-linear Refiner on Current Image

Given the clustering performed on the image planes, we then design a refining process to better exploit the information from multiple trackers and improve the estimation of both the camera pose q 2 se(3) 2 R 6 (the minimal representation of transformation {R, t}) and planar equations ⇧ simultaneously. In traditional SLAM systems, this process is usually handled by a non-linear optimization framework, which minimizes the re-projection error on image space of extracted landmarks such as keypoints (Bundle Adjustment).

To handle homography transformations, a similar process can be applied via a non-linear least square Gauss-Newton optimization process which minimizes the re-projection error E between pixels (p n 2 2

H 1 p n 1 ) 2 , n = 1, .., N p as number of pixels, w.r.t. camera pose q and the plane parameter ⇧ 1 = {n 1 , d}. This is expressed as:

{b q, c ⇧ 1 } = argmin q,⇧1 E(q) = argmin q,⇧1 Np X n p n 2 2 H 1 p n 1 2
(4) To compute the re-projection error, we use vertices from the Delaunay triangulation process of each template tracker.

Similarly to [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF], sharing multiple homographies in a static environment can be interpreted as the relation of a set of homographies estimated by trackers {H i } and a shared transformation in world coordinate frame w T o 2 SE(3) (o represents origin of the frame) represented by local transforms w T ri (from the reference frame r i of template tracker i to its current position) for all trackers, where i = 1, .., N tt as the number of trackers:

w T r = w T o r T 1 o , w T r = { w R r , w t r } H i = w R ri + w t ri d i n ri > (5)
We can therefore propose a refiner for estimating camera pose and planar equations simultaneously from multiple trackers homographies. Note that we already know the correspondence mapping from {⇧ i } to clustered and grouped planes {⇧ c } by mean shift and data association. Rather than considering each plane separately for each tracker, during the optimization process we group planes together in {⇧ i } following the mean shift clustering.

{ c q w , { d ⇧ c w }} = arg min qw,{⇧ c w } Ntt X i Np i X n p n wi w H ri p n ri 2 (6)
with p n w and p n ri are the vertices of tracking regions from the current frame and the corresponded reference frame of the template tracker i respectively, their sum quantity is N pi and number of trackers N tt . Remember that the camera pose c q w and planar equation d ⇧ c w are actually in the world coordinates, thus a transform of Eq. 5 from global coordinate to local coordinate is mandatory as the homography is defined only between the reference frame and current one. For simplicity, we denote w H ri by an abuse of notation and hide the transform in Eq. 6.

A warm start for the optimization can be given directly from the last camera pose and also by searching for the previous global planar results for each template tracker. With the help of template trackers, plane data association is no longer a problem as we already know which template tracker generates each plane. Simple searching and comparing of trackers is performed.

B. Bundle Adjustment-like Refiner

The plane map refiner consists of an optimization framework that refines all keyframes' poses and their common planes found by the plane matching process. Each keyframe contains multiple planes and their vertices. Once the joint plane information is gained over different keyframes, like global BA for point-based SLAMs, this procedure eliminates the drifting problem, alleviates scale ambiguity, and refines camera trajectory w.r.t whole sequence.

By analogy, we propose a Bundle Adjustment (BA) system for refining every frame's pose and the joint plane information by mutually minimizing their re-projection error:

arg min qt,{⇧ c t } Nt X t Ntt X i Np i X n p n t t H ri p n ri 2 (7)
where t and i are the index of frame and tracker number, N t and N tt represent the total frame and template trackers number respectively.

C. Planar Map 1) Plane merging and keyframes: We also deploy a plane merging scheme to fuse close planes given a metric on plane normal vector n and orthogonal distance d. Ideally, we don't rely on well-selected keyframes such as [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF] since keypoint homographies are prone to errors with insufficient translations. In contrast, template trackers allow us to track planes along the sequence, and wait until the estimation is stable before generating keyframes.

2) Template rejection: Unlike RANSAC-based methods, template trackers maximize the similarity of all pixels in the region. This makes the outlier rejection critical for a SLAM system: any ill-tracked template tracker is capable of adding noise in the overall camera and plane estimation. Besides applying a robust loss function such as Huber loss [START_REF] Huber | Robust estimation of a location parameter[END_REF], we also propose a template rejection procedure for preventing ill-tracked templates. Three main points are chosen here to filter out bad trackers:

• The lack of convergence or high tracking cost led by tracker's optimization, which usually occurs when initialising on texture-less or non-planar regions. • The voting distance during the ambiguity elimination process: if none of the computed solution is close to the common voted translational direction. • Unstable templates: we monitor each template in terms of their plane equations and prune trackers which fail to generate stable plane in measure of their parameters.

VII. EXPERIMENTS AND DISCUSSIONS

We test our proposed method in two different scenarios: indoor and outdoor environments.

