Emmanuel Pietriga
email: emmanuel.pietriga@inria.fr

Caroline Appert
email: appert@lri.fr

Sigma Lenses: Focus-Context Transitions Combining Space, Time and Translucence

Keywords: Multi-scale interfaces, Focus + Context, Fisheye lenses, Translucence, Focus targeting, Controlled experiment ACM Classification H. Information Systems H.5 Information Interfaces and Presentation H.5.2 User Interfaces (H.1.2, I.3.6)

Focus + context techniques such as fisheye lenses are used to navigate and manipulate objects in multi-scale worlds. They provide in-place magnification of a region without requiring users to zoom the whole representation and consequently lose context. Their adoption is however hindered by usability problems mostly due to the nature of the transition between focus and context. Existing transitions are often based on a physical metaphor (magnifying glass, fisheye, rubber sheet), and are almost always achieved through a single dimension: space. We investigate how other dimensions, namely time and translucence, can be used to achieve more efficient transitions. We present an extension to Carpendale's framework for unifying presentation space accommodating these new dimensions. We define new lenses in that space, called Sigma lenses, and compare them to existing lenses through experiments based on a generic task: focus targeting. Results show that one new lens, the SPEED-COUPLED BLENDING lens, significantly outperforms all others.

INTRODUCTION

Many techniques can be used in combination with classical pan & zoom to navigate large multi-scale worlds. Among them, a range of bifocal display techniques have been designed, which can be broadly categorized as either overview + detail or focus + context techniques. Overview + detail techniques [START_REF] Plaisant | Image-browser taxonomy and guidelines for designers[END_REF] usually put the context view in a small inset located in a corner of the screen, leaving most of the latter to the detailed view, while focus + context techniques do the opposite: the context occupies the whole screen except for a small area that provides in-place magnification of a limited region of the context. While overview + detail techniques are generally favored and have been shown to perform well in some situations [START_REF] Hornbaek | Navigation patterns and usability of zoomable user interfaces with and without an overview[END_REF][START_REF] North | Snap-together visualization: a user interface for coordinating visualizations via relational schemata[END_REF][START_REF] Pietriga | Pointing and Beyond: an Operationalization and Preliminary Evaluation of Multi-scale Searching[END_REF], there are cases where they show their limits: for instance, when navigating a map of a densely populated region to look for particular localities, overview + detail techniques can only use a few pixels to display each of them in the context view. On the contrary, focus + context techniques can convey additional information in the context view, such as the localities' names, thus providing users with more contextual information that can guide navigation. They have also been shown to perform efficiently in other situations, e.g., for large steering tasks [START_REF] Gutwin | Fisheyes are good for large steering tasks[END_REF] or when selecting small targets with a stylus [START_REF] Ramos | Pointing lenses: facilitating stylus input through visual-and motor-space magnification[END_REF].

Even though they have been studied for some time, the adoption of focus + context techniques remains limited, mostly due to comprehension and low-level interaction problems [START_REF] Carpendale | Making distortions comprehensible[END_REF][START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF] related to how the transition between the context and the magnified focus region is achieved. Many of the transitions described in the literature are inspired by the physical world and are presented through metaphors such as magnifying glasses, rubber sheets [START_REF] Sarkar | Stretching the rubber sheet: a metaphor for viewing large layouts on small screens[END_REF], and more generally surface deformations [START_REF] Carpendale | 3-dimensional pliable surfaces: for the effective presentation of visual information[END_REF]; in other words, spatial transitions caus-ing various problems that can hinder performance. For instance simple magnifying glasses (Figure 1-a) create occlusion of the immediate context adjacent to the magnified region [START_REF] Robertson | The document lens[END_REF]; graphical fisheyes [START_REF] Sarkar | Graphical fisheye views[END_REF], also known as distortion lenses (Figure 1-b), make it difficult to acquire targets [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF], especially for high magnification factors. To cancel the negative effects of distortion associated with fisheyes, Gutwin proposed Speed-coupled flattening lenses [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF], introducing time as a dimension to transition between focus and context. The comparison of these time-based lenses with plain fisheye lenses demonstrated that the performance of lens-based techniques can be improved by using dimensions other than space to control the transition between focus and context.

In addition to space and time, we argue that other dimensions readily available in the electronic world can be used to provide more efficient transitions between focus and context.

In this paper we introduce a generalization of Carpendale's framework for unifying presentation space [START_REF] Carpendale | A framework for unifying presentation space[END_REF]. This generalization encompasses transitions based on two orthogonal dimensions: space and translucence (Figure 1-c), which can be combined with a third dimension: time (Figure 1-d). This opens up a large design space, called the Sigma lens design space, in which we identify interesting points. We report on the results of an evaluation of five lenses on the generic task of focus targeting, a basic motor task involved in many highlevel navigation tasks. The main finding of these evaluations is that one new lens, the SPEED-COUPLED BLENDING lens, significantly outperforms all other types of lenses for that task.

RELATED WORK

Focus + context techniques are mainly differentiated by the way they transition between the focus and context regions.

Techniques such as the DragMag [START_REF] Ware | The DragMag image magnifier[END_REF] and Manhattan lenses [START_REF] Carpendale | A framework for unifying presentation space[END_REF] display the focus as an inset which is offset from the corresponding context region so as not to occlude the local context adjacent to that region. In this particular case, there is no actual transition between focus and context, which are simply connected through lines serving as visual cues. Techniques that do not offset the focus region provide an in situ magnification that sits on top of the corresponding context region [START_REF] Keahey | Techniques for non-linear magnification transformations[END_REF]. They have to use some type of transition in order to avoid occlusion of the adjacent context. This is almost always achieved by distorting the representation, so as to smoothly integrate the focus into the context. The distortion can affect the entire representation: Graphical Fisheyes [START_REF] Sarkar | Graphical fisheye views[END_REF], the Rubber Sheet [START_REF] Sarkar | Stretching the rubber sheet: a metaphor for viewing large layouts on small screens[END_REF], the Document Lens [START_REF] Robertson | The document lens[END_REF], the Perspective Wall [START_REF] Mackinlay | The perspective wall: detail and context smoothly integrated[END_REF]. Or it can be restricted to a specific region, in which case they are called constrained lenses [START_REF] Carpendale | A framework for unifying presentation space[END_REF][START_REF] Keahey | Techniques for non-linear magnification transformations[END_REF]. These have the advantage of distorting only a limited region around the focus, leaving most of the context untouched.

They have been shown to work better than full screen lenses for some tasks [START_REF] Gutwin | A comparison of fisheye lenses for interactive layout tasks[END_REF], and should be favored when the focus has to be relocated often, as they reduce the amount of visual changes during lens movements (focus retargeting). Various improvements to these techniques have been proposed, such as ways to achieve higher magnification [START_REF] Carpendale | Achieving higher magnification in context[END_REF], and visual cues that can help in comprehending distortion [START_REF] Carpendale | Making distortions comprehensible[END_REF]. In almost all cases, however, the transition between focus and context is achieved through one single dimension: space.

Magic Lens filters, part of the See-Through Interface [START_REF] Bier | Toolglass and magic lenses: the see-through interface[END_REF], are powerful generic lenses that are used to modify the rendering of objects seen through them. However, to our knowledge, they have not been used to specifically address the problem of smoothly transitioning between focus and context, whether through space, time, or translucence. Lieberman used translucence in Powers of Ten Thousands [START_REF] Lieberman | Powers of ten thousand: navigating in large information spaces[END_REF], a bifocal display technique that makes the focus and context views share the same physical screen space, by using multiple translucent layers. But as with the DragMag, there is no actual transition between focus and context, which are overlaid on top of one another. Even though it has been shown to be usable in exploratory studies [START_REF] Cox | The usability of transparent overview layers[END_REF][START_REF] Harrison | Transparent layered user interfaces: an evaluation of a display design to enhance focused and divided attention[END_REF], this type of representation based on transparent or translucent layers is cognitively demanding, causing visual interferences that are the source of serious legibility problems, and requiring additional mental effort from the user to relate focus and context. Translucence remains, however, an interesting dimension which has been used successfully to reclaim some screen real-estate, either in combination with other filters such as in multiblending [START_REF] Baudisch | Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending[END_REF] or by making the translucence level dynamically vary as a function of cursor movements [START_REF] Gutwin | The effects of dynamic transparency on targeting performance[END_REF]. As mentioned earlier, cursor movements have been used in a different context, closer to our problem, for controlling the magnification factor of speed-coupled flattening lenses [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF] over time, with the effect of increasing focus targeting performance compared to the equivalent static fisheye lenses. Another technique, Speed-dependent automatic zooming [START_REF] Igarashi | Speed-dependent automatic zooming for browsing large documents[END_REF], couples zoom level in a window with scroll rate, zooming-out as speed increases. We believe that new types of lenses can be created by more systematically combining the above dimensions, namely space, translucence and time, in order to provide more efficient transitions between focus and context in multi-scale interfaces.

SPACE, TIME, TRANSLUCENCE, AND BEYOND

The basic concepts for describing spatial distortion between focus and context have been defined in Carpendale's framework for unifying presentation space [START_REF] Carpendale | A framework for unifying presentation space[END_REF]. In this section we reformulate these concepts in a slightly different, but equivalent way in order to accommodate our generalization of transitions between focus and context. This formulation is based on space-scale diagrams [START_REF] Furnas | Space-scale diagrams: understanding multiscale interfaces[END_REF] and uses the associated terminology. Basic knowledge about these diagrams is assumed.

