Olivier Chapuis
email: chapuis@lri.frlabrune@media.mit.edu

Jean-Baptiste Labrune

Emmanuel Pietriga
email: emmanuel.pietriga@inria.fr

DynaSpot: Speed-Dependent Area Cursor

Keywords: ACM Classification H.5.2 Information Systems: Information Interfaces and Presentation -User Interfaces, Input Devices and Strategies Area cursor, Bubble cursor, DynaSpot, Fitts' Law

We present DynaSpot, a new technique for acquiring targets based on the area cursor. DynaSpot couples the cursor's activation area with its speed, behaving like a point cursor at low speed or when motionless. This technique minimizes visual distraction and allows pointing anywhere in empty space without requiring an explicit mode switch, thus enabling users to perform common interactions such as region selections seamlessly. The results of our controlled experiments show that the performance of DynaSpot can be modeled by Fitts' law, and that DynaSpot significantly outperforms the point cursor and achieves, in most conditions, the same level of performance as one of the most promising techniques to date, the Bubble cursor.

INTRODUCTION

The increase in both resolution and size of computer displays requires users of desktop interfaces based on the ubiquitous WIMP paradigm to make highly precise pointing movements to acquire small interface components over possibly long distances when using a conventional point cursor. Several techniques have been proposed to make this fundamental task easier. Many have been shown to perform better than the point cursor in experimental settings that were consisting of isolated targets on fairly sparse desktops [START_REF] Asano | Predictive interaction using the delphian desktop[END_REF][START_REF] Baudisch | Drag-andpop and drag-and-pick: Techniques for accessing remote screen content on touch and pen-operated systems[END_REF][START_REF] Blanch | Semantic pointing: improving target acquisition with controldisplay ratio adaptation[END_REF][START_REF] Guiard | Object pointing: a complement to bitmap pointing in GUIs[END_REF]. However, these techniques are very sensitive to the layout and density of interface components, and difficulties arise when selecting one target among multiple objects that are spatially close together. As noted by Baudisch et al. [START_REF] Baudisch | Starburst: a target expansion algorithm for non-uniform target distributions[END_REF], non-uniform target distributions with clusters of small targets are commonplace in GUIs. In such configurations, these techniques do not provide a significant advantage and some can actually degrade performance.

Other promising techniques have been proposed recently that work better in a wider range of configurations, including many variations on expanding targets [START_REF] Cockburn | Human on-line response to visual and motor target expansion[END_REF][START_REF] Cockburn | Improving the acquisition of small targets[END_REF][START_REF] Mcguffin | Acquisition of expanding targets[END_REF][START_REF] Mcguffin | Fitts' law and expanding targets: Experimental studies and designs for user interfaces[END_REF], the Ninja cursor [START_REF] Kobayashi | Ninja cursors: using multiple cursors to assist target acquisition on large screens[END_REF] and Starburst [START_REF] Baudisch | Starburst: a target expansion algorithm for non-uniform target distributions[END_REF]. One of the most promising technique, the Bubble cursor [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF], is a variation on the Area cursor [START_REF] Kabbash | The "prince" technique: Fitts' law and selection using area cursors[END_REF][START_REF] Worden | Making computers easier for older adults to use: area cursors and sticky icons[END_REF] that dynamically adapts its activation area to encompass the closest object only. This is achieved by expanding the boundaries of each target based on a Voronoi tessellation that fills the empty space surrounding each potential target thus maximizing their effective size. While this optimizes pointing performance, problems arise when considering interaction beyond the acquisition of a single interface component. First, as with several of the abovementioned techniques, selecting a position in the "empty" space between targets requires a mode switch. Yet empty space selection is crucial to many common interactions, e.g., to select groups of objects. The mode switch solution results in "a slightly less than seamless interaction style" [START_REF] Balakrishnan | Beating" Fitts' law: virtual enhancements for pointing facilitation[END_REF] for these essential object manipulation features [START_REF] Kobayashi | Ninja cursors: using multiple cursors to assist target acquisition on large screens[END_REF]. Second, rapid and large changes of the bubble size in non-uniform target distributions may distract the user and hinder user acceptance [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF][START_REF] Laukkanen | The cone and the lazy bubble: two efficient alternatives between the point cursor and the bubble cursor[END_REF][START_REF] Hertzum | Input techniques that dynamically change their cursor activation area: A comparison of bubble and cell cursors[END_REF], a crucial factor [START_REF] Balakrishnan | Beating" Fitts' law: virtual enhancements for pointing facilitation[END_REF] that is sometimes overlooked.

In this paper, we present DynaSpot, a new type of area cursor that couples the cursor's activation area with its speed, as illustrated in Figure 1. The activation area grows as a function of speed up to a maximum size, typically set to a few dozen pixels, thus minimizing visual distraction. At low speed and when motionless, DynaSpot behaves as a regular point cursor, making all conventional point cursor interactions, including empty space selection, possible without the need for an explicit mode switch. After a review of related work, we discuss the design and implementation of DynaSpot, and report the results of two controlled experiments. Results show that DynaSpot significantly outperforms the point cursor and achieves levels of pointing performance similar to the Bubble cursor in most layout configurations, including densely populated scenes. We then show that its performance can be modeled with Fitts' law. We conclude with a discussion of our findings and directions for future work.

RELATED WORK

Fitts' law is the fundamental tool used to study pointing in human-computer interfaces [START_REF] Mackenzie | Fitts' law as a research and design tool in human-computer interaction[END_REF][START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF]. It makes it possible to predict movement time M T with the following equation:

M T = a + b × log 2 ( A W + 1)
where A is the distance to the target (amplitude of movement), W the width of the target, and a, b are two coefficients determined empirically, depending on factors such as input device and population of users. Techniques developed to facilitate pointing in virtual worlds try to decrease movement time either by reducing A, increasing W , or a combination of both. We direct interested readers to a survey by Balakrishnan [START_REF] Balakrishnan | Beating" Fitts' law: virtual enhancements for pointing facilitation[END_REF] and an overview by Grossman et al. [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF] that follow this categorization to review existing techniques. In the following, we consider existing techniques from a slightly different perspective, considering not only performance but compatibility with conventional cursor interactions beyond single target acquisition, and user acceptance.

Sticky icons [START_REF] Worden | Making computers easier for older adults to use: area cursors and sticky icons[END_REF] and Semantic pointing [START_REF] Blanch | Semantic pointing: improving target acquisition with controldisplay ratio adaptation[END_REF] dynamically adapt the control-display ratio, slowing down the cursor as it approaches a potential target. These techniques support conventional point cursor interactions. They are, however, very sensitive to the layout and density of potential targets; while they work well in sparsely populated workspaces, intervening distractors on the path to the actual intended target in denser workspaces slow down cursor movements, possibly degrading performance compared to a regular point cursor. Cockburn and Firth [7] propose to enable the control-display adaptation on one axis only depending on the widget's orientation, thus partially solving the problem for some types of widgets such as scrollbars.

Drag-and-pop [START_REF] Baudisch | Drag-andpop and drag-and-pick: Techniques for accessing remote screen content on touch and pen-operated systems[END_REF] reduces amplitude of movement (A) when dragging an object by temporarily bringing potential targets, closer to the cursor. As such, the technique efficiently solves one particular type of pointing-based interaction, but is not a general desktop pointing technique. Object pointing [START_REF] Guiard | Object pointing: a complement to bitmap pointing in GUIs[END_REF] takes a radical approach, ignoring the empty space between targets by making the cursor jump from one object to the nearest one in the direction of movement, thus considerably reducing A. The Delphian desktop [START_REF] Asano | Predictive interaction using the delphian desktop[END_REF] follows the same principle, taking into account peak velocity to determine the goal target, allowing to jump over potential distractors. Both techniques are very sensitive to the layout and density of objects, which can have a strong impact on the accuracy of the goal target prediction method. Lank et al., describe an enhanced endpoint prediction method [START_REF] Lank | Endpoint prediction using motion kinematics[END_REF] achieving 42% accuracy and an additional 39% of predictions falling on an adjacent target, with one third of gesture time remaining. Still, wrong predictions can be frustrating, and the behavior of the cursor, jumping from object to object, can be annoying. By skipping empty space, these techniques do not allow the user to perform some useful point cursor interactions, such as region selection, without an explicit mode switch. Kobayashi and Igarashi propose another promising way to reduce the amplitude of movement (A) by having multiple cursor instances all synchronized with the same input device: by distributing the cursors over the screen, Ninja cursor [START_REF] Kobayashi | Ninja cursors: using multiple cursors to assist target acquisition on large screens[END_REF] reduces the average distance to any given target using interactive, seamless disambiguation methods to activate the appropriate cursor. General point cursor interactions that require clicking in empty space are however not possible without mode switching, except for a restricted form of lasso selection.