For the indoor environments, we test three levels of difficulty and complexity from simplest to most complex: single plane scenario, multiple planes scenario, and a complex multiple planar real room.

Single (fr nstr loop) and multiple (fr str far) plane scenarios are tested with the TUM RGB-D dataset [START_REF] Sturm | A benchmark for the evaluation of rgb-d slam systems[END_REF] which is also utilised by many planar or dense SLAM methods [START_REF]Dense Piecewise Planar Tracking and Mapping from a Monocular Sequence[END_REF], [START_REF] Greene | Multi-level mapping: Real-time dense monocular slam[END_REF], [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF]. The scene is composed of rich textured planar structures and relative homogeneous color distribution area. It raises challenges for superpixel decomposition and template trackers as sometimes RoIs might spawn at the middle line of two different planes and mislead the following estimations. However, the proposed system handles well the single and multiple planar scenes, as displayed in Table. I for the comparison of Absolute Pose Error (APE) with ORB-SLAM [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF], LSD-SLAM [START_REF] Engel | Lsd-slam: Large-scale direct monocular slam[END_REF], Multi-Level Mapping [START_REF] Greene | Multi-level mapping: Real-time dense monocular slam[END_REF], DPPTAM [START_REF]Dense Piecewise Planar Tracking and Mapping from a Monocular Sequence[END_REF] and our previous work: a ransac-based multi-planar method [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF]. We demonstrate in subtables fr nstr loop and fr str far for single and multiple plane scenarios. Our method outperforms all dense and RANSAC methods and reaches a good level of precision against a state-of-the-art monocular sparse keypoint-based SLAM [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF] which only provides a sparse point cloud mapping. One explanation about the precision drop comparing with [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF] in the single planar scene (fr nstr loop) is that without using keypoints and specially designed relocalization module, the system tends to accumulate errors along the tracking and is negatively influenced by motion blur taken during the image acquisition. It also explains other dense methods' ill-performance. Comparison of APE along the sequence fr str far is shown in Fig. 5, our method yields lower level error along the whole trajectory. Generated planar maps are viewed in Fig. 6. Dense planar maps are created by reprojecting tracker regions according to computed planar equations at each frame. It's observed that the map conserves well the perpendicularity without applying any Manhattan assumptions.

The second experiment of the indoor scene is a drone dataset EuRoc [START_REF] Burri | The euroc micro aerial vehicle datasets[END_REF]: a drone recorded grey-level dataset in a test room of a flight sequence. We take a segment (⇠ 400 frames) of the scene v1 01 easy as the environment is not specifically designed for planar SLAM and some texture-less sections and regions fail template trackers. As shown by the results in the third section of Table. I, we also achieve a good level of precision compared to all dense methods and even better than ORB-SLAM [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF] on the median error metric. Fig. 5: Absolute Pose Error (APE) metric for the sequence fr str far of Dataset [START_REF] Sturm | A benchmark for the evaluation of rgb-d slam systems[END_REF] shows that our dense mapping method outperforms all dense and semi-dense methods and reaches a decent precision level compared to ORB-SLAM which only provides a sparse point cloud map. [START_REF] Sturm | A benchmark for the evaluation of rgb-d slam systems[END_REF] generated by our method. Our proposed method is able to estimate camera trajectory and planar map representation simultaneously. The proposed method (TT-SLAM) outperforms DPPTAM [START_REF]Dense Piecewise Planar Tracking and Mapping from a Monocular Sequence[END_REF], LSD-SLAM [START_REF] Engel | Lsd-slam: Large-scale direct monocular slam[END_REF] and Multi-Level Mapping [START_REF] Greene | Multi-level mapping: Real-time dense monocular slam[END_REF], ransac-based pose estimation from multi-homographies [START_REF] Wang | Relative pose estimation and planar reconstruction via superpixel-driven multiple homographies[END_REF]. Despite behind ORB-SLAM [START_REF] Mur-Artal | Orb-slam: A versatile and accurate monocular slam system[END_REF] performance (a keypoint sparse SLAM without planar assumption), our approach provides a dense map representation. (* means lost a portion during tracking,means no reported data, x means initialization failure)

For the outdoor experiment, we test our system on a sequence from a hand-held gray-level dataset [START_REF] Engel | A photometrically calibrated benchmark for monocular visual odometry[END_REF], in a scene of a corridor-like environment. Fig. 7 displays that our system retrieves the corridor's perpendicular planar structure as well as a camera trajectory from the input sequence. Fig. 7: Reconstructing on the dataset [START_REF] Engel | A photometrically calibrated benchmark for monocular visual odometry[END_REF], coordinates represent the camera poses. The multi-planar environment is well conserved without applying Manhattan assumptions.

VIII. CONCLUSION

We proposed a novel way of estimating camera pose and generating dense planar mapping via template trackers. Trackers are created from superpixelized image regions. A mean shift clustering technique is applied to merge similar planes. Finally, a optimization-based refiner is designed to achieve better performance.