General Properties

We consider the focus and context regions of any lens-based representation as separate viewing windows in a space-scale diagram. The final rendered viewing window is a composition of points from both windows.

All constrained lenses, no matter how they transition between focus and context, have the following properties:

• M M : the maximum magnification in the focus region (a.k.a the flat-top), • R I : the radius of the flat-top region, which we call inner radius, • R O : the radius of the lens at its base (i.e., its extent), which we call outer radius, • (x c , y c ) : the coordinates of the lens' center. The final viewing window obtained at rendering time can be seen as a combination of the two abstract windows introduced above: the rendering of the focus window is integrated, after some transformation, in the context window.

Spatial Transitions

The most common transformation consists in displacing all points in the focus window to achieve a smooth transition between focus and context through spatial distortion [START_REF] Carpendale | A framework for unifying presentation space[END_REF]. This type of transformation can be defined through a drop-off function, such as a Gaussian (see Figure 2), which models the magnification profile of the lens. Associated with a distance function d, the drop-off function is defined as:

G scale : (x, y, d) → s
with s a scaling factor. G scale is usually a monotonically decreasing function with a range of [1, M M ]. This is not a strong requirement; other functions may however introduce discontinuities in the spatial transition.

The rendering of point (x, y) in the final viewing window is then defined through the displacement function r:

r(x, y) =                (xc + x-xc M M , yc + y-yc M M ) {∀(x, y)|d(x, y) R I } (1) (xc +
x-xc

G scale (x,y,d) , yc + y-yc G scale (x,y,d) ) {∀(x, y)|R I < d(x, y) < R O } (2) (x, y) {∀(x, y)|d(x, y) R O } (3)
The flat-top region corresponds to case (1), the transition to case (2), and the region beyond the lens boundaries (i.e., the context) corresponds to case (3). Distance function d is based on L p -metrics, and is defined as follows:

d : (x, y) → P |x -x c | P + |y -y c | P
where (x, y) are the coordinates of a point seen through a lens centered in (x c , y c ), and P ∈ N * . Most lenses are either radial (P = 2, circular shape) or orthogonal (P = ∞, square shape). A Gaussian function is often used to define drop-off function G scale , as it provides one of the smoothest visual transitions between focus and context. Figures 2 and1-b illustrate Gaussian distortion lenses. It is not the purpose of this article to provide a detailed survey of all possible dropoff and distance functions, which are already well-described in the literature [START_REF] Carpendale | A framework for unifying presentation space[END_REF][START_REF] Carpendale | Achieving higher magnification in context[END_REF].

2•R I v u O s s•MM 2•R O 2•MM•R O 2•R I 2•R O Rendering in

Translucence as a Transition Dimension

Digital image compositing and more particularly alpha blending represents another, yet unexplored, method for transitioning between the focus and context regions of a constrained lens. As with spatial distortion, the final viewing window obtained at rendering time is a combination of the two abstract viewing windows: here, points of the focus window are composited with points of the context window. For instance, using gradually increasing translucence, it is possible to smoothly blend the focus viewing window into the context, thus achieving a transition without resorting to distortion (see Figures 3 and1-c).

The continuity between focus and context is realized through compositing only. Given two points with (r, g, b) color components, one in the focus window and one in the context window, we note:

p context ⊗ α p f ocus
the point p comp resulting from compositing them using Porter & Duff's Source atop Destination alpha blending rule [START_REF] Porter | Compositing digital images[END_REF] with a value of α, the source being the focus viewing window and the destination the context viewing window:

p comp = α • r f ocus + (1 -α) • rcontext α • g f ocus + (1 -α) • gcontext α • b f ocus + (1 -α) • bcontext
As with scale for distortion lenses, the translucence profile can be defined by a drop-off function that maps a translucence level to a point (x, y) located at a distance d from the lens center:

G alpha : (x, y, d) → α
with α an alpha blending value in [0, α F T ], α F T being the lowest translucence level used in the lens' flat-top. Note that it does not necessarily have to be 1.0 (opaque), though it will often be close to it. Drop-off function G alpha is usually a monotonically decreasing function. Again, this is not a requirement, but other types of functions may introduce discontinuities in the blending gradient.

The rendering of a point (x, y) in the final viewing window is then defined through the blending function b:

b(x, y) =                  (xc + x-xc M M , yc + y-yc M M ) N α F T (x, y) {∀(x, y)|d(x, y) R I } (1) (xc + x-xc M M , yc + y-yc M M ) N G alpha (x,y,d) (x, y) {∀(x, y)|R I < d(x, y) < R O } (2) (x, y) {∀(x, y)|d(x, y) R O } (3)
Figure 3 shows how translucence is used to transition between focus and context in what we call a BLENDING lens. This dimension offers an alternate way to smoothly transition between focus and context without resorting to spatial distortion, thus eliminating the drawbacks specifically associated with the latter. As we will discuss in the evaluation section, this transition type introduces problems of its own.

2•R I v u O s s•MM 2•R O 2•MM•R O 2•R I 2•R O Rendering in

Time-based Transitions

The transition functions described in the previous sections make it possible to create a broad range of lenses. However, as is the case with most lenses reported in the literature, the properties of these lenses are defined statically. One notable exception is the Speed-coupled flattening lens [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF] which uses the lens' dynamics (velocity and acceleration) to automatically control magnification: basically, M M decreases toward 1.0 as the speed of the lens (operated by the user) increases, therefore "flattening" the lens into the context, and increases back to its original value as the lens comes to a full stop. Speed-coupled flattening lenses have been demonstrated to outperform their static counterpart, and represent a first step in the direction of using time-dependent transitions to improve the usability of lenses.

The magnification factor of a lens (M M ) is an obvious parameter to control over time. There is no reason however to limit the use of the lens' dynamics to this one alone. Other candidates include the lens' radii R I and R O , as well as the lens' translucence value in its flat-top α F T .

We note F(t) any time-based function returning a numerical value that can be used to dynamically change one or more of the above-mentioned lens properties. In the following we focus on one particular function: the lens' velocity and acceleration over time. This is however just one possible function

Overall Lens Design Space

Spatial transitions and transitions based on translucence can be combined in a single lens, each with their own drop-off and distance functions. Additionally, several lens properties can be made time-dependent. This makes for a rather complex expression for computing the rendering of a point (x, y) seen through the lens, which reflects the richness of our new design space. Table 1 gives a summary of the properties of both existing and new lenses within this design space.

The first three lenses already exist in the literature. The MAGNIFYING GLASS, illustrated in Figure 1 The last two techniques are new contributions identified while exploring our design space. The BLENDING lens, illustrated in Figures 1-c and3, can be seen as the simplest example of a translucence-based transition: it is like a MAGNIFYING GLASS that gradually blends into the context. Smoothness of transition is achieved without resorting to spatial distortion: context pixels gradually fade out as we get closer to the lens' center, while focus pixels gradually fade in.

The last lens, called SPEED-COUPLED BLENDING, is even closer to a MAGNIFYING GLASS. It shares all of its properties except that its α F T depends on the lens' movements. When still, the lens looks like a MAGNIFYING GLASS. But the flattop becomes increasingly and uniformly translucent as the lens moves faster, becoming fully transparent beyond a given speed threshold S. The same type of low-pass filter as that governing the behavior of the SPEED-COUPLED FLATTENING lens is used. Figure 1-d shows a screenshot of a SPEED-COUPLED BLENDING lens moving at slow speed. Figure 4 illustrates the behavior of this lens when moving it from left to right in the scene introduced in the previous section: (t1) the lens stands still on the left side of the color spectrum; (t2) the user starts moving the lens to position it at the other end of the scene: the context can be seen through the focus (which is itself still visible) by translucence; (t3) the lens is moved fast, beyond threshold speed S; the focus is thus completely transparent: only the context is visible; (t4) the user slows down, the lens' focus gradually reappears; (t5) the user has reached the desired position, the lens comes to a full stop, and the focus is opaque again. A small inner circle can be noticed inside the lens at (t2), (t3) and (t4). This circle identifies, at the scale of the context, what region is magnified in the flat-top. The visibility of this translucent circle is controlled by 1 -α F T : invisible when the lens stands still, it becomes more and more apparent as the lens moves faster, and conversely. This indicator was added as a result of a pilot study: we discovered that feedback, in the context view, of the position and size of the region to be magnified helped targeting objects more efficiently. The same type of indicator was then added to our version of the SPEED-COUPLED FLATTENING lens; in that case, the small circle expands and shrinks during lens movements, as its size directly depends on M M . This inherent instability makes it less convenient than its SPEED-COUPLED BLENDING counterpart, but it is still of great help when targeting an object.

BLENDING and SPEED-COUPLED BLENDING lenses are just two of several new interesting focus+context techniques that have been identified in the Sigma lens design space. The latter could actually be further extended to include other rendering techniques to achieve focus-context transitions, such as those based on multiblending [START_REF] Baudisch | Multiblending: displaying overlapping windows simultaneously without the drawbacks of alpha blending[END_REF], to highlight particular features of objects in the transition area. These are however still too computationally expensive to achieve acceptable frame rates on most personal computers, and are left as future work.