Several techniques focus on increasing target width (W ).

Techniques based on lenses coupled with the cursor magnify objects but usually operate in the original, unmagnified, motor space, thus providing no actual advantage in terms of pointing facilitation [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF][START_REF] Pietriga | Sigma lenses: focus-context transitions combining space, time and translucence[END_REF]. Ramos et al.'s Pointing lenses [START_REF] Ramos | Pointing lenses: facilitating stylus input through visual-and motor-space magnification[END_REF] are an exception, increasing target size in both visual and motor space for the acquisition of small targets with a stylus. Another solution consists in expanding targets dynamically when a point cursor approaches them. McGuffin and Balakrishnan [START_REF] Mcguffin | Acquisition of expanding targets[END_REF] have found that users can still benefit from expansions that occur as late as after 90% of the movement has been completed. They were further studied in [START_REF] Mcguffin | Fitts' law and expanding targets: Experimental studies and designs for user interfaces[END_REF], and experiments by Cockburn and Brock suggest that visual expansion plays a more important role than motor expansion [START_REF] Cockburn | Human on-line response to visual and motor target expansion[END_REF]. They also note that "enlarged motor-spaces actually make the targets appear smaller than they really are", as empty space around objects is actually empty in visual space only, not in motor space, meaning that it cannot be used for interactions such as region selection.

Fitts' law can accurately model pointing to thin targets using area cursors with a simple modification to the equation: instead of representing the target width, the term W represents the cursor width [START_REF] Kabbash | The "prince" technique: Fitts' law and selection using area cursors[END_REF]. This implies that cursors with larger activation areas make pointing easier, but such larger areas are more likely to encompass several objects, thus creating ambiguities. These can be resolved by using a secondary point cursor [START_REF] Worden | Making computers easier for older adults to use: area cursors and sticky icons[END_REF] or by interactively adjusting the cursor area on multi-point touchpads [START_REF] Moscovich | Multi-finger cursor techniques[END_REF]. The Bubble cursor [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF] improves upon the area cursor by partitioning empty space so as to maximize the activation area of each target. Starburst [START_REF] Baudisch | Starburst: a target expansion algorithm for non-uniform target distributions[END_REF] relies on a different partitioning of space, better adapted to non-uniform target distributions. As mentioned earlier, this optimizes pointing performance, but prevents point cursor interactions that require clicking in empty space. The Bubble cursor's growing/shrinking area has also been reported to cause visual distraction in some situations [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF][START_REF] Laukkanen | The cone and the lazy bubble: two efficient alternatives between the point cursor and the bubble cursor[END_REF][START_REF] Hertzum | Input techniques that dynamically change their cursor activation area: A comparison of bubble and cell cursors[END_REF]. Several variations on the technique have been designed [START_REF] Laukkanen | The cone and the lazy bubble: two efficient alternatives between the point cursor and the bubble cursor[END_REF][START_REF] Hertzum | Input techniques that dynamically change their cursor activation area: A comparison of bubble and cell cursors[END_REF], but have had limited success both in terms of performance and user acceptance. The lazy bubble [START_REF] Laukkanen | The cone and the lazy bubble: two efficient alternatives between the point cursor and the bubble cursor[END_REF] makes it possible to point in some areas of empty space, but these are severely limited and difficult to identify, making interactions such as region selection impractical.

DYNASPOT

In his survey of pointing facilitation techniques [START_REF] Balakrishnan | Beating" Fitts' law: virtual enhancements for pointing facilitation[END_REF], Balakrishnan identifies the final acceptability of a technique by end-users as a critical measure, seen as a complement to quantitative performance measures such as selection times and error rates. The visual distraction caused by some techniques and the mode switches required by earlier-mentioned techniques hinder their acceptance for many types of applications and environments. DynaSpot has been designed to facilitate pointing while taking this more qualitative measure into account. It was not designed to perform better than all other techniques under all conditions, but to strike a balance between performance, end-user acceptance and implementation in a realistic context.

DynaSpot builds upon area cursors. It uses the dynamic characteristics of the pointer to adapt the size of the cursor's activation area and facilitate difficult pointing tasks while behaving as a conventional point cursor when appropriate, without the need for an explicit mode switch. DynaSpot takes inspiration from other techniques that have successfully made use of the cursor's dynamic characteristics, such as Speed-Dependent Automatic Zooming [START_REF] Igarashi | Speed-dependent automatic zooming for browsing large documents[END_REF], Sigma Lenses [START_REF] Pietriga | Sigma lenses: focus-context transitions combining space, time and translucence[END_REF] and the Speed-coupled flattening lens [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF].

As shown in Figure 2, the size of the activation area (which we term spot from now on) starts to increase as a function of cursor speed past a given threshold, and up to a maximal size SPOTWIDTH. When the cursor comes to a full stop, reduction of the spot starts after a certain duration LAG, and takes REDUCTIME to complete. As with regular area cursors, the spot is made translucent so as to avoid obscuring screen information relevant to the task [START_REF] Worden | Making computers easier for older adults to use: area cursors and sticky icons[END_REF]. A target can be selected as soon as the spot overlaps it. While early area cursor designs [START_REF] Kabbash | The "prince" technique: Fitts' law and selection using area cursors[END_REF][START_REF] Worden | Making computers easier for older adults to use: area cursors and sticky icons[END_REF] used a square shape, Dy-naSpot's activation area takes the shape of a circle, as does Bubble cursor's, so as to ensure that the nearest target is captured first. Still, as opposed to the latter technique, there can be situations where the spot overlaps more than one potential target, creating ambiguities regarding the one to select.

To resolve such ambiguities, DynaSpot always selects the target closest to the cursor center (see Figure 1-b). This implies that the system should provide feedback about which target is currently selected (if any), as is the case for Bubble cursor. If the spot does not intersect any potential target, then the background (or "empty space") is selected, no matter the current spot width, allowing the user to perform any action initiated by a button press in empty space, such as a region selection (see Figure 1-c).

According to Fitts' law, DynaSpot should facilitate pointing because the potential effective width of a target can be larger than its actual width. For instance, if we consider an isolated circular target of width W and a spot width of SW at the time of actual target selection (i.e., when clicking), then the potential effective width is EW = W + SW . Thus, when the user clicks on the target before the spot starts shrinking (before the end of LAG in Figure 2), the effective width of the target is EW = W + SPOTWIDTH, as illustrated in Figure 3-a. If we consider a target surrounded by other targets with empty space between them of width IS, as in Figure 3-b, then the potential effective width depends on the spot width and what we term the interspace between targets, IS. If IS ≤ SPOTWIDTH, then the potential effective width is EW = W + IS. The optimal SPOTWIDTH will depend on a number of factors: interface type, display resolution, input device, but also on each user. In a typical desktop environment, a SPOTWIDTH between 16 and 32 pixels represents a good compromise: it is large enough to facilitate the acquisition of small targets, yet small enough to prevent size variations from causing too much visual distraction.

Speed-dependent Behavior

Figure 2 gives a general idea of the speed coupling between cursor speed and spot width. The details of this coupling play a fundamental role in the overall usability of the technique, and are described in this section. The behavior rules are as follows:

• when the cursor is moved fast enough (beyond a threshold speed S ≥ MINSPEED pixel.s -1 ), the width of the spot is increased, provided that it has not yet reached its maximal value SPOTWIDTH; • when the cursor comes to a full stop and does not move for a period of time equal to LAG, the spot shrinks to a point (1 pixel) over a period of REDUCTIME, provided the user does not move it again, in which case it would grow again; • for slow movements below the speed threshold, the spot width remains constant.

Threshold speed MINSPEED allows the user to perform small, precise pointing movements using a conventional point cursor, without being distracted by a growing spot. When the cursor is moved faster, beyond this threshold, the spot grows, facilitating distant target acquisition. We have found 100 pixel.s -1 to be a reasonable value for MINSPEED.