Our perspective comprehends three directions: first relying on heterogeneous information such as keypoints, and depth information to improve robustness and tracking quality. The second direction consists in using a deep-learning segmentation and planar region detection rather than superpixels. Third, we aim at exploiting planar maps for relocalization tasks and data association in general SLAM systems.

Fig. 1 :

 1 Fig. 1: We propose a visual SLAM method which tracks and clusters template-based trackers, estimates camera poses, and maps three dimensional multi-planar environments on color image sequences acquired by a monocular camera. Each color represents a different plane.

Fig. 2 :

 2 Fig. a: input image Fig. b: polygonized region Fig. c: tracking and clustering of template trackers Fig. d: multiple planar map

Fig. 3 :

 3 Fig. 3: An example of template tracker generation process. The left image shows the cluster contours of a superpixelized image. Polygonized regions and corresponding template trackers with triangulated RoIs are displayed in the middle and right images respectively.

Fig. 4 :

 4 Fig. 4: Clustered and matched template trackers in middle subfig (same color represents same clustered 3D plane), and correspondent depth is generated on trackers region (right).

Fig. 6 :

 6 Fig.6: 3D multiple (subfig a) and single plane map (subfig b) of the dataset TUM[START_REF] Sturm | A benchmark for the evaluation of rgb-d slam systems[END_REF] generated by our method. Our proposed method is able to estimate camera trajectory and planar map representation simultaneously.

TABLE I :

 I ATE Evaluation:


Mariana H Staia
email: mariana.staia@ucv.ve

A Trocelis

Amel Zairi

M Suarez

Eli Saúl Puchi-Cabrera

Alain Iost

Alex Montagne

Eli Saúl

E S Puchi-Cabrera

ASSESSMENT OF THE MECHANICAL AND TRIBOLOGICAL PERFORMANCE OF A ZrN PVD COATING

Keywords: sliding wear, corrosive solution, nanoindentation, ZrN coatings, PVD _______________________________________________________________________________________________________________________________

published or not. The documents may come

Introduction

ZrN belongs to the nitride coatings family that has demonstrated the possibility of being used in many applications. Among the interesting properties exhibited by zirconium nitrides are their high hardness and wear resistance, low friction coefficient and high corrosion resistance that are of great interest to different industries in applications such as diffusion barriers in integrated circuits, decorative coatings for jewelry, production of cryogenic thermometers, for power reactors in the aerospace industry and in the cutting tools industry, among others. The main properties of these coatings, their use, as well as the processes employed for their production have been recently reviewed by [START_REF] Ningshen | Corrosion Study of ZrN deposited on 304L Stainless Steel[END_REF].

ZrN coatings have also been considered as important candidates for the semiconductor IC packaging molding dies protection. It has been shown that CrN, ZrN, and TiAlCrN produced by closed field unbalanced magnetron sputter ion plating (CFUBMSIP) could substitute the hard chromium coating, considering its excellent anti-adhesion properties [START_REF] Sun | Surface Free Energy of Alloy Nitride Coatings Deposited Using Closed Field Unbalanced Magnetron Sputter Ion Plating[END_REF]. However, additional important issues that arise between the epoxy molding compound and the encapsulation molds are those related to the mold releasing problems and the tribological performance of these coatings (Lina et al., 2006).

Different wear studies at room temperature of ZrN coatings deposited by reactive unbalanced magnetron sputtering against different counterparts such as steel [START_REF] Fragiel | Influence of the N2 partial pressure on the mechanical properties and tribological behavior of zirconium nitride deposited by reactive magnetron sputtering[END_REF][START_REF] Valerini | Adhesion and wear of ZrN films sputtered on tungsten carbide substrates[END_REF], WC-Co [START_REF] Auger | Hardness and tribology measurements on ZrN coatings deposited by reactive sputtering technique[END_REF], alumina (Lopez and Staia, 2008) and silicon nitride balls [START_REF] Singh | Tribological properties of sputter deposited ZrN coatings on titanium modified austenitic stainless steel[END_REF] have been reported in the literature. Nevertheless, the behavior against the steel ball as counterpart, indicates an adequate performance as long as the ZrN coating has a good adhesion to the substrate, achieved either by optimizing the deposition parameters or by using buffer thin films such as Zr between the coating and the substrate in order to improve it [START_REF] Chou | Corrosion resistance of ZrN films on AISI 304 stainless steel substrate[END_REF][START_REF] Jianxin | Wear mechanisms of PVD ZrN coated tools in machining[END_REF]. It is well known that mass transfer from the steel ball to the coating and back will take place as a consequence of the differences between the hardness values of the mating surfaces. In the case of counterparts exhibiting similar or higher hardness than ZrN coatings, an important abrasion process will occur and the wear process will be enhanced due to the presence of debris.