EXPERIMENT 1: FOCUS TARGETING PERFORMANCE

We conducted an experiment to compare the performance and limits of the three existing and two new lenses described in the previous section. Participants were asked to perform a simple task, namely focus targeting, which consists in putting a given target in the flat-top of the lens. Focus targeting is one of the building blocks of many higher-level navigation tasks such as searching [START_REF] Pietriga | Pointing and Beyond: an Operationalization and Preliminary Evaluation of Multi-scale Searching[END_REF].

Focus targeting performance was evaluated at five different magnification factors (M M ). Higher magnification factors make the task increasingly difficult: (i) the transition area becomes harder to understand as it must integrate a larger part of the world in the same rendering area, and (ii) it becomes harder to precisely position the target in the flat-top of the lens, the latter being controlled in the motor space of the context window. To test the limits of each lens, we included factors up to 14x.

Apparatus

We used a Dell Precision 380 equipped with a 3 GHz Pentium D processor, an NVidia Quadro FX4500 graphics card, a 1600 x 1200 LCD monitor (21") and a Dell optical mouse. The program was written in Java 1.6 using the open source ZVTM toolkit [START_REF] Pietriga | A Toolkit for Addressing HCI Issues in Visual Language Environments[END_REF] which offers a wide range of distortion lenses and could easily be extended to support translucenceand time-based transitions. The application was limited to a 1400 x 1200 window with a black padding of 100 pixels in order to accommodate instruction messages and simulate screen real-estate that would usually be taken by control and information widgets.

Participants

Ten unpaid adult volunteers (7 male, 3 female), from 23 to 40 year-old (average 26.4, median 25), all with normal or corrected to normal vision, served in the experiment.

Task and Procedure

Our focus targeting task consisted in acquiring a target in the flat-top of the lens as quick as possible. In our experimental setting, the lens was centered on the mouse cursor. The task ended when the participant clicked the left mouse button, provided that the target was fully contained within the flat-top. As focus targeting consists not only in correctly positioning the lens, but also in looking at the magnified target, additional conditions were imposed on some lenses to guarantee sufficient target visibility. The SPEED-COUPLED FLATTENING lens had to be magnifying enough (M M ≥ 60% of max. value), and the SPEED-COUPLED BLENDING lens had to be opaque enough (α F T ≥ 0.4). If all conditions were met when the participant clicked the mouse button for the first time, the targeting was counted as a hit, otherwise, as a miss. Each trial consisted in performing 24 successive focus targeting tasks. As illustrated in Figure 5, the targets were laid out in a circular manner. The order of appearance forced participants to perform focus targeting tasks in every direction, as recommended by the ISO9241-9 standard [START_REF] Iso | 9241-9 Ergonomic requirements for office work with visual display terminals (VDTs)-Part 9: Requirements for non-keyboard input devices[END_REF]. We decided to have only one target visible at a time, as we noticed during a pilot experiment in which all targets were visible that some participants were often taking advantage of the layout pattern to acquire the object set as the current target by positioning the lens relative to that object's siblings.

Our experiment was a 5 × 5 within-participant design: each participant had to perform several trials using each of the five lenses (Lens ∈ {MAGNIFYING GLASS, FISHEYE, BLENDING, SPEED-COUPLED FLATTENING, SPEED-COUPLED BLENDING}) with five different magnification factors (M M ∈ {2, 4, 6, 10, 14}). We grouped trials into five blocks, one per lens, so as not to disturb participants with too many changes between lenses. To avoid a non-controlled effect of order, we used a Latin square to compute five different orders of presentation for lenses and assigned two participants per order. Within a Lens block, each participant had to perform ten trials (i.e. 10 × 24 focus targeting tasks), 2 trials with each of the five different values of M M . Trials within a block were presented in a random order after a training phase containing 3 trials (M M = 2, 6 and 14), allowing participants to get familiar with a given lens before empirical measures were collected. The 24 targeting tasks of a trial 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 11500 actual focus targeting tasks were thus taken into account in the analysis. The experimenter first introduced the task, and then each lens immediately before the corresponding block, and made sure that participants did understand how each one worked and how best to operate it.

Predictions

We drew the following predictions based on each lens' properties, the results of previous studies and a theoretical analysis of the motor movements involved in focus targeting.

H 1 BLENDING lenses outperform FISHEYE lenses. Transitioning through space introduces distortion that makes objects move away from the approaching lens focus before moving toward it very fast, making focus targeting difficult [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF]. Translucence-based transitions used in BLENDING lenses have their own problems, with a negative impact on targeting performance, but these might not be as strong as that commonly associated with distortion.

H 2 SPEED-COUPLED FLATTENING and SPEED-COUPLED BLEND-ING lenses outperform all other lenses. Each focus targeting task can be divided into two phases: in the first phase, the user moves the lens quickly to reach the target's vicinity, while in the second phase, she moves it slowly to precisely position the target in the focus. In the first phase, the user is not interested in information provided in the focus region since she is trying to reach a distant object in the context as quick as possible. This hypothesis motivated the design of SPEED-COUPLED FLATTENING lenses and is supported by the results of the study conducted in [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF]: SPEED-COUPLED FLATTENING lenses outperform FISHEYE lenses when performing focus targeting tasks (SPEED-COUPLED FLATTENING ≥ FISH-EYE) 1 . Here, we hypothesize that no matter the transition dimensions involved, providing a detailed view during the first phase is of limited value and has a negative effect on performance, leading to the conclusion that smoothly and automatically neutralizing the focus and transition regions during this phase, and then restoring them, can help the user. This leads to the following partial order: SPEED-COUPLED FLATTEN-ING ≥ FISHEYE and SPEED-COUPLED BLENDING ≥ MAGNIFYING GLASS.

H 3 Focus targeting is easier with MAGNIFYING GLASS lenses and SPEED-COUPLED BLENDING lenses. From a pure motor perspective, the difficulty of a focus targeting task can be evaluated as a view pointing task in a fixed-scale interface [START_REF] Guiard | Target acquisition in multiscale electronic worlds[END_REF]. We can thus use Formula (1) in Figure 6 to quantify the difficulty of moving the lens' flat-top, of size W f ocus , to a position where it will contain the target, of size W target , initially located at a distance D from the lens' center. Formula (1) computes the Index of Difficulty, ID, of our focus targeting task. The lens' position in the context window is controlled in the visual and motor space of that window. W target , W f ocus and D are thus expressed in context pixels: in our experiment, W target = 8 pixels and D = 800 pixels, while W f ocus depends on a given Lens × M M condition: W f ocus = (2 × R I )/M M . As M M increases, the size of W f ocus decreases, making the task more difficult. For lenses of equal size (R O ), the size of the flat-top (R I ), and thus W f ocus , vary depending on the lens type. MAGNIFYING GLASS and SPEED-COUPLED BLENDING lenses are made of a flattop only: W f ocus = W lens = 200, while other lenses have to accommodate the transition within the same overall area: W f ocus = W lens /2 = 100 in our implementation. MAGNIFY-ING GLASS and SPEED-COUPLED BLENDING thus feature a larger flat-top than other lenses with the same overall size, consequently making focus targeting easier from a motor perspective: ID ranges from 3.2 to 6.3 for MAGNIFYING GLASS and SPEED-COUPLED BLENDING while it ranges from 4.2 to 8 for FISHEYE, SPEED-COUPLED FLATTENING and BLENDING. This reasoning however does not take into account non-motor aspects of the task which also depend on the type of lens used. For instance, occlusion caused by the always-opaque MAG-NIFYING GLASS should increasingly hinder performance in the second phase of the task (precise positioning) as M M gets bigger: W f ocus becomes smaller while W lens remains constant, making the occlusion zone between focus and context on the path to the target larger, along with the chances of losing track of the target.

Altogether, these three hypotheses only provide a partial order of performance between the five lenses. One strong expectation is that the SPEED-COUPLED BLENDING lens will perform efficiently as it addresses many issues: it does not distort the representation, the dynamically controlled translucent flat-top reduces occlusion problems, and its large size makes the task easier from a motor perspective.

Results and Discussion

Analysis of variance revealed a significant simple effect on number of errors (miss) for M M (F 4,36 = 46, p < 0.0001), for Lens (F 4,36 = 6, p < 0.0001), and a significant interaction effect on number of errors for Lens × M M (F 16,144 = 4, p < 0.0001). As the mean number of errors for each lens and the total number of errors are low (from 0.05 for BLEND-ING to 0.02 for MAGNIFYING GLASS for a total of 380 misses, about 3%), we focus the following analyses on hits only. We verified that there was no effect of lens presentation order on time and observed that learning effects were not significant for each lens. We observed a significant simple effect on time for Lens (F 4,36 = 66, p < 0.0001). Tukey post hoc tests revealed that SPEED-COUPLED BLENDING is the fastest lens and SPEED-COUPLED BLENDING the slowest, while BLENDING, FISHEYE and SPEED-COUPLED FLATTENING do not significantly differ in terms of performance. We also observed a significant simple effect on time for M M (F 4,36 = 648, p < 0.0001) and a significant interaction effect on time for Lens × M M (F 16,144 = 88, p < 0.0001). Figure 7 illustrates these results.