The transitions from point cursor to area cursor and conversely can be achieved in various ways. We tested several possibilities through trial and error, and made the following observations. The spot should grow quickly once MINSPEED has been reached, but the growth profile does not seem to play an important role. We found that an exponential growth (up to SPOTWIDTH) by a factor of 1.2 at each input event works well.

The reduction transition, controlled by LAG and REDUCTIME (see Figure 2), is more complex because it has a direct impact on the potential effective width at the time of target selection. Higher values for both parameters should make the task easier. However, too high values imply that the user will potentially have to wait longer before she can perform interactions initiated by an implicit selection in empty space.

In addition, the reduction profile applied during REDUCTIME also plays a role. We informally tested three methods to perform this reduction, as illustrated in Figure 4: (i) an "exponential" one where the spot width is reduced by a given percentage at each step;

(ii) a "linear" one where the spot width is reduced by a given constant at each step, and (iii) a "co-exponential" one that mirrors the first method. We found that the exponential reduction yields more target acquisition errors, probably because of the abrupt transition after the LAG period, due to the fast reduction of the spot. The co-exponential method starts reducing the spot at a lower pace, providing a smoother transition than the linear and exponential methods.

PRELIMINARY STUDY: LAG AND REDUCTION TIME

Before comparing DynaSpot with other pointing techniques, we ran a preliminary experiment in which we formally evaluated different values of LAG and REDUCTIME for the co-exponential transition in order to fine-tune the technique.

Apparatus

We used a 3.2 GHz Pentium4 PC running X Window under Linux, equipped with an NVidia Quadro FX 1500 graphics card, a 1600 x 1200 LCD monitor (21"), and a standard optical mouse (400 dpi) with the default X Window acceleration function. Our program was written in Java using the OpenGL pipeline for graphics rendering. We carefully checked the refresh rate (50 fps), ensuring that timers were matching the lag and reduction set for each condition.

Participants

Eight unpaid adult volunteers (7 male, 1 female), from 22 to 41 year-old (average 26.6, median 24), all right-handed, experienced mouse users, served in the experiment.

Procedure and Design

The task was a simple reciprocal pointing task. The two targets were represented as circles 8 pixels in diameter, painted with a green fill color and outlined in black. They were centered horizontally, with a distance of 512 pixels between them, and were each surrounded by four distractors of the same size, painted with a white fill color and outlined in black. These four distractors were laid out so that the interspace IS between a distractor and the target would always match the SPOTWIDTH set for the current trial, as illustrated in Figure 8-b. We focused on small targets in this preliminary study as DynaSpot is expected to be most useful in this type of configuration. The object captured by the cursor (distractor or actual target, if any) was filled with a red color. Each target had to actually be selected before proceeding to the next: clicks outside the current target were counted as errors but did not end the task.

Our experiment was a 2 × 3 × 3 within-participant design.

Each participant had to perform several trials using two spot widths: SPOTWIDTH ∈ {16, 32} with three durations for both lag and reduction time: LAG ∈ {60ms, 100ms, 140ms} and REDUCTIME ∈ {100ms, 180ms, 260ms}.

We grouped trials into two blocks, one for each spot width. Four participants started with the small DynaSpot (16 pixels) while the four others started with the larger one (32 pixels). Within a block, trials were grouped by LAG × REDUCTIME condition presented in a pseudo-random order, each subblock containing three series of 16 reciprocal pointing tasks. The first series was used for training, allowing participants to adapt to the new parameters before we measured their performance. They were then instructed to be as accurate and as fast as possible. The 16 pointing tasks of a series had to be performed in a row, but participants were allowed to rest between trials. The first targeting task of each trial was ignored. A total of 4,320 actual pointing tasks were thus taken into account in the analysis (240 measures for each SPOTWIDTH × LAG × REDUCTIME condition). The experiment started with a 3 minute training session where the experimenter explained DynaSpot's behavior and how to operate it to the participant. The experiment lasted approximately 20 minutes.

Results

Repeated measures analysis of variance reveals a significant simple effect on movement time for SPOTWIDTH (F 1,7 = 97.0, p < 0.0001), LAG (F 2,14 = 11.5, p = 0.0011) and REDUCTIME (F 2,14 = 7.5, p = 0.006). The only significant interaction is for LAG × REDUCTIME (F 4,28 = 3.3, p = 0.0238).

Mean movement time is 884 ms for SPOTWIDTH = 16 and 760 ms for SPOTWIDTH = 32. The LAG × REDUCTIME effect can be observed on Figure 5 (left): LAG seems to have an effect for REDUCTIME equal to 100 and 180 ms but not for REDUCTIME = 260 ms. This is confirmed by post-hoc tests, which show a significant difference in mean between all LAG values for REDUCTIME = 100, between LAG 60 and 100 for REDUCTIME = 180, but no significant difference for REDUC-TIME = 260. The overall error rate is 4.5%. Repeated measures analysis of variance reveals no effect on error rate for SPOTWIDTH (F 1,7 = 0.4, p = 0.522), but a significant effect for LAG (F 2,14 = 10.8, p = 0.0014) and REDUCTIME (F 2,14 = 17.7, p < 0.0001). As for movement time, we observe a significant interaction for LAG × REDUCTIME only (F 4,28 = 3.4, p = 0.0227), as illustrated in Figure 5 (right).

These results show that for a long-enough REDUCTIME, LAG can be set to any value within the considered range. For shorter REDUCTIMEs, the duration of LAG has a significant effect on both movement time and error rate, and has to be chosen carefully. Overall, the fastest and least error prone condition evaluated was LAG = 140 ms and REDUCTIME = 180 ms. For our implementation of DynaSpot, we did not want the full reduction phase to last longer than 300 ms, as longer delays can be frustrating. We thus used the following values: LAG = 120 ms and REDUCTIME = 180 ms.

MAIN EXPERIMENT: DYNASPOT VS. BUBBLE VS. POINT

Having fine-tuned DynaSpot's parameters, we ran a second experiment to evaluate the quantitative performance of Dy-naSpot and get the subjective impressions of participants.

We compared two DynaSpots with different spot widths (16 and 32 pixels) against a regular point cursor, serving as a baseline, and the Bubble cursor [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF], one of the most efficient general pointing techniques to date (Figure 6).

W EW Figure 6. The Bubble cursor captures the target closest to its center. The shape of the targets are expanded to a maximal shape obtained by a Voronoi tesselation. The bubble's effective width, EW , is thus defined by the corresponding shape.

Apparatus

We used a workstation running X Window under Linux, equipped with two double core 64-bits 2.4 GHz processors, an NVidia Quadro FX4500 graphics card, a 1600 x 1200 LCD monitor (21") and a standard optical mouse (400 dpi) with the default X Window acceleration function. Our program was written in Java using the OpenGL pipeline for graphics rendering, thus ensuring a minimum frame rate of 50 fps even for large alpha-blended Bubble cursor areas (something impossible with the default Java2D rendering pipeline).

Participants

Twelve unpaid adult volunteers (all male), from 21 to 33 year-old (average 25.2, median 25), all right-handed, experienced mouse users, served in the experiment.

Task and Procedure

We followed the same general procedure as the one used by Grossman and Balakrishnan to compare Bubble cursor with object pointing and a point cursor [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF]: participants had to select a target rendered as a solid green circle outlined in black, surrounded by a set of distractors. Additional distractors were placed on the path from the trial start point to the target. As illustrated in Figure 7, all distractors were the same size as the target and were rendered as black outlined circles. As in our preliminary experiment, the object captured by the cursor (if any) was painted red. The bubble cursor area and the DynaSpot disc were both rendered with a semitransparent gray. As in the Bubble cursor paper's experiment, four main distractor targets were positioned to control the interspace IS around, and thus the effective width EW of, the goal target1 . Two were placed along the direction of movement, one on each side of the target, while the other two were placed perpendicular to the direction of movement (see Figure 3-b). The remaining distractors were laid out so as to match the density condition DD on the path to the target. For DD = 0, there were no additional distractors on the path to the target. For DD = 1, additional distractors were packed from the start point to the closest main distractor, and offset in the direction perpendicular to the line of movement by a pseudo-random length, keeping them within a 20 degree slice centered in this line of movement. Additional distractors outside this slice were placed pseudo-randomly to match the density within the slice. For DD = 0.5, there were half as many distractors.