Few tribocorrosion studies have also been carried out on ZrN coated systems. [START_REF] Ferreira | Tribocorrosion behaviour of ZrOxNy thin films for decorative applications[END_REF] investigated the behavior of ZrOxNy and ZrN coatings, of 3.2 to 6.2 m thickness deposited on an AISI M2 steel by magnetron sputtering. Wear testing was carried out under potentiostatic control in an artificial sweat solution. The authors reported that both the amount of material removed and the time needed for the film to be removed from the contact zone depend on the coating thickness. Moreover, it was determined that the dissolution of the substrate governed the degradation of the coated system.

In the present communication, the main results concerning the mechanical and morphological characterization of a ZrN coating produced by a CFUBMSIP process are reported. Buffer films, such as Mo and MoN, were used to improve the coating adhesion to the steel substrate. Wear tests were performed both in air and under the simultaneous action of mechanical wear and a chemical aggressive environment. A correlation of the wear performance of the ZrN coating in both environments with the mechanical, morphological and coated system architecture characteristics is also presented.

Experimental

Materials and coatings deposition

The CFUBMSIP deposition process has been used to produce a ZrN coating of approximately 1.3 m in thickness. The deposition process was carried out industrially at Teer Coatings Ltd., Worcestershire, England. H13 steel substrate samples, of 3 cm diameter, were prepared by using standard metallographic techniques and then cleaned ultrasonically in methanol. Subsequently, they were cleaned in situ prior to the deposition process by means of argon sputter etching. Two metallic targets of Mo and Zr, respectively were employed. The Mo target was used first and allowed the deposition of a very thin metallic Mo layer, aimed at ensuring a proper adhesion between the ZrN coating and the H13 steel substrate. By allowing an Ar-N2 gas mixture inside the reactor, a thin film of 0.2 m of a molybdenum nitride phase was subsequently formed, before ramping in Zr to form the main ZrN layer of 1.1 m.

Coating characterization.

Figs. 1a and 1b illustrate the SEM micrographs of the coating surface and its cross section, respectively after being fractured by impact. Fig. 1b shows the cross section of the fractured sample with a morphology that corresponds to the boundary between zone 1 and the T zone of Thornton's structure zone classification. It is characterized by the presence of dense and not very well defined fibrous crystals, with a small amount of voids between them, typical of PVD processes of relatively low adatom mobilities [START_REF] Thornton | The microstructure of sputter-deposited coatings[END_REF]. The coating structural characterization was carried out by performing X-ray analysis with a Siemens D5000 diffractometer employing Co-Kα radiation (λ=1.78897), a 0.02° scanning step size, 4 second of count time per step and a 2ϴ angle range between 30° and 90°. The XRD pattern is presented in Fig. 2, where the diffraction lines correspond to ZrN (cubic structure, ICDD PDF#35-0753). It could be observed that the ZrN film has a (111) preferred orientation. The small peaks could be attributed to a Mo2N compound, since its thickness is very small (200 nm). In this pattern, both tetragonal and cubic structures were indicated (ICDD PDF#24-0768 and ICDD PDF#25-1366, respectively). However, Jauberteau et al. (2006) have already pointed out that it is not easy to differentiate between -Mo2N and -Mo2N by conventional X-ray diffraction techniques. Therefore, the precise structure of molybdenum nitrides cannot be unambiguously determined. Additionally, characteristics peaks of Fe () and Fe () are also indicated in the pattern.

The surface roughness of the coating was measured by means of optical profilometry, using a Veeco Wyko NT9300 profilometer. The results indicated a smooth appearance with a roughness of 0.03 m. The hardness and elastic modulus of the ZrN coating were determined by means of nanoindentation tests using a MTS XP Nano Indenter under a continuous stiffness measurement mode and equipped with a Berkovich indenter. Prior to indentation, the indenter tip calibration was carried out on fused silica. 25 indentations were conducted on three different samples and the elastic modulus, E, and hardness, H, were recorded continuously versus the indentation depth, h, up to 2000 nm, at a constant indentation rate of 0.05 s -1 . As far as the computation of the hardness and elastic modulus is concern, the coated system is considered to be composed of a 0.2 m layer of molybdenum nitride and a 1.1 m layer of zirconium nitride.

Tribological characterization

The tribological characterization was carried out by means of sliding wear tests, employing a tribometer under a ball-on-disc configuration. The samples were immersed in a special device able to hold the aggressive solution. The wear tests were carried out in the presence of a 3.5 wt% NaCl solution with a pH value = 6.2. In each test, 25 ± 1 ml of the solution was used and the tests were performed by triplicate. For this purpose, a 6 mm diameter alumina ball was used as counterpart, with an applied normal load of 2 N, a sliding distance of 200 m and a constant speed of 5 cm/s.