As expected, SPEED-COUPLED BLENDING performs better than all other lenses. Other predictions are only partially supported by the measures we collected. First, H 1 is not supported. Our results reveal that FISHEYE BLENDING. Eliminating distortion by switching from a spatial transition to a smooth translucence-based transition does not seem to provide an advantage. Feedback collected from participants leads us to believe that this might be due to the high cognitive effort required to comprehend transitions based on gradually increasing translucence which, as opposed to distortionbased transitions, do not rely on a familiar physical metaphor. H 2 is partially supported: (i) smoothly neutralizing and restoring the focus of a MAGNIFYING GLASS by making it translucent (α F T as a function of lens speed) does improve performance (SPEED-COUPLED BLENDING > MAGNIFYING GLASS); but (ii) flattening a fisheye (M M as a function of lens speed) does not yield a significant improvement over FISHEYE (SPEED-COUPLED FLATTENING FISHEYE). This last result is surprising since the study reported in [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF] showed that SPEED-COUPLED FLATTENING outperfoms FISHEYE for a distortion level of 5 (i.e., M M = 6). This inconsistency can be explained by taking a closer look at implementation details. First, we implemented SPEED-COUPLED FLATTENING as a constrained lens while it was implemented as a full-screen lens by Gutwin. In full-screen lenses, distortion affects the whole representation, which thus benefits more from the neutralization effect than constrained lenses that only affect a limited area. Second, as we require that M M ≥ 60% of max. value to end a trial, our task is a little bit longer than the one described in [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF] in the SPEED-COUPLED FLATTENING condition, whereas this constraint does not exist in the FISHEYE condition. Finally, H 3 is supported: SPEED-COUPLED BLENDING, with its large flat-top, outperforms all other lenses starting at M M = 4. Conversely the performance of MAGNIFYING GLASS goes down rapidly as M M gets higher. It becomes the worst lens starting at M M = 6, due to the earlier-mentioned negative effects of occlusion that make precise positioning difficult. It is interesting to note that for the lowest value of M M , MAGNIFYING GLASS outperforms all other lenses. Occlusion caused by the lens' opacity still causes the user to temporarily loose track of the target. But the occlusion zone is small at such low magnification. The negative impact of occlusion on performance is thus not significant compared to the positive impact of the larger flat top. Compared to SPEED-COUPLED BLENDING, MAGNIFYING GLASS also has the advantage of not requiring the user to wait several hundred milliseconds for the flat top to become opaque enough. In the particular case of very low magnification factors (M M ≤ 2), MAGNIFY-ING GLASS should thus be considered by interface designers.

Participants

Six unpaid adult volunteers (5 male, 1 female), from 23 to 40 year-old (average 27.8, median 25.5), all with normal or corrected to normal vision, served in the experiment.

Task and Procedure

The focus targeting task was exactly the same as the one used in Experiment 1. To reduce the length of this experiment, we picked two representative magnification factors: M M ∈ {8, 12}. This experiment was thus a 3 × 2 withinparticipant design. We again grouped trials by lens type. We used a Latin square to compute three different presentation orders for lenses and assigned two participants per order. Each participant performed three Lens blocks. Within a block, each participant had to perform two trials (i.e., 2 × 24 focus targeting tasks), one trial per value of M M . For a given lens presentation order, one participant saw trials in order M M = 8 then M M = 12, while the other one saw trials in order M M = 12 then M M = 8. Each block began with a two-trial training phase, one per value of M M .

Results and Discussion

Analysis of variance revealed a simple effect of T echnique on time (F 2,10 = 53, p < 0.0001), a simple effect of M M on time (F 1,5 = 230, p < 0.0001), and an interaction effect of T echnique × M M on time (F 2,10 = 8, p < 0.0001).

Tukey post hoc tests revealed the following lens performance order: SPEED-C. BLENDING > SPEED-C. BLENDING small > SPEED-C. FLATTENING, as illustrated in Figure 8. These results show that even at the same level of motor difficulty (i.e., with equal flat-top sizes), the SPEED-COUPLED BLENDING lens still performs better than the SPEED-COUPLED FLATTENING lens. This means that interface designers are given several options to improve upon a classical lens such as FISHEYE: 1) they can either get a smaller but more efficient lens (in terms of focus targeting performance), saving screen real-estate for the context, 2) if the latter is not critical they can make the SPEED-COUPLED BLENDING lens occupy the same space as a FISHEYE would, further improving focus targeting performance, or 3) find a balance between these two solutions.

EXPERIMENT 3: INFLUENCE OF TARGET VISIBILITY

Translucence can affect targeting performance [START_REF] Gutwin | The effects of dynamic transparency on targeting performance[END_REF], especially when targets are superimposed on a complex background such as a map or photograph. As the simple abstract world we used in the first two experiments might have hidden negative effects of translucence on lenses, we conducted a third experiment to check whether our comparative lens performance ordering was still valid when targeting objects that blend into a realistic background. Apparatus was the same as before.

Participants

Eight unpaid adult volunteers (6 male, 2 female), from 23-28 years (avg. 24.7, med. 24.5), all with normal or corrected to normal vision, no color blindness, served in the experiment.

Task and Procedure

The task was essentially the same as before, except for the fact that the 24 targets were laid out on a satellite photograph (Figure 9), and could either be filled with a fully opaque red color (α = 1.0) or with a translucent red (α = 0.5), in which case they blended into the background and were less easily identifiable. The satellite photograph was a 7000x5000 pixels portion of NASA's Blue Marble Next Generation world map [START_REF] Stockli | The Blue Marble Next Generation -A true color earth dataset including seasonal dynamics from MODIS[END_REF], providing appropriate levels of detail in both the focus and context regions. To limit the length of this ex-periment, we discarded the poorly performing MAGNIFYING GLASS and picked only two representative magnification factors (M M ∈ {8, 12}). This experiment was thus a 4 Lens× 2 M M × 2 Opacity within-participant design. Trials were again grouped by lens type. Participants performed four blocks which were presented in four varying orders computed through a Latin square. Each block was made of four trials (i.e., 4 × 24 focus targeting tasks), one per randomly distributed Opacity × M M condition, and was preceded with a training phase of two trials (M M = 8, Opacity = 1 and M M = 12, Opacity = 0.5). As we were mainly interested in the effect of target visibility on the ending phase of our focus targeting task, we added two visual hints to help participants find the next target's location in the context, so as to control and reduce the associated visual search time as much as possible: 1) after a successful targeting, the next target appeared and its border flashed white for one second; 2) four red bars were located on the four edges of the context window (indicated by black arrows in Figure 9-a) so that the target was at their virtual intersection.

Results and Discussion

Results were consistent with that of previous experiments, and matched participants' subjective preferences. Analysis of variance revealed a simple effect of T echnique on time (F 3,21 = 56, p < 0.0001), a simple effect of M M on time (F 1,7 = 212, p < 0.0001), and an interaction effect of T echnique × M M on time (F 3,21 = 12, p < 0.0001).

Our initial performance ordering was preserved. The only difference was that SPEED-COUPLED FLATTENING significantly outperformed FISHEYE (Figure 10). We tentatively attribute this higher significance to the more disturbing effects of distortion during lens movements on a complex background, to be confirmed by further evaluations.

Regarding the specific effect of target visibility, we found a simple effect of Opacity on time (F 1,7 = 14, p = 0.007), and an interaction effect of T echnique × Opacity on time (F 3,21 = 6, p = 0.005), confirming that lens performance does depend on this factor. However, Tukey HSD post hoc tests revealed that conditions Opacity = 0.5 and Opacity = 1 were in two different groups only for the BLENDING lens. This result is not unexpected as the BLENDING lens can be prone to visual interference between focus and context in the transition region depending on the nature of the representation, especially when non-contrasted objects are targeted.

No matter how aesthetically pleasing (several participants noted that it produced very nice graphical renderings), the BLENDING lens suffers from its earlier-mentioned lack of reliance on a familiar physical metaphor, and proneness to visual interference in the transition region. The SPEED-COUPLED BLENDING lens, however, does not suffer from these problems, as its use of translucence is very different: it can be seen as a magnifying glass whose content smoothly fades out to prevent occlusion at focus targeting time.

CONCLUSION

Sigma lenses form a rich and unified design space which includes a wide range of constrained lenses, from those that transition between focus and context through the spatial di- mension only, to new ones that achieve this transition using a combination of up to three dimensions among space, time, and translucence. We compared two such new lenses with three representatives of the first category using a focus targeting task. Empirical data revealed that our new SPEED-COUPLED BLENDING lens outperforms all other lenses. These results encourage us to further investigate the use of non-spatial dimensions to transition between focus and context. First and foremost, the exploration of our design space has revealed several potentially interesting new lenses, based on innovative combinations of space and translucence, on the coupling of lens speed with properties such as its radii, or on the use of time-based functions other than lens speed. Secondly, we have seen that, depending on the lens and task studied, non-motor aspects can have a significant influence on performance, e.g., flat-top size and legibility, occlusion and search (depending on layout). We thus plan to formally evaluate lenses based on a wider range of tasks, including high-level cognitive ones.

Figure 1 .

 1 Figure 1. Various transitions between focus and context: (a) step transition causing occlusion, (b) distorting space, (c) using gradually increasing translucence, (d) using a combination of translucence and time.

Figures 2

 2 Figures 2 illustrates these definitions using a distortion lens applied to a scene made of a series of equal-size rectangles that form a regular color spectrum. The context viewing window corresponds to what is seen in the absence of any lens. If it is positioned at s on scale axis v, the focus viewing window is necessarily positioned at s • M M . Points A and B represent the boundaries of the constrained lens within the context viewing window, at a distance R O from the lens' center C. The focus viewing window is then a flat magnification by a factor of M M of the region delimited by A and B. Its size is thus 2 • M M •R O . R I controls the size of the lens' flat-top. If R I = R O , the lens is a mere magnifier lens (or magnifying glass) as illustrated in Figure 1-a. If R I is zero, the flat-top is reduced to a single point at the center of the lens, which is then the only point at full magnification.