We made the following adjustments to the original design. Instead of making the next target appear in an unpredictable location, we laid out all 16 targets of a trial series in a circular manner. The order of appearance followed the recommendations of the ISO 9241-9 standard forcing participants to perform pointing tasks in every direction [START_REF] Douglas | Testing pointing device performance and user assessment with the ISO 9241, part 9 standard[END_REF]. We chose this more predictable behavior of targets, encountered in several pointing experiments, e.g., [START_REF] Cockburn | Human on-line response to visual and motor target expansion[END_REF][START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF][START_REF] Pietriga | Sigma lenses: focus-context transitions combining space, time and translucence[END_REF][START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF], as it better simulates situations where users have a rough idea about the direction of the target they are aiming at before starting the pointing task. Each target had to actually be selected before proceeding to the next: clicks outside the current target were counted as errors but did not end the task.

Design

Our experiment was a 4 × 3 × 3 × 3 × 3 within-participant design with the following factors: (i) four techniques TECH: Bubble, DynaSpot16 (SPOTWIDTH = 16), DynaSpot32 (SPOT-WIDTH = 32) and Point Cursor; (ii) three target widths W: 8, 16 and 32 pixels; (iii) three amplitudes A: 256, 512 and 768 pixels; (iv) three EW/W ratios: 1.5, 2 and 3; (v) three distractor densities DD: 0, 0.5 and 1.

We grouped trials into four blocks, one per technique. Each TECH block was divided into 3 sub-blocks, one per EW/W condition. Each of these sub-blocks was composed of 3 W × 3 A series of 16 pointing tasks where each DD was used 5 times (the first task of a series was not recorded). An additional sub-block at the beginning (W and A random) was used for training. To counterbalance the presentation order of conditions, we computed a Latin square for TECH and a Latin square for EW/W and crossed them, obtaining 12 orders, one for each participant. The order of the W × A conditions, as well as the density DD, were chosen randomly but the same order was used for each TECH across participants for the 15 recorded tasks of a series.

The experiment started with a training session consisting of 4 TECH × 3 EW/W series, each with W = 16 and A = 512. The experimenter introduced each technique to the participant during the first series of each corresponding TECH block; the two remaining blocks being used as actual training. For the series actually recorded, participants were instructed to be as accurate and as fast as possible. The 16 pointing tasks of a series had to be performed in a row, but participants were allowed to rest between series. A total of 19,440 actual pointing tasks were thus taken into account in the analysis (60 measures for each unique condition). The experiment lasted approximately 45 minutes.

Combined Width and Hypotheses

One of the main factors used in the experiment comparing Bubble cursor to other techniques [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF] was the EW/W ratio (effective width of the goal target by its actual width). The combination of this and factor W controls the distance between the goal target and the four distractors surrounding it. This abstraction, well-adapted to the former experiment, is however not best suited to analyze the different conditions with DynaSpot. Since the distractors are uniformly placed around the target, the ratio can be expressed in terms of interspace IS between the goal target and the distractors: EW = W + IS and (EW/W ) = (W + IS)/W . As illustrated in Figure 8, this formulation helps identify the three main conditions for Dy-naSpot: the spot width can be (a) larger than, (b) equal to, or (c) smaller than, the interspace IS. The factors W and EW/W can be grouped into one factor that we call the combined width CW. In the remainder of this paper, we use the following notation for each pair of conditions W × EW/W:

(BW, DW 16 , DW 32 , W )

where BW is the Bubble cursor's effective width, DW [START_REF] Lank | Endpoint prediction using motion kinematics[END_REF] and DW 32 are the potential effective widths for the two Dy-naSpot sizes, and W is the target's width (which corresponds to the effective width of the target for the point cursor). The factors described in the previous section yield nine combined widths CW, listed in Table 2. When the interspace IS is equal to one of the DynaSpot TECH's potential effective width (case (b) of Figure 8), we underline the corresponding Dy-naSpot (16 and 32 pixels).

Our main hypothesis is that for a given combined width CW, the effective width EW for each technique should determine the performance ordering among techniques: if the effective width for technique a is larger than for technique b (for a given combined width), then a should be faster than b (for this combined width). When the effective widths of two techniques are equal, we do not expect to find significant differences in terms of performance. However, we expect a performance degradation when DynaSpot is at its limit effective width (underlined width in the CW notation). Indeed, in this particular case, the spot reduction and small intersection between the target and the spot may forbid the user to use the full potential effective width of DynaSpot. Additionally, we hypothesize that density DD will have a similar effect on point cursor and both DynaSpots, as the behavior of all three techniques is not directly impacted by density. On the contrary, we expect a performance degradation for low densities in the case of Bubble cursor, consistent with Grossman and Balakrishnan's observations regarding visual distraction in this condition [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF].

Results

Results of the repeated measures analysis of variance are reported in Table 1. We verified that there was no effect of TECH presentation order and observed that learning effects Figure 9 shows the mean movement time for each TECH by combined width CW. Table 2 gives the results of the Tukey HSD post-hoc test for differences in mean between techniques by combined width (where a < b means that TECH b is significantly faster than TECH a). The test shows that Bubble and DynaSpot are both significantly faster than Point and that there is little difference between Bubble and DynaSpot. Figure 10-a shows mean movement time for each technique grouped by distractor density. We see that movement time increases as density increases for Point cursor and DynaSpot, but not for Bubble cursor. For Bubble cursor, a post-hoc Tukey test reveals that it is faster for DD=0.5 than for DD=0, confirming the results of [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF]. The test also reveals that each of DynaSpot16, DynaSpot32 and Point cursor is faster for DD=0 than for DD=1. Moreover, as shown in Table 2, Bubble cursor is slower than DynaSpot for DD=0 in most conditions where the effective widths are equal, while Bubble cursor is faster than DynaSpot for DD=1 when the Bubble's effective width is larger than the DynaSpot's effective width.

Figure 10-b shows mean movement time for each technique grouped by movement amplitude. We see that the difference between Bubble cursor and DynaSpot increases with amplitude. A post-hoc Tukey test shows that DynaSpot32 is faster than Bubble for an amplitude of 768, but no such difference is detected for smaller amplitudes. Moreover, removing the data for which DD=0 makes this significant difference disappear (a cause of the TECH × DD × A interaction).

These results show that the effective width determines the performance ordering among techniques only under certain conditions regarding distractor density. Our hypothesis is thus only partially verified. Distractor density affects Bubble cursor performance, especially for large movement amplitudes. As predicted, a significant degradation is observed when DD=0, i.e., when the bubble's envelope varies most during movement, causing visual distraction. Finally, distractor density also affects Point cursor and DynaSpot in a similar way, degrading performance as it increases.

Regarding errors, we find an overall error rate of 6.5%. Repeated measures analysis of variance shows a significant effect on error rate for TECH (F 3,33 = 11.6, p < 0.0001), CW (F 8,88 = 8.3, p < 0.0001) and A (F 2,22 = 5.7, p = 0.0097).

Interestingly, there is no significant effect of DD (F 2,22 = 1.4, p = 0.262). Error rate was 9.7% for Point cursor, 6.5% for Bubble cursor, and 4.9% for both DynaSpot16 and Dy-naSpot32. As usual in pointing task experiments, error rate decreases as the (effective) width grows and the amplitude decreases. Again, we find a significant interaction between TECH and CW (F 24,264 = 2.6, p < 0.0001). Figure 11 shows error rate for each TECH grouped by combined width CW. Removing errors trials or taking the time of the first click (instead of first successful click) does not change the results.

We checked the number of outliers by counting the number of trials where the time is 3 standard deviations away from the mean movement time (by participant, technique, combined width, and amplitude). The data contains only 0.99% such outliers; 87% of them are errors, and none of them is more than 3.6 standard deviations away. Again the analysis without these outliers yields the same results.

Performance results for Point and Bubble cursors are consistent with those in [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF]. However, our participants perform faster overall: 10.6% faster for Bubble cursor and 9.6% faster for Point cursor. This can be explained by the use of a ratio of 1.5 instead of 1.3 for the smallest value of EW/W, a larger error rate in our experiment, and by the details of the task: the location of the next target in our case was predictable, whereas it was not in [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF].

