Meirav Taieb-Maimon
email: meiravta@bgu.ac.il

Lior Limonad
email: liorli@il.ibm.com

David Amid
email: davida@il.ibm.com

David Boaz
email: davidbo@il.ibm.com

Ateret Anaby-Tavor
email: atereta@il.ibm.com

Evaluating Multivariate Visualizations as Multi-Objective Decision Aids

Keywords: Multi-criterion decision making, Multivariate visualizations, Information Visualization, Usage experience evaluation

When choosing a solution, decision makers are often required to account for multiple conflicting objectives. This is a situation that can result in a potentially huge number of candidate solutions. Despite the wide selection of multivariate visualizations that can potentially help decide between various candidates, no designated means exist to assess the effectiveness of these visualizations under different circumstances. As a first contribution in this work, we developed a method to evaluate different types of multivariate visualization. The method focuses on the visualization's ability to facilitate a better understanding of inter-objective trade-offs as a proxy to more sensible decision making. We used the method to evaluate two existing visualization aids: Parallel-Coordinates and an adaptation of Self Organizing Maps (SOM). Both visualizations were compared with tabular data presentation. Our results show that the first visualization is more effective than a plain tabular visualization for the purpose of multi-objective decision making.

Introduction

There are many circumstances where a person has to decide among competing alternatives. From a consumer trying to choose the right car, house, or cell phone to a business executive who must decide upon a new portfolio of product offerings, and on to elected representative voting on national health policies-all of them must choose among multiple, often competing, alternatives. Many studies in the area of multicriterion decision making (MCDM) attempt to help decision-makers reach better conclusions in a more efficient way [START_REF] Köksalan | Multiple Criteria Decision Making: From Early History to the 21st Century[END_REF]. The multi-criterion decision making process typically examines various alternatives with respect to their values for each criterion.

In most practical scenarios, the number of options is too large to be examined by a human, and decision makers aspire to examine a limited set of options. Towards this end, the MCDM research community has identified two major challenges: (a) reducing the number of options by means of an optimization process that yields a smaller set of optimal solutions, termed Pareto Frontier [START_REF] Ehrgott | Multicriteria optimization[END_REF], and (b) effectively visualizing these solutions (namely, the solution space) to help users select the solutions that best satisfy their subjective criteria. The task of visualizing the Pareto Frontier is based upon multivariate visualization, and is generally considered a hard problem for more than three objectives [START_REF] Korhonen | Visualization in the multiple objective decision-making framework[END_REF].

The decision making process becomes even more challenging when some of the objectives being considered conflict with each other. In this conflicting relationship, the performance in one objective is seen to deteriorate as performance in another is improved. In such settings, actual choices should ideally reflect the tradeoffs that are in keeping with the decision maker's priorities. For example, given a certain budget, a person who travels frequently and wants to buy an new laptop would tend to give weight a higher priority over performance, while a "gamer" would aim for increased performance and settle for a heavier weight.

We distinguish between sensible and non-sensible choices. Sensible choices faithfully correspond to the decision-maker's subjective perception of inter-objective tradeoffs and non-sensible choices do not. According to Lotov et al. [START_REF] Lotov | Visualizing the Pareto frontier[END_REF], "Tradeoff information is extremely important for the decision maker since it helps to identify the most preferred point along the tradeoff curve." Hence, it is expected that the better the decision-maker's understanding of the various tradeoffs in the solution space, the more sensible their choices will be. Correspondingly, we introduce the following as an underlying premise: Assumption 1: A better understanding of the inter-objective conflicts results in more sensible decision making. Derived from the above assumption, our main objective in this work is to provide decision makers with a concrete means to improve the understanding of interobjective conflicts.

Ideally, identifying a sensible choice should rely on first discovering the perceived trade-offs the decision maker may have with regard to a given set of objectives [START_REF] Green | Conjoint analysis in consumer research: issues and outlook[END_REF][START_REF] Green | New Way to Measure Consumers' Judgments[END_REF][START_REF] Orme | Getting started with conjoint analysis[END_REF]. Pragmatically, extracting even a single trade-off function seems to be highly cumbersome, and in some cases very inaccurate [START_REF] Horn | Multicriteria decision making and evolutionary computation[END_REF]. Furthermore, in some cases, the decision maker may become aware of subjective preferences only after confronting the actual solution space [START_REF] Horn | Multicriteria decision making and evolutionary computation[END_REF].