Figure 2 .

 2 Figure 2. Gaussian distortion lens in a 1+1D space-scale diagram, and corresponding 2D rendering.

Figure 3 .

 3 Figure 3. Blending lens in a 1+1D space-scale diagram, and corresponding 2D rendering.

  -a, consists only of a flat-top (R O = R I ) which occludes the immediate surroundings of the magnified region. FISHEYE denotes the common graphical fisheye lens. Here we use a Gaussian drop-off function to transition, through space only, between focus and context (Figures 1-b and 2). The SPEED-COUPLED FLATTENING lens is a variation on the one introduced by Gutwin [11], applied here to constrained lenses. It uses a simple interpolated low-pass filter inspired by the one of trailing widgets [8] as a time-based function to control the magnification factor based on the lens' velocity and acceleration.

Figure 4 .

 4 Figure 4. Speed-Coupled Blending Lens moving from left to right over time.

Figure 5 .

 5 Figure 5. Exp. 1 & 2: Targets' order of appearance in a trial (targets have been made twice their actual relative size for legibility purposes).

Figure 6 .

 6 Figure 6. Focus Targeting Task in a space scale diagram.

1 SCBFigure 7 .

 17 Figure 7. Mean completion time per T echnique × M M condition.

2 Figure 8 .

 28 Figure 8. Mean completion time per M M × T echnique condition.

Figure 9 .

 9 Figure 9. Exp. 3: targets are laid out radially (a), and can be either easily distinguished from the background (b), or blend into it (c).

3 Figure 10 .

 310 Figure 10. Mean completion time per Opacity ×T echnique condition.

Table 1 .

 1 Properties of existing and new lenses in the design space of time, and we plan to investigate other functions in future work.

		MAGNIF.	FISHEYE	SPEED-C.	BLENDING SPEED-C.
		GLASS		FLAT.		BLEND.
	Magnif.	M M	M M	M M •F(t) M M	M M
	Factor
	Spatial	step	Gaussian Gaussian	step	step
	drop-off	function			function	function
	α F T	1.0	1.0	1.0	α	α • F(t)
	Blending	step	step	step	Gaussian step
	drop-off	function	function	function		function

Acknowledgements

We wish to thank Olivier Bau, Michel Beaudouin-Lafon, Olivier Chapuis, Andy Cockburn, as well as Sheelagh Carpendale, Yves Guiard, Gonzalo Ramos, Dan Vogel, and the anonymous reviewers for their feedback.


Emmanuel Pietriga
email: emmanuel.pietriga@inria.fr

Caroline Appert
email: appert@lri.fr

Michel Beaudouin-Lafon

Pointing and Beyond: an Operationalization and Preliminary Evaluation of Multi-scale Searching

Keywords: Multi-scale interfaces, Searching task, Controlled Experiment, Focus + Context, Overview + Detail, Zoom ACM Classification H. Information Systems H.5 Information Interfaces and Presentation H.5.2 User Interfaces (H.1.2, I.3.6)

A number of experimental studies based on domain-specific tasks have evaluated the efficiency of navigation techniques for searching multi-scale worlds. The discrepancies among their results call for a more generic framework similar in spirit to Fitts' reciprocal pointing task, but adapted to a task that significantly differs from pure pointing. We introduce such a framework based on an abstract task and evaluate how four multi-scale navigation techniques perform in one particular multi-scale world configuration. Experimental findings indicate that, in this context, pan & zoom combined with an overview is the most efficient technique of all four, and that focus + context techniques perform better than classical pan & zoom. We relate these findings to more realistic situations, discuss their applicability, and how the framework can be used to cover a broad range of situations.

INTRODUCTION

Multi-scale interfaces (also called Zoomable User Interfaces or ZUIs) have generated a growing interest over the past decade as a powerful way of representing, navigating and manipulating large sets of data. A number of multi-scale navigation techniques have been designed and implemented, ranging from the original pan & zoom [START_REF] Perlin | Pad: an alternative approach to the computer interface[END_REF] to various fo-cus+context techniques [START_REF] Card | Readings in information visualization: using vision to think[END_REF][START_REF] Carpendale | A framework for unifying presentation space[END_REF][START_REF] Ware | The DragMag image magnifier[END_REF]. Up until now, the efficiency of these techniques has been evaluated with two kinds of experimental studies: usability studies based on domainspecific tasks and controlled experiments based on multiscale versions of Fitts' pointing paradigm.

The usability studies that relied on domain-specific tasks such as searching for items on geographical maps [START_REF] Hornbaek | Navigation patterns and usability of zoomable user interfaces with and without an overview[END_REF], comparing hierarchical data structures [START_REF] Nekrasovski | An evaluation of pan & zoom and rubber sheet navigation with and without an overview[END_REF], or reading textual documents [START_REF] Hornbaek | Reading of electronic documents: the usability of linear, fisheye, and overview+detail interfaces[END_REF] have typically produced inconclusive and sometimes contradictory results. More precisely, experimental findings varied from experiment to experiment, but since application domains varied dramatically, neither these findings can be compared nor generalized. Such results are to be expected since the performance of a given technique is indeed dependent on its context of use [START_REF] Appert | Context matters: Evaluating interaction techniques with the CIS model[END_REF].

A better understanding of the fundamental aspects of multiscale navigation could help explain -or even predict -such results, therefore saving valuable time and allowing better exploration of novel techniques. Fitts' pointing paradigm provides such a fundamental tool for exploring and understanding the elementary task of reaching a known target as fast as possible. Originally devised to study pointing in the real world [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF], it has been used repeatedly in HCI for evaluating a variety of pointing techniques and devices [START_REF] Balakrishnan | Beating" Fitts' law: virtual enhancements for pointing facilitation[END_REF][START_REF] Appert | OrthoZoom scroller: 1D multi-scale navigation[END_REF][START_REF] Ramos | Zliding: fluid zooming and sliding for high precision parameter manipulation[END_REF]. Fitts' law has proven remarkably robust, to the point of being used as part of an ISO standard for pointing devices [START_REF] Soukoreff | Towards a standard for pointing device evaluation, perspectives on 27 years of fitts' law research in hci[END_REF]. Fitts' pointing task has also been used with multi-scale interfaces and it has been shown that Fitts' law still applies for pointing targets with pan & zoom [START_REF] Guiard | Target acquisition in multiscale electronic worlds[END_REF]. In particular, it has been shown that Fitts' paradigm could address navigation, not just pointing, in interfaces that require scrolling [START_REF] Hinckley | Quantitative analysis of scrolling techniques[END_REF] or zooming [START_REF] Guiard | Target acquisition in multiscale electronic worlds[END_REF]. While Fitts' pointing paradigm is very powerful, it models a very specific task: that of reaching a target whose location is known to the user. However, this scenario only captures one of several navigation tasks in multi-scale worlds. Users might only have partial information about the target's location and appearance, thus requiring them to search for potential targets and get more details about each one until the actual target is identified. Consider for example a user searching for Brisbane on a multi-scale world map, only knowing that it is a large Australian city. The strategy first consists in zooming towards Australia to then inspect each large city one by one, zooming in to discover that it is not the right one, zooming out, maybe as far as the whole continent, and zooming in to the next potential target until the right city is found. Exploring large spaces in search of a particular target differs from pure pointing, as it requires users to perform additional motor actions to identify the target.

In the same way as Fitts' reciprocal pointing task operationalizes the task of reaching a known target, we propose in this paper to operationalize the above search task in a way that is easily amenable to controlled experiments. We then evaluate how four multi-scale navigation techniques perform in one particular configuration of a multi-scale world: classical pan & zoom, overview + detail, and two focus + context techniques, namely distortion (graphical fisheye) lenses and a variation on the DragMag image magnifier which, to the best of our knowledge, has not yet been evaluated. Our results indicate that in this context overview + detail outperforms the other three, and that the two focus + context techniques outperform classical pan & zoom. However, this multi-scale world configuration is only one particular case in a range of situations. We discuss the limits of this preliminary study, describe the design space that is covered by our abstract search task and present an environment that we have developed to help explore this design space.

RELATED WORK

A number of experimental studies have compared the performance of different multi-scale navigation techniques and have reported contrasted results. Classical pan & zoom was compared with fisheye and overview + detail on high-level cognitive tasks involving electronic documents [START_REF] Hornbaek | Reading of electronic documents: the usability of linear, fisheye, and overview+detail interfaces[END_REF]: writing an essay after having explored a document, and finding answers to questions within that document. Classical pan & zoom was the least efficient technique; participants read faster using the fisheye; they wrote better essays using the overview + detail, but took more time to answer questions. In North and Shneiderman's experiment [START_REF] North | Snap-together visualization: a user interface for coordinating visualizations via relational schemata[END_REF], participants had to browse the database of U.S. states and counties to answer questions using a detail-only scrollable interface or an overview + detail interface. The overview + detail interface outperformed the detail-only interface by 30-80% depending on the task. However, in another study [START_REF] Nekrasovski | An evaluation of pan & zoom and rubber sheet navigation with and without an overview[END_REF], pan & zoom or overview + detail were not significantly different when participants had to navigate a large node-link representation and make topological comparisons. On the contrary, Hornbaeck et al. [START_REF] Hornbaek | Navigation patterns and usability of zoomable user interfaces with and without an overview[END_REF] have reported that their overview + detail interface was more efficient than pan & zoom. This, however, was true for only one of the two geographical maps that participants had to explore in their experiment.