Qualitative Results

Participants were asked to rank the techniques by subjective preference in a post-hoc questionnaire. All participants ranked DynaSpot (either 16 or 32) as their preferred technique, followed by the other DynaSpot in second. Only two participants chose another technique than the other Dy-naSpot as the second best. One ranked the Bubble cursor second, the other DynaSpot third and Point last, while the other participant ranked the Point cursor second, the other DynaSpot third, and Bubble cursor last. Most participants complained about the visual distraction caused by the Bubble cursor envelope's strong variations under certain conditions, leading seven of them to rank that technique last. This is again consistent with earlier results [START_REF] Grossman | The bubble cursor: enhancing target acquisition by dynamic resizing of the cursor's activation area[END_REF][START_REF] Hertzum | Input techniques that dynamically change their cursor activation area: A comparison of bubble and cell cursors[END_REF]. For instance, one participant said that "Bubble cursor is distracting when the target is far away because the bubble has a big size".

Fitts' Law and Effective Width(s)

Figure 12 plots movement time as a function of IDE, the index of difficulty computed with the target's potential effective width. We take the mean for each combined width, amplitude and technique, fitting 27 points for each technique. Table 3 gives the intercept, the slope and the adjusted r 2 for both IDE and ID, the latter being computed using the actual width of the target. We see that using the effective width yields higher r 2 values and improves the fit. When fitting all the data, we obtain the equation M T = 85 + 181.IDE with an adjusted r 2 of 0.962 (for 108 points). This shows that the potential effective width for DynaSpot provides a "definition" of the width appropriate for applying Fitts' Law. Figure 13 shows the position of user clicks relative to the target, and the potential/effective target width for one combined width: (64,48,64,32). We observe that clicks are scattered across a larger area for Bubble cursor than for Dy-naSpot32, even though both have the same effective width for this combined width. We explain this by the fact that, for DynaSpot32, this corresponds to the case described in Figure 8-b, with the interspace equal to the spot's width, preventing users from fully taking advantage of the effective width. Interestingly, we observe that users do not use the full potential of the Bubble cursor either, as there are very few clicks in the corners of the target's activation area.

In an effort to formalize these observations, we measured the distance to the center of the target for all clicks by combined width, and analyzed the 95% quantile of these distances. As expected, effective widths are reflected in these distances. But other observations can be made. For instance when Dy-naSpot is at its limit potential effective width (underlined conditions in CW), as for DynaSpot32 in Figure 13, we do find a significant difference between DynaSpot and Bubble cursor, as observed above, but also between DynaSpot32 and DynaSpot16 when the latter is at its limit potential effective width. Another interesting observation is that none of the 95%-quantile distances are larger than the effective width, confirming our initial observation that the corner of the Bubble's activation area are seldom used.

Another type of "effective width", that we call the a posteriori effective width and denote W e , was introduced by Crossmann in his 1956 doctoral dissertation and advocated by MacKenzie and others in the field of HCI [START_REF] Mackenzie | Fitts' law as a research and design tool in human-computer interaction[END_REF][START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF][START_REF] Zhai | Speed-accuracy tradeoff in Fitts' law tasks: on the equivalency of actual and nominal pointing precision[END_REF]. This a posteriori effective width comes from the idea of performing an "adjustment for accuracy": the width of the target is corrected so that, under certain hypotheses, the data gives raise to an error rate of 4%. A priori, this normalization process leads to more robust results, allowing for better comparisons between experiments. In the following, we check that this definition of effective width can be used to model DynaSpot movement time.

We refer the reader to [START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF] for details about the computation of W e . This involves removing outliers, using the time at first button press, computing by participant and full condi- Zhai's index of occupation [START_REF] Zhai | Speed-accuracy tradeoff in Fitts' law tasks: on the equivalency of actual and nominal pointing precision[END_REF], I u = log 2 (W e /EW ), is given in parentheses. I u indicates the degree to which the participants over-utilize (positive I u ) or under-utilize (negative I u ) the potential effective target. We observe that the index of occupation is systematically higher for Point cursor, and then for Bubble cursor, and that it globally decreases as the width grows. This can be explained by the error rate (see Figure 11) especially for Point cursor. When comparing Bubble cursor and DynaSpot, which have similar error rates, this confirms that participants better use the full effective target width with Bubble rather than with DynaSpot.

The counterpart of W e , the a posteriori effective amplitude A e , is computed as the mean of the distance from the movement start point to the point where the user clicks. We can compute the effective index of difficulty:

ID e = log 2 (A e /W e + 1)

Table 4 gives Fitts' law equation parameters for ID e , and the throughput in bit • s -1 , computed using either the slope of Fitts' equation, or the formula recommended in [START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF]. This throughput has the advantage of taking the intercept into account and to be less dependent both on the ID range used [START_REF] Soukoreff | Towards a standard for pointing device evaluation: Perspectives on 27 years of Fitts' law research in HCI[END_REF] and on the users' nominal pointing speed [START_REF] Mackenzie | Fitts' throughput and the speed-accuracy tradeoff[END_REF]. Thus, it may be a good index of performance to compare techniques among papers. Note that the r2 values obtained here do not look as good as with the other method, but in this case we fit 324 points by technique, which are subject to participant performance variability.

DISCUSSION AND FUTURE DIRECTIONS

The results of our experiments are very encouraging. They show that DynaSpot provides an average speed-up of 18% over a conventional point cursor, and that for equivalent effective widths it achieves the same level of performance as the Bubble cursor, one of the more promising techniques to date. DynaSpot is slightly more efficient for low object densities and slightly less efficient for high ones. But most importantly, DynaSpot provides these quantitative performance benefits without departing too much from the conventional point cursor technique. This has at least three significant practical consequences. First, end-users are more likely to adopt the new technique in their daily use of GUIs because DynaSpot behaves "almost like" a point cursor and does not cause a strong visual distraction. Second, DynaSpot is compatible with all point cursor interactions such as region selections initiated by clicking in empty space without requiring an explicit mode switch. Finally, implementing DynaSpot does not require significant changes to existing GUI frameworks to support the technique: we implemented support for DynaSpot in the ZVTM Java toolkit 2 in less than 500 lines of code, and a lazy version of the technique3 was implemented in the Metisse windowing system 4 , relying solely on the accessibility API to make the technique work across unmodified applications.

Quantitative and theoretical analyses of performance results show that DynaSpot performance can be modeled with both the a priori and a posteriori effective widths. Somewhat unexpectedly, DynaSpot proves to be on a par with Bubble cursor in most targeting situations. If Bubble cursor's effective width is sufficiently larger than DynaSpot's, then Bubble cursor is faster. However, this happens mostly in configurations where the bubble cursor size is likely to vary dramatically, causing visual distractions that both hinder performance and user acceptance of the technique.

As future work we would like to evaluate area selection. We can predict what should happen with DynaSpot: (i) if empty space between targets is sufficiently large compared to the maximum spot size, the time it takes to initiate a selection in empty space should be similar to the time it takes with a point cursor; (ii) in a dense layout, we expect DynaSpot to be penalized because of the lag+reduction time (300ms). In this particular situation, an explicit mode-switching mechanism might represent an interesting compromise. DynaSpot would then have to be compared, for dense layouts, to Bubble and Area cursors augmented with such an explicit modeswitch, but also to an augmented DynaSpot featuring both time-based (implicit) and explicit mode-switching. We also plan to investigate the use of speed coupling in other pointing techniques, as this seems to be an efficient way of adapting a technique's behavior.

Figure 1 .

 1 Figure 1. (a) DynaSpot's activation area is coupled to cursor speed. (b) Multiple objects intersect the area: the target closest to the cursor center is highlighted and selected. (c) Empty space selection is possible whenever the activation area is not intersecting any object.

Figure 2 .

 2 Figure 2. DynaSpot: spot width as a function of cursor speed.

Figure 3 .

 3 Figure 3. (a) Isolated target: potential effective width EW = W +SPOTWIDTH. (b) Small interspace between targets IS ≤ SPOT-WIDTH: potential effective width is EW = W + IS.

Figure 4 .

 4 Figure 4. Spot width as a function of time for the three reduction methods (LAG = 120 ms, REDUCTIME = 180 ms).

Figure 5 .

 5 Figure 5. Movement time (left) and error rate (right) as a function of LAG, grouped by REDUCTIME.

Figure 7 .

 7 Figure 7. Sixth pointing task of a series (ISO 9241-9 circular layout)

Figure 8 .