Prior to each test, the samples were ultrasonically cleaned and dried in air. The worn samples morphologies were evaluated by means of SEM techniques. Optical profilometry was employed to assess the topography of the wear scars and to compute their cross section areas, which are needed to determine the wear volumes.

Results

Mechanical properties

Figures 3(a) and 3(b) illustrate the change both in hardness (H) and elastic modulus (E) with indentation depth (), for the coated system under study. The experimental data include approximately eleven thousand points. In the case of the hardness curve, the data is distributed in a wide scatter band, particularly when   350 nm. In this range of values, H can be considered to be constant, with a magnitude of approximately 25 GPa. As  increases, H decreases with the trend of achieving the substrate hardness, of approximately 6 GPa. As can be observed in Figure 1, all the data points for which  < 100 nm were disregarded, as indicated by the calibration procedure of the Berkovich indenter that was performed with the fused silica standard.

The H versus  curve that was determined experimentally for this bi-layer coating can be readily described by means of the general methodology proposed by Puchi-Cabrera et al. (2015a) for the analysis of the hardness response of multilayer coated systems. Such analytical procedure is founded on the different models previously proposed for the description of the H versus  curve for those coated systems which involve monolayer coatings. Particularly, if the model advanced by [START_REF] Puchi-Cabrera | A new model for the computation of the composite hardness of coated systems[END_REF][START_REF] Puchi-Cabrera | Computation of composite hardness of coated systems[END_REF] for monolayer coatings is extended to the analysis of this bi-layer system, the description of the experimental data would encompass the determination of the intrinsic hardness of both the ZrN and Mo2N layers (HZrN and HMo 2 N, respectively), as well as the coating thickness fractions from which the Mo2N film or substrate would start to contribute to the composite hardness. The different equations that describe the computational instrumentation of this kind of analysis have been reported elsewhere [Puchi-Cabrera et al., 2015a;[START_REF] Staia | Mechanical characterization of a prototype a-C:Cr,Si and its tribological behavior at high temperature[END_REF]. Accordingly, HZrN = 24.2 GPa and HMo 2 N = 18.2, whereas HH13 = 6.1 GPa. It is important to point out that in this indentation analysis, no indentation size effect (ISE) either of the films or steel substrate was considered.

Similar hardness values, varying between 23 to 25.1 GPa, for ZrN coatings deposited by ion plating on 316 stainless steel have been reported by [START_REF] Huang | Effect of film thickness on the structure and properties of nanocrystalline ZrN thin films produced by ion plating[END_REF], when studying the variation of thickness and its effect on their structure and properties. However, changes in the applied bias, in the range of 0 to -120, during the reactively DC magnetron sputtering process employed, had shown a major influence on the hardness, whose value could change from 22 to 33 GPa, as determined by [START_REF] Pilloud | Reactively sputtered zirconium nitride coatings: structural, mechanical,optical and electrical characteristics[END_REF]. On the other hand, the relatively lower hardness value determined for the Mo2N, HMo2N = 18.2, points out the presence of -Mo2N in our system rather than the -Mo2N, as indicated by the hardness value of 12 GPa reported by Jauberteau et al., (2015) for a -Mo2N film. Figure 3(a) illustrates the description provided by the model, together with the mean curve corresponding to the experimental data. It can be clearly observed that the model is able to describe quite accurately the change in hardness with indentation depth by considering the above indicated hardness values, as well as the correct sequence in which both films and substrate contribute to the composite hardness.

The computed values of the corresponding volume fractions of the different layers, which encompass the coated system, indicate that the ZrN film determines entirely the hardness of the coated system up to indentation depths in the range of 315 nm, which explains the constant hardness value observed at the beginning of the curve. Subsequently, from indentation depths greater than 315 nm both the Mo2N and substrate start to contribute almost simultaneously to the composite hardness.

At an indentation depth of approximately 480 nm, the volume fraction of the Mo2N film, which contributes to the composite hardness, overcomes that of the ZrN film, and reaches its maximum, of about 0.53, at an indentation depth of 630 nm. From an indentation depth of approximately 760 nm, the substrate becomes the predominant constituent of the coated system, contributing to the composite hardness. At indentation depths in the range of approximately 2000 nm, the composite hardness is basically determined by the substrate (fSubst. = 0.95) and to a much lesser extent by the Mo2N film (fZrN = 0.05).

Concerning the change in the elastic modulus of the coated system with indentation depth, Figure 3(b) also illustrates that the experimental results are also encompassed in a wide scatter band. Therefore, together with the experimental data points, the mean experimental curve has also been included in the Figure . For analyzing the change in this elastic property with indentation depth, only the experimental data points determined at indentation depths greater than 30 nm were considered. The points determined at smaller depths were disregarded in view of the results of the calibration procedure conducted with the fused silica standard for this property. Such a procedure indicated that the elastic modulus of the silica standard could be reproduced above indentation depths greater than approximately 7-10 nm.