The findings of these experiments show that the use of domain-dependent tasks makes it difficult to get consistent results that can be generalized, even more so when they require a significant amount of cognitive effort from the participants. Identifying and isolating lower-level, domain-independent tasks can help reach more generalizable results. From a motor perspective, one recurring task performed by users of multi-scale interfaces is to search for targets among sets of objects by navigating through space and scale. This article describes an experimental setup for the controlled evaluation of various interaction techniques considered as appropriate for the task of searching a multi-scale world.

OPERATIONALIZING MULTI-SCALE SEARCHING

Studying a task through a controlled experiment requires operationalizing it, i.e., defining it as a function of variables of interest (independent variables) that researchers can act upon to collect measures (dependent variables). The pointing task is a well-known example in the field of HCI, initially operationalized in psychology by Fitts [START_REF] Fitts | The information capacity of the human motor system in controlling the amplitude of movement[END_REF]: to study the performance of pointing techniques, researchers act on the index of difficulty (ID) variable and measure the movement time on a reciprocal pointing task. We seek to operationalize multi-scale searching in a similar way. In a multi-scale world, users navigate and look at objects until they find the target. Users have to navigate in both space and scale to a position that reveals enough details about each object, in order to decide whether it is the target or a distractor. Initially, users make a blind choice of a "potential target" at a high scale and navigate to it to acquire enough information. If it is a distractor, they have to navigate to another object, typically by zooming-out, panning, then zooming-in [START_REF] Guiard | Target acquisition in multiscale electronic worlds[END_REF].

Since we are interested in studying the performance in time and error rate to find a target according to the required "quantity" of exploration from a purely motor perspective, we abstract the representation from any semantic or topological relationship among objects that could help participants identify the target in an uncontrolled manner (for instance, having reasonable knowledge of the geography of Russia could help locate Saint Petersburg once Moscow has been found on a map, or knowing that Chicago is on the shores of lake Michigan would reduce the area to be explored significantly). To quantify exploration, our experimental setup consists of a multi-scale world containing a set of n objects, one of them being the target and the others distractors. We define the "quantity" of exploration as the number k of distractors that users have to visit before finding the target: the larger the number of visited distractors, the larger the quantity of exploration. k is probabilistically dependent on n: the larger the number of objects, the higher the probability of having a large number of objects to visit before reaching the target. We control this parameter by forcing participants to visit a predefined number of objects before finding the target; if we chose a priori which object is the target, participants could find it immediately by chance, or on the contrary they could spend a lot of time searching for it, and this uncontrolled factor would have a significant impact on our measurements. We design our experiment to ensure that the target is the k th object visited, no matter the order of exploration chosen by each participant. The system thus has to know i) when objects are seen by the participant, and ii) whether or not enough detail is displayed about these objects in order to differentiate the target from distractors. Making the system aware of these two pieces of information in a fully reliable manner requires answering the following two questions:

• What minimal scale provides enough information? This depends on visual acuity, which is user-dependent.

• In which region of the screen and for how long should an object be displayed to consider it seen? Assuming that the user visually scans the whole screen is too strong an hypothesis, and probably an unfounded one. Also, if only part of an object is in the viewport, the system cannot know for sure whether or not the user has seen it.

The gray area in the current viewport marks the position of the secondary view window. We address these problems as follows. First, we set a minimum scale (minScale) at which the user can collect enough information to detect a target: all objects seem identical except for the target, which reveals a different piece of information when displayed at or above minScale. In order to avoid differences among participants, all objects are displayed identically at all scales until the user explicitly asks to reveal the disambiguating piece of information. This explicit "unveiling" action is available only when the scale is minScale or more. Second, we make sure that the user cannot reveal several objects simultaneously. Once an object has been revealed, the user has to process the information and, provided that the object is the target, take an additional explicit action to tell the system that this object is the target.

While we cannot be sure that participants actually look at targets when unveiling them, it is in their own interest to do so in order to perform the search task as fast as possible. Therefore we believe that this design operationalizes a realistic search task without having to use more complex devices such as eye trackers. Before presenting a first experiment based on this task, we introduce the multi-scale navigation techniques that we have tested.

MULTI-SCALE INTERACTION TECHNIQUES

Many representation and navigation techniques have been proposed to interact with multi-scale worlds, some being variations on others. For our study, we narrowed down the possibilities to four techniques, chosen to be representative of the most widespread and/or efficient techniques currently available. Figure 1 illustrates these techniques using spacescale diagrams [START_REF] Furnas | Space-scale diagrams: understanding multiscale interfaces[END_REF].

The first technique is the classical Pan & Zoom (Figure 1a). In order to get more detail about specific elements of the representation, users have to move the entire viewport both in space and scale, respectively by panning and zooming. No contextual information is provided; this method is therefore prone to user disorientation.

One way to address disorientation consists in using overview + detail techniques. One such technique, Pan & Zoom + Overview (Figure 1-b), enhances classical Pan & Zoom by providing users with an inset containing a representation of the region surrounding the area currently seen in the main viewport at a lower scale. The overview is located inside the main viewport, typically in one of the four corners. The goal is to minimize the visual interference caused by occlusion of the elements in focus, but this introduces the problem of divided attention [START_REF] Posner | The attention system of the human brain[END_REF].

In overview + detail representations, more screen real-estate is dedicated to the focus than to the context. Conversely, focus + context techniques allocate more screen real-estate to the context than to the focus. We selected two techniques that we consider relevant to the multi-scale searching task: constrained distortion lenses [START_REF] Carpendale | A framework for unifying presentation space[END_REF] and a variation on the original DragMag Image Magnifier [START_REF] Ware | The DragMag image magnifier[END_REF]. Constrained distortion lenses (Figure 1-c) provide a detailin-context representation through the local magnification of a region of the screen (the focus of attention). This focus region is integrated in the surrounding context by distorting the representation in the transition region. The distortion is defined by a drop-off function (see [START_REF] Carpendale | A framework for unifying presentation space[END_REF] for more details).

We chose a Gaussian profile as it provides a smooth transition between focus and distortion, and between distortion and context. Our lens also features a flat top because many tasks require the focal region not to be distorted [START_REF] Carpendale | Making distortions comprehensible[END_REF]. The in situ magnification of these lenses solves the problem of divided attention but introduces a distortion that can cause recognition problems.

The DragMag (Figure 1-d) can be considered a special case of fisheye lens often called Manhattan lens, featuring a perpendicular drop-off function. There is no region between the focus and the context, but as a result the region immediately surrounding the focus is occluded. To address this issue, the focus region is translated by a usercontrolled offset (du in Figure 1-d). This results in the occlusion of another region of the context, which is often considered less important than the immediate surroundings of the focus. However, this reintroduces the problem of divided attention encountered with overview + detail representations, and the occlusion can be more cumbersome to handle than with the overview.

EXPERIMENT

We conducted a 4x9 within-subject controlled experiment to compare the efficiency of these four techniques on one instantiation of the multi-scale search task introduced earlier.

Task

The task consisted in finding a target among a set of objects as quick as possible while minimizing the number of errors.

The virtual scene contained nine light gray squares organized into a 3x3 grid layout and embedded inside a large, darker gray square. We used a grid layout so participants would easily know where the potential targets were. This regular layout also prevented performance to be biased by uneven traveled distances between trials of the same rank k.

A dark red grid was superimposed on the display in order to minimize desert-fog [START_REF] Jul | Critical zones in desert fog: Aids to multiscale navigation[END_REF] (see Figure 2-b). The grid was adaptive to scale, i.e., new grid lines would fade in when zooming in and some grid lines would fade out when zooming out so that the display would always contain a reasonable number of grid lines. All nine objects had square corners except for the target which had rounded corners. The rounded corners could only be seen when the target was displayed at a large enough scale, called minScale (Figure 3). Participants thus had to zoom in onto each square in order to find out whether it was the actual target or not. Zooming in was not sufficient however: once minScale was reached, a black border was displayed around the square in focus. Participants could then use the space bar to unveil the object: this would permanently reveal whether the object was the target (round corners) or not. Note that this "unveiling" step does not affect the ecological validity of our task since it penalizes all techniques equally.

Figure 2 shows a storyboard of the task: participants started each trial by pressing a button located at the center of the screen (Figure 2-a). The view was initialized so that the region containing potential targets (dark gray area) was not centered on the screen, requiring participants to reach the region by panning and zooming. The goal was both to better simulate a multi-scale navigation & search task and to avoid a learning effect with respect to the participant's initial move. Participants had to navigate to that region (Figure 2-b) and then inspect each object more closely by magnifying it using the current navigation technique (Figure 2-c).

Participants were allowed to zoom-in further, but zooming in too far would have the object fill the display and make it impossible to find out if it was the target. Once minScale was reached for an object, participants could unveil that object by pressing the space bar. The object's border flashed green for 400 milliseconds, informing the participant that the object had actually been unveiled. If the object's corners remained square, this meant that the object was not the target and participants had to navigate to the next potential target using the current navigation technique. If, on the contrary, the object's Participants were instructed to go as fast as possible to complete a trial (i.e., between hitting the Continue button and hitting F1), but they were allowed to rest between successive trials. They were also instructed to minimize the number of visits to the same object and the number of misses, i.e., hitting F1 when the object was not the target. Such misses terminated the trial and were counted as errors.