 8 Figure 8. (a) IS < DynaSpot Width: Bubble and DynaSpot have the same EW . (b) IS = DynaSpot Width: Bubble and DynaSpot have the same EW , but different effective target shapes. (c) IS > DynaSpot Width: Bubble's EW is greater than DynaSpot's EW .

Figure 10 .

 10 Figure 10. (a) Movement time for each TECH grouped by distractor density. (b) Movement time for each TECH grouped by amplitude.

Figure 13 .

 13 Figure[START_REF] Igarashi | Speed-dependent automatic zooming for browsing large documents[END_REF]. Position of user clicks (after a coordinates change to match a right-to-left horizontal target acquisition) for each technique for combined width CW (64,48,64,32) -Bubble effective width: 64, DynaSpot16 (resp., DynaSpot32) max. effective width: 48 (resp., 64), and target width: 32.

Table 1 .

 1 Results of the ANOVA for MT ∼ TECH × CW × DD × A.were not significant. As expected CW and A have a significant effect on movement time MT. We also observe an effect of TECH on movement time. Mean movement time is 976 ms for Point cursor, 831 ms for Bubble, 819 ms for DynaSpot16 and 791 ms for DynaSpot32. However, the ANOVA also reveals significant interactions: TECH × CW, TECH × DD and TECH × A. A thorough comparison between techniques must thus take into account combined width, density of distractors, and amplitude.

	Factors	DF DFDen	F	p
	TECH	3	33 115.5 < 0.0001
	CW	8	88 509.0 < 0.0001
	DD	2	22 28.5 < 0.0001
	A	2	22 409.6 < 0.0001
	TECH × CW	24	264 12.6 < 0.0001
	TECH × DD	6	66	9.0 < 0.0001
	TECH × A	6	66	2.3	0.0470
	CW × DD	16	176	5.6 < 0.0001
	CW × A	16	176	2.1	0.0085
	DD × A	4	44	1.8	0.1435
	TECH × CW × DD	48	528	1.0	0.3746
	TECH × CW × A	48	528	1.2	0.1628
	TECH × DD × A	12	132	2.3	0.0123
	CW × DD × A	32	352	1.1	0.2637
	TECH × CW × DD × A 96	1056	1.2	0.0904

Table 2 .

 2 Significant differences for mean movement time MT between TECH, by CW. The two rightmost columns show how the results are modified if we restrict our analysis to distractor densities 0 and 1.

  12,12,12,08 16,16,16,08 24,24,24,08 24,24,24,16 32,32,32,16 48,32,48,16 48,48,48,32 64,48,64,32 96,48,64,32

	Errors (%)	6 8 10 12 14	Bubble DynaSpot16 DynaSpot32 Point
		4
		2
		0
		Combined Width
	Figure 11. Error rate for each TECH grouped by combined width CW.

Table 3 .

 3 Linear fit: intercept, slope and adjusted r 2 using ID or IDE.

	IDE

  tion, with W e = 4.133•sd where sd is the standard deviation of the oriented distance from the click to the target's center divided by √ 2. Mean values of W e for each technique TECH at each combined width CW are given in the table below.

	CW	Bubble	DynaSpot16 DynaSpot32	Point
	(12,12,12,08) 15.37 (+0.36) 13.89 (+0.21) 13.94 (+0.22) 11.51 (+0.52)
	(16,16,16,08) 20.04 (+0.32) 17.12 (+0.10) 17.26 (+0.11) 11.47 (+0.52)
	(24,24,24,08) 27.31 (+0.19) 20.38 (-0.24) 26.41 (+0.14) 11.30 (+0.50)
	(24,24,24,16) 26.27 (+0.13) 23.53 (-0.03) 25.38 (+0.08) 18.54 (+0.21)
	(32,32,32,16) 36.15 (+0.18) 29.85 (-0.10) 32.68 (+0.03) 19.25 (+0.27)
	(48,32,48,16) 52.41 (+0.13) 30.74 (-0.06) 43.35 (-0.15) 17.22 (+0.11)
	(48,48,48,32) 50.03 (+0.06) 46.31 (-0.05) 48.12 (+0.00) 36.20 (+0.18)
	(64,48,64,32) 68.61 (+0.10) 48.51 (+0.02) 57.19 (-0.16) 34.82 (+0.12)
	(96,48,64,32) 91.57 (-0.07) 45.80 (-0.07) 59.96 (-0.09) 35.69 (+0.16)

Table 4 .

 4 Fitts' law equation parameters for IDe and throughputs.

		M T = a + b.IDe TP = 1000/b TP mean of mean
		a	b	adj. r 2	IDe (IDE)	[25]
	Bubble	46 186	0.825	5.38 (5.15)	5.09
	DynaSpot16 85 161	0.781	6.21 (5.85)	5.56
	DynaSpot32 51 169	0.809	5.92 (5.68)	5.55
	Point	49 179	0.756	5.59 (5.46)	5.34
	All	57 174	0.792	5.75 (5.52)	5.38

The original Bubble cursor experiment controlled the interspace in terms of EW/W ratio (Figure6), which we will also use here for cross-experiments comparisons.

http://zvtm.sf.net

Which only needs to know the position and shape of interface components at click time, but does not feature target highlighting.

http://insitu.lri.fr/metisse


Sandwich honeycomb structures (aluminum core bonded to Carbon Fiber Reinforced Polymer (CFRP) sheets on either side) are widely employed in the aerospace industry for their high strength to mass ratio. However, they might be subjected to damages such as delaminations of the composite sheets or debondings between the face sheets and the core due to impacts or thermo-mechanical aging. In order to reduce maintaining costs and extend the service time, Guided Waves (GW) based Structural Health Monitoring (SHM) systems are considered an adequate solution. Indeed, GW propagate over long distances and exhibit low attenuation, thus allowing to monitor wide areas with a limited number of sensors. Defect imaging on CFRP composites and honeycomb composite structures using both Delay-And-Sum [1] and correlation-based algorithm Excitelet [2] is presented in this communication.

A machine learning algorithm is finally implemented in order to automatically identify and isolate defects on a given cartography map. The machine learning algorithm is trained on an experimental database of false and positive results obtained on representative specimens.

INTRODUCTION

In the past years, the use of composite materials in the aeronautic industry has considerably increased. This rapid growth is mainly due to the considerable economic benefits due to the mass reduction allowed by the use of composites. These materials are now used for a wide range of complex structures, such as aircraft nacelles, which are of interest in this study. The aircraft nacelle, the housing of the aircraft engine, is _____________ mostly made of honeycomb composite (aluminum cores encapsulated by carbon fiber based composite sheets on the top and bottom surfaces). These composite structures exhibit excellent strength-to-weight ratio, stiffness, toughness and corrosion resistance.

However, appearance of defects such as face sheets delamination or core-sheet debonding due to impacts or thermo-mechanical aging may decrease these properties. Guided elastic waves are considered an adequate mean to monitor such systems in a Structural Health Monitoring (SHM) context. Indeed, Guided Waves (GW) propagate over long distances with low attenuation, allowing to monitor wide areas with a limited number of sensors [START_REF] Su | Guided lamb waves for identification of damage in composite structures: a review[END_REF]. However, the analysis of GW signals is of increasing complexity as the structure becomes more complex, due to their multi-modal and dispersive behavior.

In this study, we mainly focus on damage detection and localization in Carbon Fiber Reinforced Polymer (CFRP) and honeycomb composite structures. Two imaging algorithms, Delay-And-Sum (DAS) [START_REF] Michaels | Guided wave signal processing and image fusion for in situ damage localization in plates[END_REF] and Excitelet [START_REF] Masson | Assessment of a novel imaging technique for commercial structural health monitoring and NDT systems[END_REF] are implemented and tested on multiple samples of different materials. A machine learning algorithm is finally implemented in order to automatically identify and isolate defects on a given cartography obtained by GW imaging. The machine learning algorithm is trained on an experimental database of false and positive results obtained on representative specimens.