Since a purely analytic approach is deemed unfeasible, we chose to focus on the area of 'visual analytics,' in which visual interfaces are used to facilitate interactive reasoning [START_REF] Keim | Visual Analytics : Definition , Process , and Challenges[END_REF]. Having decision makers closely involved in data exploration and processing cycles eliminates the need to extract and formalize their subjective preferences. Despite the plethora of multivariate visualization aids that exist in this domain (e.g., SOM [START_REF] Obayashi | Multi-objective design exploration for aerodynamic configurations[END_REF], Interactive Decision Maps [START_REF] Lotov | Interactive decision maps: Approximation and visualization of Pareto frontier[END_REF], Parallel Coordinates (PC) [START_REF] Inselberg | Parallel coordinates: a tool for visualizing multi-dimensional geometry[END_REF]), we found no prior work on user-experience evaluation to direct our selection of a designated visual interface that would facilitate multi-objective decision making. As a result, we decided to investigate and test the effectiveness of existing visual interfaces in promoting the selection of sensible choices. The evaluation of information visualization is an area in which the development of designated metrics and benchmarks has been identified as invaluable [START_REF] Plaisant | The challenge of information visualization evaluation[END_REF]. Our work is also unique in tackling the special circumstances in which any choice made is deemed acceptable since all competing alternatives are quantitatively equivalent (all being on the pareto frontier). It is the sole (unknown) preference of each decision maker that can determine the subjective ranking of the solution space.

We consider our contribution as twofold: (1) providing a pragmatic method and a carefully adapted measurement scale for testing the effectiveness and usageexperience of multivariate visualization aids for MCDM, and (2) providing a first glance into the actual performance of two existing visualization techniques for promoting effective MCDM. In the following sections we present the preliminary process of adopting and refining our experimental instruments, followed by a complete report of our experimental settings and results.

The Effectiveness of Visualization Aids

The presented work is driven by the growing desire evident in the HCI literature for the development of alternative methods to evaluate visualization and encourage more widespread adoption of visualization [START_REF] Shneiderman | Strategies for evaluating information visualization tools: multi-dimensional in-depth long-term case studies[END_REF]. Specifically, we focused on the unique nature of interaction with multivariate information visualization to more effectively benefit from and measure insights discovered [START_REF] Shneiderman | Creativity support tools: Report from a US National Science Foundation sponsored workshop[END_REF] rather than extracting efficiency measures such as time to complete a task. In our experimental configuration, we did include a measurement of task completion time for which no significant differences had been found across the different visualization types 1 . Hence, we considered effectiveness according to the following proposition:

Proposition 1: A (multi-dimensional) visual representation of the solution space promotes better decision making sensibility than a plain representation of the solution space.

For the purpose of a visual representation, we used two alternative techniques: Parallel Coordinates (PC), which is considered the prevalent technique for the visualization of multi-objective data [START_REF] Bagajewicz | Pareto optimal solutions visualization techniques for multiobjective design and upgrade of instrumentation networks[END_REF][START_REF] Fleming | Many-objective optimization: An engineering design perspective[END_REF][START_REF] Witowski | Decision making in Multi-Objective Optimization for Industrial Applications-Data mining and visualization of Pareto data[END_REF], and Self-Organizing Map for Multi Objective (SOMMOS), a recent adaptation of a Self-Organizing Map (SOM) [START_REF] Kohonen | Self-Organizing Maps[END_REF] visualization being developed by IBM as a proprietary visualization for exploring and visualizing a Pareto Frontier. Figure 1 illustrates an example for the two visualizations, showing three different apartments being considered for rent. Each alternative is measured based on three objectives: number of roommates, price, and distance from the university. On the left hand side, the PC visualization is depicted with each axis assigned a corresponding objective. Along each axis, an arrow indicates the aspiration of the decision maker to either minimize or maximize the specific objective. In Figure 1, the decision maker's goal is to minimize all three objectives. Each choice is depicted as a line that intersects every axis in accordance with the associated objective's value. The decision maker can observe the extent of conflict between objectives by searching for a cross (an 'x' pattern) between axes. For instance, based on the cross pattern apparent between the 'Roommates' axis and the 'Price' axis, the decision maker can infer a strong conflict between the corresponding objectives. In contrast, by examining the lines between the 'Price' axis and the 'Distance from University' axis, the decision maker can conclude that there is no conflict between the corresponding objectives based on the absence of any crossing. On the right hand side, the same solution space is depicted using SOMMOS. SOMMOS is a variation of the well-known self-organizing map (SOM) algorithm [START_REF] Kohonen | Self-Organizing Maps[END_REF] adapted for visualizing Pareto Frontiers. The SOMMOS visualization comprises three pillars: a map layout, a visual representation of individual choices, and interactive capabilities. The map layout enables the user to explore and draw insights based on its structure. The objectives are represented by the vertices of the map. For example, the three objectives in Figure 1 form a triangular layout. One of SOMMOS' virtues is the ability to navigate through the map. Specifically, the decision maker can expect that the closer the choice is to a vertex of an objective, the closer its value is towards the goal of that objective. Each choice on the map is encoded using polar area chart glyphs. Each objective is assigned a corresponding colored slice. By noting the level of colored filling, decision makers are able to understand the nature of the compromise in an area, spot an area of choices that maximize\minimize one of the objectives at the expense of the other, and identify cases in which objectives are correlative. In Figure 1, the decision maker can clearly identify that the Roommates objective is in conflict with both Price and Distance from University such that as the slice filling for Roommates decreases, the slice filling for Price and Distance increases. The decision maker can also observe that across all choices, the filling pattern for both Distance from University and Price is consistent. Hence, there is no conflict between the two.