Techniques

The first independent variable we manipulated in our experiment was the technique. The first technique was pan & zoom (PZ). Participants could pan the view by moving the mouse while holding the left mouse button, and zoom in/out by rotating the mouse wheel. These three degrees of freedom could be controlled simultaneously. The magnification factor per wheel step was tuned so as to get an average zooming speed of 8x per second, as advocated in [START_REF] Hornbaek | Navigation patterns and usability of zoomable user interfaces with and without an overview[END_REF]. With this technique, participants panned & zoomed the entire view to get enough details about each object. Each of the other three techniques allowed participants to pan & zoom using the above commands.

The second technique was overview + detail (OD). The region seen through the main viewport was represented by a bright green rectangle in the inset containing the overview (see Figure 4-a). This rectangle could be dragged, resulting in changing the content of the main viewport. With these additional two degrees of freedom, participants could do finegrain panning in the main viewport and coarse-grain panning in the overview. The representation in the overview was dynamic: it was not necessarily showing all objects in the virtual world, as it followed the camera associated with the detailed view in space and scale when the scale difference between the overview and the detailed view was larger than a factor of 24. The overview implemented by Google Maps1 demonstrates such a behavior.

The third technique featured a constrained distortion lens, also called graphical fisheye lens (FL). It allowed for magnification of the region around the mouse cursor (see Figure 4-b). We used a 100-pixel radial lens defined by a Gaussian drop-off function and the L(2) distance metric [START_REF] Carpendale | A framework for unifying presentation space[END_REF] with a 60pixel radius flat top. The lens was not activated at the start of a trial. Participants could activate it by clicking the left mouse button, and deactivate it by clicking the right mouse button. The lens was always centered on the mouse cursor. When the lens was active, participants were still able to pan the context by dragging outside the lens with the left mouse button. The default magnification factor within the flat top was set to 4 times the scale factor of the context (the scale factor in the lens focus is always defined relative to that of the context, since the context can itself be panned and zoomed). Participants could change the lens' magnification by using the mouse wheel, within the limits of twice and twelve times the scale factor of the context. This technique therefore featured five degrees of freedom (2D panning of context, 2D panning of lens focus, and either the lens magnification factor or the context scale factor depending on whether the lens is active or not). Lens activation and deactivation were both animated by smoothly increasing the lens' magnification factor from 1.0 to its default value (4.0) over a period of 300 milliseconds for the sake of perceptual continuity [START_REF] Robertson | Information visualization using 3d interactive animation[END_REF]. The lens thus seemed to "emerge" from the flat surface when activated, and flatten itself when deactivated.

The last technique was inspired by the DragMag Image Magnifier (DM), but interaction with the windows differed significantly from the original prototypes [START_REF] Ware | The DragMag image magnifier[END_REF]. Figure 4-c shows the two windows composing the DragMag: the mag window outlines the region magnified in the zoom window.

Participants could activate and deactivate the DragMag by clicking on the right mouse button. The mag window would then appear centered around the mouse cursor, the zoom window being offset by a default distance of 200 pixels to the southeast of the mag window. As with the previous technique, both DragMag activation and deactivation were smoothly animated over a period of 300 milliseconds, with the zoom window "emerging" from the mag window. Participants could drag the mag region, thus changing the content of the zoom window; they could also drag "through" the zoom window for small scale adjustments, though this feature was not very useful in the context of the experiment.

Participants could also move the zoom window by dragging the thick bar at its top. This feature was useful to reveal objects occluded by the zoom window. The mouse wheel was used to control magnification. Operating the mouse wheel while the cursor was in the zoom window controlled that window's magnification factor. Operating the mouse wheel anywhere outside this window controlled the scale of the context. The technique therefore featured six degrees of freedom (the context scale factor and the zoom window magnification factor could both be controlled when the DragMag was active). The default magnification factor in the zoom window was 4 times the scale factor of the context, as for the distortion lens. The zoom window was not resizable.

For the purpose of comparing the techniques, the overview of OD, the lens of FL, and the zoom window of DM all used the same amount of screen real-estate: a 200 x 200 pixels region, which represented 4.5% of the total available display area.

Predictions

Our predictions were as follows:

• Time is linearly dependent on the rank k of the target. We hypothesized that, whatever the technique, the user has to navigate to inspect objects one by one and that each navigation incurs the same cost. Since the cost of revisiting an object is fairly high, we hypothesized that the number of revisits would be very small. Therefore the overall task completion time should be linearly dependent on the "quantity" of exploration, i.e., the target's rank k in the sequence of visited objects.

• Focus + Context (FL, DM) and Overview + Detail (OD) outperform classical Pan & Zoom (PZ). With PZ, navigating from one object to the next typically consists in zooming out to acquire the next object then zooming in and panning to magnify it. With DM, FL and OD, it simply consists in moving the focus onto the next object. Since the position of the focus can be controlled from the context, we hypothesized that the zoom-out/pan/zoom-in sequence of PZ would take more time than relocating the focus within the context.

• Overview + Detail (OD) outperforms Focus + Context (DM and FL). With OD, DM and FL, navigating from object a to object b consists in moving the focus from a to b. This movement can be seen as a pointing task. With DM and FL, pointing is achieved by relocating the focus (i.e., the DragMag window or the lens' focus region) while with OD, pointing is achieved by relocating the detailed view. According to Guiard et al. [START_REF] Guiard | View size and pointing difficulty in multi-scale navigation[END_REF], such pointing tasks are view pointing tasks whose Index of Difficulty depends on view size. Since the detailed view is significantly larger than the lens' focus and the DragMag's zoom window, we predicted that OD would outperform the two Focus + Context techniques (FL, DM).

Participants

Twelve unpaid adult volunteers, 11 males and 1 female, ranging from 23 to 52 years old (28 on average, with a median of 25.5), served in the experiment. Before starting, the experimenter checked that they could perceive the rounded corners at minScale, showing them squares with squared and rounded corners successively. The experiment was divided into four blocks, one block per technique. Before each block, participants were shown how to achieve the task using the corresponding technique. They were then asked to practice on randomly-chosen trials until they felt comfortable with the technique. The experimenter observed participants and encouraged them to keep practicing until they were familiar enough with the technique.

Apparatus

We used a Dell Precision 380 equipped with a 3 GHz Pentium D processor, an NVidia Quadro FX4500 graphics card, a 1280x1024 LCD monitor (19") and a Dell optical mouse with a scroll wheel. The program was written in Java 1.5 using the open source ZVTM toolkit [START_REF] Pietriga | A Toolkit for Addressing HCI Issues in Visual Language Environments[END_REF] which features a wide range of multi-scale interaction techniques, thanks to different types of portals [START_REF] Perlin | Pad: an alternative approach to the computer interface[END_REF] and arbitrary distortion lenses 2 .

The application was limited to a 1080x824 window with a black padding of 100 pixels in order to accommodate instruction messages and simulate screen real-estate that would usually be taken by control and information widgets.

Counterbalancing strategy

We used a 9x4 within-subject design: we tested 9 target ranks (k ∈ [1..9]) for the 4 techniques (PZ, FL, DM and OD), i.e., 9 * 4 = 36 conditions. Each condition was replicated 3 times so that each participant performed 9 * 4 * 3 = 108 trials (≈ 45 minutes). The initial position of the area containing the objects was different for each of these 3 replications and was counterbalanced among blocks with a Latin square. We grouped the trials into 4 blocks, one block per technique, to minimize negative skill transfers. To minimize ordering effects, we computed four different technique orders using a Latin square and composed 4 groups of 3 participants (G 1 , G 2 , G 3 , G 4 ), one group per ordering.

We also counterbalanced the presentation order of the different values of k within a block: we used a Latin square to compute 9 possible orders for presenting the values of k and concatenated 3 orders to compose a block (3 orders of 9 trials = 27 trials per block). Three block compositions (bc 1 , bc 2 , bc 3 ) were obtained through a Latin square. We mapped one block composition per participant within a group. Table 1 summarizes our counterbalancing strategy among participants. While we told participants that the target was selected randomly by the program, this was not, in fact, the case: instead, the program counted the objects being visited by the participant during the trial, and displayed the target when the k th object was unveiled by the participant. This allowed us to fully control the rank variable. Note that even if the participants had known (or guessed) the actual working of the program, this would not have given them any advantage.

G 1 G 2 G 3 G 4 bc 1 S 1 S 4 S

Results

For each trial, the program collected the completion time, whether it was a hit or a miss, the order of visit of each object and the time at which it was unveiled. It also logged cinematic data from the cameras associated with the focus and context viewports. We also collected the participants' preferences among the techniques in a post-hoc test.

For our analyses, we first removed 14 miss trials (about 1%) and then 31 outliers (about 2,5% of the hit trials). We verified that misses and outliers were randomly distributed across participants, techniques and ranks and that there was no effect of technique presentation order on time. Learning effects were not significant for PZ (p = 0.42) and FL (p = 0.75), and were significant but moderate for DM (p = 0.03) and OD (p = 0.02).

We isolated the rank variable (k) by analyzing it separately for each technique. We computed the linear regression of time relative to the rank, treating participants as a random variable. We obtained the high correlation coefficients listed in Table 2. This supports our first prediction: completion time is linearly dependent on the rank (see Figure 5-a).