GUIDED WAVE IMAGING

Delay-And-Sum (DAS) and Excitelet are two guided wave based imaging algorithms and require a similar type of measurement procedure. In particular, the knowledge of the initial state of the studied structure, the baseline signal, is required for both methodologies. The specimen of interest is instrumented by a sparse array of piezoelectric (PZT) sensors and each pair of sensors acts sequentially as emitter and receiver of guided waves, thus creating a scan of the specimen. Two identical scans of the studied structure are taken in a healthy and a damaged state. The residual signal is obtained as the difference between both scans, thus removing the incident wave packets and the reflection from the edges. A schematic of the scanning process of the specimens is represented in the Figure 1. For each pair of sensors, the first wave-packets of the residual signal, corresponds to the 'echoes' from defect, i.e. the energy reflected from the flaw. In order to build a cartography representing the health of the specimen, the entire upper surface of the specimen is discretized in a grid where each pixel is given a Damage Index (DI) value that can be interpreted as a probability of the presence of a defect presence at each pixel. The methodologies DAS and Excitelet use different strategies to calculate the DI.

Delay and sum (DAS)

The process to compute a DI with DAS is the following: 1) the residual signal is computed as the difference between the scans measured in the reference and a damaged state; 2) For each pair of sensor, the received baseline signal is delayed of the theoretical time of flight, computed using the propagation speed of the GW, creating a DI for this pair of sensors; 3) The DI contribution of each pair is summed for all pair of sensors, creating the final DI map. The algorithm DAS requires only the knowledge of the directional group velocity of the GW mode and the frequency of interest. The detailed process of computing a DI with DAS can be found in [START_REF] Sharif-Khodaei | Assessment of delay-and-sum algorithms for damage detection in aluminium and composite plates[END_REF]. Considering that GW are dispersive, it is required to use a single GW mode with a narrow bandwidth excitation in order to mitigate the dispersion effects.

Excitelet

The process to compute a DI with Excitelet is the following: 1) For each pair of sensors and each pixel (Xi, Yi), the theoretical contribution that would be received by the receiver from a wave packet generated by the emitter and reflected by pixel (Xi, Yi) is computed; 2) the correlation coefficient is computed for each pixel of the cartography as the correlation between the theoretical and the measured residual signals. The detailed process of computing a DI with Excitelet can be found in [START_REF] Masson | Assessment of a novel imaging technique for commercial structural health monitoring and NDT systems[END_REF]. Unlike DAS, by comparing the measured wave packets to the theoretical ones, the dispersion is taken into account in the process, therefore Excitelet is generally highly accurate but computationally intensive. However, Excitelet requires the knowledge of the dispersion curves of the studied specimen.

In this work, we make the far-field-radiation approximation (FFA) assumption to compute the theoretical signals. For anisotropic samples, the angular dependency of guided waves is measured using a laser vibrometer and taken into account in the computation of the theoretical signals.

EXPERIMENTAL RESULTS

First, two CFRP plates are studied. The first plate is made of 8 layers with a [0°,45°,0°45°]s layup and of dimensions 400 x 400 x 2.2 mm 3 . The second plate is made of 21 plies all aligned with the 0° orientation and of dimensions 1000 x 600 x 5.6 mm 3 . Four PZT sensors are permanently glued on the first plate, as represented in Figure 3 and six on the second. The excitation signal is a 40 kHz burst modulated by a two-cycle Hann window with an amplitude of 10V. This frequency is chosen as the wave propagated is dominated by the A0 mode under these parameters. Secondly, two honeycomb composite structures are instrumented as well by four PZT each. Both specimens are made of aluminum honeycomb cores of 29.2 mm in height and 9.375 mm in diameter bounded on each side to 2-layer CRFP plates of 0° orientation and of 0.275 mm in thickness each. The dimension of the first plate is 400 x 400 x 29.75 mm 3 while the second if 1000 x 600 x 29.75 mm 3 . The chosen excitation signal is similar to the previous by at 25 kHz. For the sake of experiment repeatability, the defect was simulated by attaching magnets of 25 mm in diameter on both sides of the structures. This type of defect is not fully representative of reflective defects but is an easy way to test imaging algorithms capabilities.

Before applying Excitelet, it is necessary to measure the dispersion relations and validate the far-field approximation. To do so, a Laser Doppler Vibrometer is used to measure B-scans in all directions for all the specimens. Dispersion relations are then extracted and used to compute Excitelet. For illustration purposes, a theoretical signal computed with the FFA is compared in Figure 4 to the same signal measured by Polytech laser Doppler.

The results of DAS for the first CFRP plate and the first honeycomb plate are represented in Figure 3. It is observed that, even though the defects are located, the results are rather inaccurate, which is mainly to the fact that DAS neglects the dispersion. The results for Excitelet on the second CFRP plate and the second honeycomb plate are presented in the Figure 4. It is observed that Excitelet detects the defects in an appropriate fashion even with four or six transducers. The results with Excitelet are more precise than the ones with DAS due to the fact that the dispersion is taken into account. Also, it is observed that with an increasing number of sensors the noise of cartography decreases and the overall quality is improved.

MACHINE LEARNING

Due to the complexity of the analysis of the cartography obtained by both algorithms and the potentially large number of images to analyze, machine learning algorithms are a solution to automatically and quickly analyze GW imaging pictures [START_REF] Ferrar | Structural health monitoring: a machine learning perspective[END_REF]. In the current context, the Support Vector Machine (SVM) classifier is used to extract the defect position from the cartographies. This approach is potentially transposable to various SHM systems with a large number of sensors with which complex images are obtained. (c) (d) The Histograms of Oriented Gradients (HOG) descriptor is a widely used tool in image processing and is capable of extracting unique features of the object [START_REF] Dalal | Histograms of Oriented Gradients for Human Detection[END_REF]. The gray scaled cartography is analyzed by an 8x8 pixels sliding widow in order to replace each pixels by a scalar among 9 possible values representing the local orientation of the cartography (0°, 20° … 180°). HOG descriptor reduces the dimension of the studied picture and highlights their important features. As the GW imaging algorithms attempt to reconstruct defects as an omnidirectional point sources, the defects detected on the previous cartographies are represented by a vortex of oriented gradients in the pictures processed by the HOG description, as represented in Figure 5.

This process can be automated for defect extraction by using a 2D window with a 50% overlap sliding along the cartography. The features extracted by HOG are feed to a SVM classifier, trained on an experimental database to automatically classify cartographies. Machine learning, and in particular SVM classifiers, is very promising to automate and speed up the processing of data obtained by SHM systems. In future works, the authors will pursue this cartography analysis in order to identify defect size and type.

CONCLUSIONS

This work reports on the comparison of DAS and Excitelet Guided Wave imaging algorithms and their application on CFRP and honeycomb composites. The far-field radiation approximation is used as an approximation of the propagated signal in order to compute the wave propagation in composite structures. A support vector classifier is applied on the images obtained by GW imaging in order to automatically extract the defect location for further analysis. The use of machine learning is encouraging to further study defect description and classification.

Figure 1 .

 1 Figure 1. Schematic of the measurement process for guided wave imaging. The blue circles represents PZT transducers acting sequentially as GW emitter and receiver. The red spot represents the defect reflecting GWs generated by PZT 1 and received by PZT 2.

Figure 2 :

 2 Figure 2: Measured (a) and theoretical (with FFA) (b) b-scans for the CFRP plate in the 0° direction. The theoretical b-scan does not take into account edge reflections.

Figure 3

 3 Figure 3 (a): CFRP plate instrumentation, with 4 PZT transducers and magnets to simulate a reflector, (b): Results of DAS imaging on the CFRP specimen and (c): Results of DAS imaging on the honeycomb composite structures. The exact defect position is denoted by the red diamond.

Figure 4 .

 4 Figure 4. Defect cartographies for CFRP (c) and honeycomb composite structures (d) obtained with Excitelet. Magenta circles denote PZT elements on the plate while the defect position is represented by the red diamond.

Figure 5 .

 5 Figure 5. Defect cartography (a) and its representation by HOG descriptor (b). Each group of 8x8 pixels is replace by a scalar among 9 possible values to reduce feature dimension. The red square denotes the defect location on the HOG descriptor representation. The appereance of a vortex of the gradient is observed and represents the defects.