As shown in Figure 3(b), the mean elastic modulus decreases continuously with indentation depth from an initial value of 420 GPa, with a clear trend of achieving the elastic modulus of the substrate, of 210 GPa, at large indentation depths. By assuming as before that the coated system is composed of two layers, it is possible to model the change in the elastic modulus of the system with indentation depth by means of the extended version of the approach earlier proposed by [START_REF] Doerner | A method for interpreting the data from depth-sensing indentation instruments[END_REF], as it has been suggested by Puchi-Cabrera et al., (2015b). Details of the computational procedure employed for the description of the changes in the elastic modulus of a multilayer coated system with indentation depth and the identification of the individual elastic modulus of each film can be found elsewhere (Puchi-Cabrera et al., 2015b;Staia el al., 2016).

The results of this analysis indicate that the ZrN film has an elastic modulus of 444 GPa, which represents the only contribution to the global modulus of the system in the indentation range of about 30-46 nm. At higher indentation depths, the Mo2N with an elastic modulus of 354 GPa and the substrate start their contribution to the composite modulus. The maximum contribution of the Mo2N occurs at indentation depths in the range of 53 nm, at which fMo 2 N = 0.74. At indentation depths somewhat greater than the latter value and up to the maximum indentation depths achieved, the global modulus is determined mainly by the steel substrate. Figure 3(b) clearly illustrates that the modified Doerner and Nix model is able to reproduce quite accurately the trend shown by the mean experimental curve. Therefore, it represents a valuable tool for determining accurate and reliable values of the elastic modulus of the different films, which compose the coated system. It is interesting to point out that a similar value of 460 GPa has been determined by [START_REF] Tӧrok | Young´s modulus of TiN[END_REF], for the elastic modulus of sputtered ZrN coatings, by means of flexural resonance frequency techniques, which was subsequently corroborated by Perry (1990), by means of X-ray residual stress measurements.

It is well known that in order to predict the behavior of the coated system under spherical indentation loading, the change in the von Mises stress from the surface of the coating system, under such loading condition, should also be accurately predicted. However, this is only possible if the change in the global elastic modulus with indentation depth is properly described by means of a sound computational procedure such as that employed in the present work.

3.1.1.Computation of the elastic contact stresses during spherical indentation

Figure 4 illustrates the predicted change in the von Mises stress with distance measured from the coating surface. In this case, it has been assumed that the coated system is subjected to spherical indentation with an applied load, F = 2 N. The determination of this plot is based on the results presented in Figure 3(b), which describes the change in the elastic modulus of the coated system as a function of indentation depth, as derived from the extended form of the Doerner and Nix model. However, the information concerning the value of the Poisson ratio for the different materials, which encompass the coated system, is also required. Thus, Table 1 summarizes the numerical data employed for conducting the required computations. *) It has been assumed that the tensile strength of the coating is equal to 1/3 of its absolute hardness.

, GPa ------------- --------------- 210 416 , MPa 8067 (*) 4833 (*) 1650 (3) --------------- (
(1) Perry, A.J, (1990) Thus, for a given depth, , measured from the surface of the coated system and taking into account the relationship between such a depth and the contact radius, a, the elastic modulus of the coating is interpolated from the predicted curve determined by means of the extended Doerner and Nix model. Subsequently, taking into consideration the elastic properties of the Al2O3 ball, the value of the reduced elastic modulus, Er(a, Eball, ball), can be determined. In this way, it is possible to solve the non-linear equation which relates a, Er(a, Eball, ball), F and the ball diameter, d, in order to compute the correct value of a. Concerning the computation of the Poisson's ratio for a given contact radius, which is required in order to determine both the principal stresses and the von Mises stress, a Heaviside step function has been employed.

The change in the von Mises stress with distance from the surface is carried out by employing the Hertzian equations, which correspond to the elastic contact between a spherical indenter and a multi-layer coating. Accordingly, the principal stresses at a given depth are determined as a function of a, the maximum pressure, Pmax, and the corresponding Poisson ratio value. In turn, Pmax depends on the load applied, F, and a.

However, in order to carry out this computation it is of utmost importance to take into consideration the strain compatibility at the ZrN/Mo2N and Mo2N/Substrate interfaces. For this purpose, as a first approximation, it can be assumed that the principal strains at each interface, computed as a function of the von Mises stress and the elastic constants of the corresponding layer material, remain constant across each interface. Details of the equations employed and the computational procedure that has been followed have already been reported elsewhere [START_REF] Staia | Mechanical characterization of a prototype a-C:Cr,Si and its tribological behavior at high temperature[END_REF].