As expected, the number of revisits was extremely low (less than 1 revisit on average for each technique) and participants optimized the order in which they visited the objects so as to minimize traveled distance. Most participants explored the objects following an S-shaped pattern, some used a spiral; very few made diagonal moves, except for one participant who adopted a very erratic search pattern across all blocks (his results were nevertheless consistent with our overall findings). Table 2 also reports slopes (a) and intercepts with the y-axis (b) for each linear regression. We note that the value of b is lower for PZ. The cinematic logs explain this difference: with DM, FL and OD, participants initially spent more time adjusting the scale and position in order to optimize their future interactions. good position of the context allows participants to only pan the detailed view through the overview or the focus from the context without having to adjust the scale.

Since we have evidence that time is linearly dependent on rank, we now analyze rank as a continuous factor. Analysis of variance with the REML method for repeated measures revealed a significant simple effect on time for rank, i.e. k, (F 1,411 = 1500.5, p < 0.0001), a significant simple effect on time for technique (F 3,411 = 91.6, p < 0.0001) and a significant interaction effect on time for rank * technique (F 3,411 = 54.2, p < 0.0001). Figure 5-b illustrates these results: the larger the rank, the larger the differences among techniques. Tukey post-hoc tests reveal that each technique is significantly different from the others: OD is the most efficient technique, followed by FL, then DM and finally PZ (OD > DM > F L > P Z). This supports our second and third predictions: the Overview + Detail technique outperforms the two Focus + Context techniques, which themselves outperform classical Pan & Zoom. We believe the lower performance of FL, compared with DM, could be due to the visual distortion introduced by the lens [START_REF] Gutwin | Improving focus targeting in interactive fisheye views[END_REF]. We note however that the difference between the means of these two techniques (F L mean = 18 s., DM mean = 17 s.) is much smaller than with the other two (OD mean = 14.8 s., P Z mean = 21.2 s.), as shown in Figure 5-c.

The subjective preferences we collected in the post-hoc questionnaire match these results. At the end of the experiment, participants were asked to rank the techniques according to their preference: 11 ranked PZ as the worst technique, and 9 ranked OD as the best technique.

DISCUSSION AND FUTURE WORK

The search task introduced in this article covers a range of situations where the user has to explore each potential target in a multi-scale environment. Unlike the tasks tested in us- ability studies, we focus on the motor and perceptual skills and try to exclude the cognitive skills involved in searching.

The goal is similar to that of Fitts' pointing paradigm and its use in HCI: to assess the limit performance of searching multi-scale worlds and to come up with predictive performance models and novel navigation techniques that improve multi-scale searching.

Our search task covers a large design space whose main dimensions are the amount of information the user has to acquire in order to decide which object is the target and the structure of the multi-scale world. Our experiment tested an extreme situation in this design space. First, the user had to look in detail at each target by navigating to it, therefore excluding the kind of visual search that occurs, e.g., in a Fitts' pointing task with distractors. Second, we used a specific configuration of the multi-scale world: a "small-world", i.e. an environment in which there exists at least one viewpoint from which all objects can be seen, that contained objects of the same relative size, i.e. same minScale, laid out uniformly on a grid. Therefore, the results reported in the previous section cannot be generalized to all search tasks and we need to devise a strategy to explore the design space and operationalize other situations.

Unfortunately, few theoretical models are available to help us structure this design space. While Guiard et al.'s degree of goal-directedness [START_REF] Guiard | Quantifying degree of goal directedness in document navigation: Application to the evaluation of the perspective-drag technique[END_REF] could help quantify the amount of information that users need to recognize a target and Furnas & Bederson's space-scale diagrams [START_REF] Furnas | Space-scale diagrams: understanding multiscale interfaces[END_REF] could help explore the structure of multi-scale worlds, neither approach is readily applicable to identify relevant points in this design space. Therefore we have developed an environment for testing re-alistic multi-scale navigation and searching tasks in order to inform our design process.

This environment (see Figure 6) displays a multi-scale version of NASA's Blue Marble Next Generation world map [START_REF] Stockli | The Blue Marble Next Generation -A true color earth dataset including seasonal dynamics from MODIS[END_REF] overlaid with geographical features such as countries, states, cities, parks and lakes. The map is 80000x40000 pixels at full resolution, or about 80x40 regular-size screens.

The geographical features can be any set of localized items found in the Geo-Names3 on-line database. The environment provides a set of navigation techniques, including those tested in the study reported in this article. A variant of this environment was used to run the experiment reported in the previous section. Both versions are implemented with the ZVTM toolkit [START_REF] Pietriga | A Toolkit for Addressing HCI Issues in Visual Language Environments[END_REF] and are publicly available 4 .

We conducted several pilot studies with this environment using a set of 1825 cities, 63 states and provinces, and 192 countries. Participants were asked to search for geographical features by locating first the country, then possibly the state or province and finally the city. Obviously, this task relies on cognitive skills such as the participant's geographical knowledge or contextual hints such as large water bodies. It was extremely useful however for observing users and collecting quantitative data and subjective evaluations and helped us identify interesting multi-scale world configurations.

For example, the configuration that we tested in the experiment described in the previous section corresponds to, e.g., finding a large city in Australia. Since there are only eight large cities spread over the whole continent (see Figure 7-a), the participant who does not know the geography of Australia has to zoom in onto each city. So the task consists in finding a city among a relatively small, well-identified, set of objects of the same relative size.

In this context, participants found the most useful technique to be Overview + Detail, followed by the constrained distortion lens and the DragMag. For the latter two, the commonly adopted search technique consisted in panning & zooming to make the entire continent fit the viewport (all cities could be seen from this altitude, though their names were not visible), and then activate a lens or DragMag to inspect the potential targets while keeping the context fixed. The same behavior was observed with the abstract task, as reported earlier. It is interesting to note however that the negative effects of distortion were less frequently mentioned for the geographical task than for the abstract task, probably because continuous representations such as world maps withstand distortion better than other types of representations, at least for searching.

Other observations of the participants' behavior with the geographical task have helped us identify situations that seem interesting for subsequent experiments. For instance, densely populated regions such as mainland Southeast Asia (see Fig- These behavior patterns lead us to hypothesize that Overview + Detail techniques work better when exploring dense regions while Focus + Context techniques are also efficient when searching for a target among a sparse set. This may be due to the fact that visual scanning plays an important role in the former case while motor actions take precedence over visual scanning in the latter, at least within the limits of the magnification factor of graphical fisheye lenses (usually 4 and rarely more than 8 [START_REF] Carpendale | Achieving higher magnification in context[END_REF]). Providing empirical evidence for this claim requires running more experiments within the framework by varying parameters such as density. Another area for future work is to test configurations in which objects have different minScale values, corresponding to situations where users have very limited information about the target, including the scale at which it is visible. Since such situations presumably prompt for more zooming actions than the one we tested, it is possible that the best navigation technique would be different.

SUMMARY

This paper has introduced a new framework based on an abstract searching task for multi-scale interfaces that operationalizes the situation where one has to look for the target before selecting it. We have used this framework to compare four multi-scale navigation techniques in the context of one specific multi-scale world configuration (small world, uniformly dense layout), showing that in this case a fixed overview afforded better performance than Focus + Context techniques and that traditional pan-and-zoom was the worst. These results cannot be immediately generalized to all multi-scale world configurations, and additional evaluations are required to cover a broader range of situations by varying parameters such as density, topology and the relative size of targets. Our framework allows for the systematic exploration of this design space. Moreover, the geographical environment we have developed can help identify interesting situations and formulate hypotheses about them. These situations can then easily be translated into configurations of the abstract task and tested with controlled experiments.

Figure 1 .

 1 Figure 1. Representation of multi-scale interaction techniques in space-scale diagrams.

Figure 2 .Figure 3 .

 23 Figure 2. Storyboard: (a) start of trial, (b) navigation to the set of objects, (c) inspection of an object (before unveiling), (d) after unveiling the targetv

Figure 4 .

 4 Figure 4. Unveiling an object with (a) pan-zoom + overview [OD], (b) a constrained distortion lens [FL], (c) a DragMag [DM]

Figure 5 .

 5 Figure 5. Fit lines for the four techniques (a), Interaction effects on time (in s) for rank * technique (b), Mean completion time per technique (c)

Figure 6 .

 6 Figure 6. Looking for Boston, Massachusetts, USA with a distortion lens on a multi-scale world map

Figure 7 .

 7 Figure 7. Exploring a sparse region with a drag-mag (a), and a dense region with an overview (b)

  ure 7-b), which feature many cities, were most commonly explored with the Overview + Detail technique because the main viewport can accommodate more cities at the scale where their names become readable (the equivalent of min-Scale defined in the abstract task), thus facilitating visual scanning.

Table 1 .

 1 7 S 10 bc 2 S 2 S 5 S 8 S 11 bc 3 S 3 S 6 S 9 S 12 Counterbalancing strategy for the 12 participants (S i ).

Table 2 .

 2 Correlation coefficients (r 2 ) and coefficients a and b (time = a * rank + b) for the four techniques.

	Indeed, with these techniques,

http://maps.google.com

The content of the lens is not a mere magnification of the original pixels, but an actual high-resolution separate rendering of the region seen through the lens, which provides more details. This mechanism also makes it possible to use semantic zooming inside the lens (see Figure6).

http://www.geonames.org

http://zvtm.sourceforge.net/eval/pb

Acknowledgements

We wish to thank the anonymous reviewers for their insightful reviews, as well as all the volunteers who participated in our experiments.