Pierre Calmon

Olivier Mesnil

Roberto Miorelli

Xavier Artusi

Bastien Chapuis
email: bastien.chapuis@cea.fr

Oscar D'almeida

Model Assisted Probability of Detection for Guided Wave Imaging Structural Health Monitoring

published or not. The documents may come

INTRODUCTION

In Structural Health Monitoring (SHM), sensors are permanently installed to monitor the integrity of a structure throughout its lifetime. Demonstrations of damage detection, localization and sometimes sizing of flaws using Guided Wave (GW) based SHM techniques can be found in the literature [START_REF] Michaels | Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors[END_REF]. The GW-SHM technique used in this article is Guided Wave Imaging (GWI), which relies on the placement of a sparse sensor array on the inspected structure. Each sensor sequentially generates and receives GWs, thus a scan of the structure between every pair of sensors is obtained. By comparing this scan to a reference one taken in a pristine state, a cartography representing the health of the structure is generated. The GWI process used in this paper, the so-called Delay-And-Sum (DAS) [START_REF] Michaels | Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors[END_REF], allows both detection and localization of the defect. However, to reach sufficient maturity of GW-SHM techniques, the performance of such techniques must be demonstrated and certified. The Probability of Detection (POD) metric is usually computed in "classical" Non Destructive Testing (NDT) and is an attractive approach for SHM too. This approach requires a large amount of data for a wide variety of configurations (sensors positions, flaw position/size, number of flaw…). Experiments can be substituted by simulation to generate this data, which corresponds to the MAPOD (Model Assisted POD) approach The goal of this work is to illustrate, on a simplistic case study, the application of the MAPOD approach for GW-SHM performance demonstration. A GWI experiment is conducted with a sparse array of piezoelectric transducers placed on an aluminum panel. A meta-model is built to ensure that the influence of every variable is taken into account, including the combined influence of multiple variables. The forward model is provided by the CIVA [2] software with full 3D computations. Hundreds of simulations are required to build and validate a meta-model, which in turns is able to generate several thousands of results to compute PODs as a function of input parameters.

GUIDED WAVE IMAGING

The GWI process used in this work is called Delay-And-Sum (DAS) [START_REF] Michaels | Detection, localization and characterization of damage in plates with an in situ array of spatially distributed ultrasonic sensors[END_REF] and relies on delaying and summing the residual signals by the theoretical time of flight for every pair of sensor. Data is generated by a spectral finite element code available in CIVA [START_REF] Mesnil | Validation of Spectral Finite Element Simulation Tools dedicated to Guided Wave Based Structure Health Monitoring[END_REF]. In order to produce simulated data representative of experimental variabilities, imaging results obtained from simulations are degraded by the following factors. First, the elastic properties of the material are modified to represent a change of temperature between the reference and the baseline state. The baseline measurement is the same for every dataset and is simulated with the elastic properties of aluminum at 20°C. Second, the responses of the sensors are degraded to represent an aging effect. Third, Gaussian noise is added to the signals to represent measurement noise. The imaging process is conducted at 40 kHz in a 400x400x3 mm 3 aluminum panel affected with a circular through-hole and instrumented by 8 piezoelectric transducers. Two examples of imaging results of a 5 mm hole and 15 mm hole are represented in Figure 1. The 5 mm hole is not detected while the 15 mm is both detected and located.

MODEL ASSISTED PROBABILITY OF DETECTION IN SHM

The POD approach in NDT consists of conducting an inspection procedure on multiple samples containing multiple defects. By repeating the inspection multiple times, possibly by multiple operators, variability intrinsic to the inspection is added to the measurement because each inspection is independent. A POD is then computed with various algorithms, for example hit-miss or signal response [START_REF] Chapuis | Best Practices for the Use of Simulation in POD Curves Estimation -Application to UT Weld Inspection[END_REF][START_REF] Jenson | Simulation supported POD: methodology and HFET validation case[END_REF]. The POD curve is finally plotted as a function of the characteristic parameter, typically the defect size. This curve is meaningful only if the variability of every parameter influencing the result of the inspection is properly captured.

In SHM, because the sensors are permanently integrated, successive inspections are dependent. Moreover in GW-SHM, since long range and highly sensitive GW are used, the sample can only contain a unique defect, otherwise the detection of one defect will interact with that of others. This leads to doable but extremely costly experimental campaigns to compute a POD in a GW-SHM setup [START_REF] Schubert Kabban | The probability of detection for structural health monitoring systems: Repeated measures data[END_REF].

The MAPOD approach allows to carry out the computation of a POD using simulated experiments, and thus to study a much wider range of configurations at a reasonable cost. MAPOD is mainly limited by the requirement of having reliable models capturing all the relevant variabilities.

In this simplistic studied configuration, the following variabilities are taken into account: -Position of the hole, -Size of the hole, -Temperature during the acquisition of the damaged state (through the change of the elastic properties), -Degradation state of the sensors, -Standard variation of the added measurement noise. Note that this list does not include the type (and shape) of defect, therefore the specific POD that will now be computed is only relevant for a through-hole, and is irrelevant for a crack for example. Even though GWI provides both detection and localization, the POD is a metric for the detection aspect only, and probability of localization is not treated in this work. From each image, a scalar value representing the success of the detection must be extracted. In this work, the contrast of the image is used as the detection metric, as it may represents the analysis realized by an operator attempting at classifying the results of at Figure 1 between pristine and damaged state. The contrast is defined as the ratio between the values of the highest pixels of the picture and the values of the lowest pixels. More refined detection approaches are not within the scope of this work.

RESULTS

A metamodel of the previously described configuration is generated using CIVA. This metamodel fully describes the imaging results obtained in the studied configuration for all the variable parameters within a predefined range. For every variability of the input parameters, 1 000 samples are evaluated using the metamodel. The POD is then computed using the hit-miss algorithm.

The samples are computed for the following input variable distributions:

-Position of the hole: anywhere within the sensor circle with a uniform distribution, -Size of the hole: from 5 to 15 mm with a uniform distribution, -Temperature during the acquisition of the damaged state: from 0°C to 40°C with a uniform distribution, -Additive white noise: Gaussian with a standard deviation equal to 10% of the amplitude of the signals The degradation of the sensors is also taken into account using the following procedure: -

The amplitude measured by the sensor is multiplied by a degradation factor represented by a normal distribution centered on 1, with standard deviation of 0.1 and an upper bound at 1. -If the sensor degradation is less than 0.9 then the sensor is removed (which significantly degrades the imaging results); -If the sensor degradation is between 0.9 and 1, the amplitude of the signals measured by this sensor is multiplied by this sensor degradation factor;

These distributions are used to draw 1000 distinct configurations on which the imaging algorithm is applied. The contrast of each resulting image is represented in Figure 2 where each blue dot represents a configuration; the horizontal axis is the size of the defect and the vertical axis is the contrast of the image. As expected, it is observed that the overall value of the contrast increases with the defect size. Then, by application of the hit-miss algorithm, the POD curve represented in Figure 3 is obtained. The defect size yielding the POD90|95 value is equal in this case to 12.0 mm.

The same process is replicated for the same distribution of the variable parameters but at a fixed temperature of 20°C. In this case, the POD curve obtained is in Figure 4 with a defect size yielding the POD90|95 value equal to 9.5 mm. This use case quantitatively illustrates how the temperature effect can influence the performance of a GW-SHM system. Even though the configuration studied in this paper is very simplistic, and some assumptions (for example concerning the representation of the sensor's degradation) must be consolidated to ensure the meaningfulness of the result produced by this procedure.

CONCLUSION

This work presents an application of the MAPOD methodology to a GWI experiment in a GW-SHM setup. It is enabled by the availability of efficient and accurate numerical models. Because simulation is used, and therefore all the data are independent, POD metrics used in NDT can directly be used. A significant effort must be accomplished to ensure that the variability of all the influencing parameters is properly captured. Once a meta-model is built, large numbers of samples can quickly be computed for multiple distributions of the variable parameters. In this paper, the influence of temperature variations between 0 and 40°C was illustrated and compared to an inspection conducted at the nominal temperature of 20°C. A degradation from 9.5 mm to 12 mm of the defect size yielding the POD90|95 value was observed, due to these variations.

Figure 1 :

 1 Example of GWI result, the blue circles represent the sensors while the color map represents the results of the DAS imaging: (a): failed imaging of a 5 mm diameter flaw and (b): successful imaging of a 15 mm diameter flaw.

Figure 2 :

 2 Figure 2: Contrast versus defect size dataset obtained with 1 000 samples. The grey line denotes the detection threshold.

Figure 3 :

 3 Figure 3: POD versus defect size (blue) for the dataset with temperature variation [0°-40°], with its 95% confidence bound (red).

Figure 4 :

 4 Figure 4: POD versus defect size (blue) for the dataset but without temperature variation, with its 95% confidence bound (red).


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