Thus, when a normal load of 2 N is applied to this coated system, the contact radius is found to be of approximately 28.5 m and a maximum pressure of approximately 1180 MPa is attained at a depth of about 270 nm. However, the maximum von Mises stress is of approximately 715 MPa and it is located at a depth of 14000 nm, that is to say, well into the substrate. Since the yield strength of the H13 substrate is of approximately 1650 MPa, it will not undergo plastic deformation. Thus, the system is expected to behave elastically and therefore, the integrity of the bi-layer coating will be preserved.

Tribological performance

Fig. 5 shows the evolution of the friction coefficient for the coated system and for the steel substrate, respectively. This variation was represented only for 100 m of sliding distance although the test was run for 200 m, since after 80 m of the sliding distance, the value of the friction coefficient of the ZrN coated system reached the same value corresponding to the steel substrate.

It is observed that for the steel substrate, an increase in the friction coefficient value to 0.3 at the beginning of the test takes place, typical for the running-in period corresponding to the contact between the alumina ball and the sample. A continuous decrease in its value, due to the wash away process of the wear debris from the contact, takes place until the end of the test, reaching a steady state value of 0.14.

However, for the ZrN coated system it is observed that the friction coefficient increases at the beginning of the test to a value of 0.17 and, subsequently, drops to a constant value of 0.12, which is maintained until 30 m of sliding distance. After this value, the friction coefficient starts to increase as a consequence of the film mechanical damage produced due to the presence of the corrosive solution. It is worth mentioning that, due to the coating morphological characteristics and its small thickness, the penetration of the corrosive solution takes place, which contributes to undermining the coating itself due to a crevice corrosion phenomenon. The latter promotes the substrate dissolution that further weakens the coating under the normal load used during the wear test, due to the reduced load-bearing capacity of the substrate.

3.5% NaCl solution

ZrN coated system

Steel substrate 30 m Fig. 5. Friction coefficient variation with the sliding distance for the coated and uncoated H13 steel substrate tested in 3.5 wt% NaCl solution Fig. 6a andb illustrate the 3D profiles of the wear track after testing in the 3.5 wt% NaCl solution, whereas Fig. 6c shows the 3D image profile of the alumina counterpart. The SEM micrograph corresponding to the morphology of the worn ZrN coating is presented in Fig. 6d, indicating that the coating experienced a severe abrasive wear mechanism, due of the combined action of the ball and the hard "debris" products resulting from the coating damage. In some places, however, the existence of the coating it is still observed, a fact that is detected with greater clarity from the EDS line concentration profile performed on this wear track (see Fig. 6 d). In order to put in evidence the synergistic effect of wear and corrosion, additional wear tests were carried out in air for shorter sliding distances, in order to check the integrity of the bi-layer coating architecture under the contact between the coating and the ball for the same loading conditions, but without the presence of the corrosive solution. These sliding distances were chosen in such a way as to allow the comparison with those distances that corresponded to the coating failure during the wear tests in the corrosive environment.

The results are presented in Fig. 7 and indicate an excellent behavior for the coating at 30 m sliding distance (test A), which corroborated that the integrity of the bi-layer coating was preserved, as predicted in section 3.1.1. As the sliding distance is increased, the debris produced as a consequence of the wear experienced by both counterparts will be present in the contact, contributing to a considerable increase in the friction coefficient value, from 0.2 (test A) to approximately 0.65 (test B). Nevertheless, under these conditions, the coated system still maintains its integrity, since the depth achieved through the coating thickness is not higher than 0.6 m, which is nearly half of its initial thickness. These latter experiments performed only in air, constituted a clear evidence of the deleterious effect of the presence of the corrosive solution, which promotes the substrate dissolution that further weakens the coating under the normal load used during the wear tests.

The SEM micrographs of the wear tracks for the 30 m and 63 m sliding distances, respectively, as well as the 3D profiles of both sample and counterpart for each condition are presented in Fig. 8. As can be observed, a small amount of abrasive wear occurred for the sample and counterpart tested for 30 m (see Fig. 2D surface profiles are shown in Fig. 9 for all the tests, showing in each case a typical example of the cross section profile of the wear track, where both the experimental and computational description of the profile are represented. In order to determine the mean cross-sectional track area, six individual wear profiles were taken into account. The method of calculation is described elsewhere [START_REF] Staia | Mechanical characterization of a prototype a-C:Cr,Si and its tribological behavior at high temperature[END_REF]. The wear volume was obtained by multiplying the cross-sectional wear track area by the length of the wear track.

The mean worn volume for the immersed coated sample was of 1.5 x10 -2 mm 3 ± 0.04 x 10 -2 mm 3 Correspondingly, the wear volume for test A was of 0.25 x 10 -4 mm 3 ± 0.01 x 10 -2 mm 3 and 6 x 10 -4 mm 3 ± 0.05 x 10 -2 mm 3 for test B, both carried out without the presence of the corrosive solution. A specific wear rate, k, could only be computed for the samples tested in air from the ratio between wear volume and the applied load per unit of sliding distance. Values of k of 0.4 x 10 -15 m 3 /N m and 5 x 10 -15 m 3 /N m, respectively, were obtained indicating an increase of one order of magnitude when the sliding distance is doubled, which shows the effect of the presence of the hard debris in the contact. For comparison, the cross sectional area of the steel substrate tested in the same conditions as test B is also presented, indicating a value of nearly 418 m 2 that corresponds to 0.85 x 10 -14 m 3 /N m, that is to say 17 times greater than that corresponding to the coated system. As indicated above, in the present research, the wear tests were carried out by immersing the samples in a corrosive solution. However, [START_REF] Ferreira | Tribocorrosion behaviour of ZrOxNy thin films for decorative applications[END_REF] have also reported a similar mechanism during wear testing of sputtered ZrOxNy coatings deposited on a M2 steel substrate, carried out under potentiostatic control in an aggressive solution, such as artificial sweat. As in the present study (see Fig. 5), the value of the friction coefficient of the tested system, measured at the end of the tests, was controlled by the friction coefficient between alumina ball and M2 steel, due to coating damage. These results clearly indicate that, in order to predict the synergistic effect between the two phenomena, simple tests such as those employed in the present work could be conducted, avoiding the need of using more complex experimental setups.

Conclusions

In the present paper, the sliding wear performance of a ZrN coating deposited by means of CFUBMSIP has been evaluated in a 3.5 wt% NaCl solution. It has been determined that under the test conditions employed, the coating experienced a severe abrasive wear mechanism, due of the combined action between the alumina ball, the hard "debris" formed as a product of the mechanical damage of the film and to a phenomenon of crevice corrosion. The latter gave rise to the substrate dissolution that further weakened the coating under the normal load used during the wear test, due to the reduced load-bearing capacity of the substrate. An important aspect, which can adversely affect the coating wear performance in the corrosive medium, was that related to its low thickness, which allowed the rapid penetration of the corrosive medium through the defects up to the coatingsubstrate interface. Nevertheless, it has been shown that the coated system is able to increase the wear resistance of the substrate by more than one order of magnitude if the wear tests are carried out in air under the same conditions. The hardness and elastic modulus of the bi-layer ZrN/Mo2N coated system were determined by means of nanoindentation techniques and modeled following an analytical approach previously proposed for multilayers coatings. The results of this analysis indicate that for the ZrN coating, HZrN = 24.2 GPa and EZrN = 444 GPa, whereas for the Mo2N coating, HMo 2 N = 18.2E and EMo 2 N = 354 GPa, respectively. The analysis of the elastic stresses under the spherical contact between the ball and the coated system indicates that it is expected to behave elastically and, therefore, that the integrity of the bi-layer coating will be preserved.

Fig. 1 .

 1 Fig.1. ZrN coating SEM micrographs: a. coating surface morphology; b. coating fractured cross section (22000X)

Fig. 2 .

 2 Fig.2. XRD pattern of the ZrN coating

Fig. 3 .

 3 Fig. 3. (a) Change in the hardness of the coated system with indentation depth; (b) Change in the elastic modulus of the coated system with indentation depth

Fig. 4 .

 4 Fig. 4. Predicted change in the von Mises stress with the distance measured from the coating surface.

Fig

  Fig. 6. (a) 3D profile of the wear track after testing in 3.5 wt% NaCl solution; (b) detailed 3D profile of the track; (c) 3D image profile of the alumina counterpart; (d) detailed SEM micrograph of the wear track; (d) EDS line concentration profile of the wear track from (d).

  8(e)). However, after 63 m, considerable amount of wear debris were deposited on top of the alumina ball (Fig (f).

Fig. 7 .Fig. 8 .

 78 Fig.7. Friction coefficient variation with the sliding distance for the coated system tested in air. The wear test was stopped for curve: test Aat 30m; test B-at 63 m

Fig. 9 .

 9 Fig.9. Typical cross section profiles of the wear track corresponding to: (a) wear track of the coated system after test in 3.5 wt% NaCl solution for 200 m; (b) wear track of the coated system after the test A carried out in air for 30 m; (c) wear track of the coated after the test B carried out in air for 60 m; (d) wear track of the substrate after the test carried in air for 60 m

Table 1 .

 1 Mechanical properties of the different materials, which constitute the coated system, employed in the computation of elastic stresses under spherical indentation loading.

		ZrN	Mo2N	AISI H13 steel	Al2O3 ball
		0.186 (1)	0.3 (2)	0.33	0.231
	E

Acknowledgements

Professor M. Staia acknowledges the financial support of the Scientific and Humanistic Development Council of the Universidad Central de Venezuela (CDCH-UCV). Professor Puchi-Cabrera acknowledges the financial support of the program Campus France and the infrastructure provided by the Laboratory LAMIH at the University of Valenciennes, France. The authors are also grateful to Teer Coatings (England) for providing the coated samples.