In addition to testing each of the visualizations, we suspected that the two visualization types may complement one another. Because each has its unique strengths and weaknesses, allowing decision makers to simultaneously interact with both could potentially yield better results. Nevertheless, it was unclear whether the cognitive effort associated with toggling between two visualizations would impair the potential impact of combining the two. As a result, our experimental settings included a visual interface that combined PC and SOMMOS.

We used a simple table for the purpose of a plain representation, being synonymously referred to as the "no visualization" in this work. We structured the table with columns designating objectives and rows designating possible choices. Table 1 shows a plain representation of the same data underlying the solution space illustrated in Figure 1. As an antecedent to the notion of decision making sensibility, we developed a designated scale (see next section) to measure subjective conflict understanding. This helped us adhere to Assumption 1, according to which sensible choices rely first and foremost on the decision maker's ability to understand the nature of trade-offs between the objectives.

Correspondingly our experimental hypothesis is as follows:

H1: A (multi-dimensional) visual representation of the solution space promotes better subjective conflict understanding than a plain representation.

In addition to the measures that relate directly to the above hypothesis, we considered several background factors that may interfere with the effectiveness of the visualization being used. We extended our research model as illustrated in Figure 2 to consider three types of moderating factors:

Subjective usage experience -Several measures were employed to reflect the way users feel about using the visualizations. Such experience may be a potential moderator to the main effect hypothesized above. However, the secondary effect of each of the visualizations on usage experience was in itself unclear. Hence, this led to a second hypothesis: H2: A (multi-dimensional) visual representation of the solution space promotes better usage experience than a plain representation. We adopted a set of concrete preliminary measures from previous literature and further refined them as part of a card sorting procedure, explained in the next section.

Problem characteristics -The particular problem domain and complexity may also be a factor affecting the degree to which the visualization means can facilitate better objective trade-off understanding. The complexity, for example, may affect its capacity to scale in size of data [START_REF] Yang | Interactive hierarchical displays: a general framework for visualization and exploration of large multivariate data sets[END_REF]. As a result, we decided to manipulate these factors to account for their influences.

Participant factors -As noted by Gemino et al. [START_REF] Gemino | A framework for empirical evaluation of conceptual modeling techniques[END_REF], individual factors can affect the effectiveness of a visualization. To account for potential interference, we included questions to measure participants' familiarity with the corresponding problem domain and their experience. The latter included general questions about experience using visual analytics and specific questions regarding experience with multi-objective decision making.

Scale Development

Aside from the main effectiveness construct, all other scales have been originally adopted from prior literature having solid foundations in the HCI literature. To ensure scale validity and reliability in the operationalization of our research model, we produced a preliminary set of questions based on existing scales, followed by a card sorting procedure [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF][START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF][START_REF] Moore | Development of an instrument to measure the perceptions of adopting an information technology innovation[END_REF]. This led us to the scale items detailed in Table 5. Card sorting2 is an iterative scale development technique in which a panel of judges is asked in several rounds to sort a set of scale items into separate categories, based on similarities and differences among them. This technique was previously used by Davis et al. [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF][START_REF] Davis | Perceived usefulness, perceived ease of use, and user acceptance of information technology[END_REF] to assess the coverage of an intended domain of constructs. Later, it was further refined [START_REF] Moore | Development of an instrument to measure the perceptions of adopting an information technology innovation[END_REF] to generally account for scale reliability (i.e., content and construct validity). Prior to conducting the first card sorting round, we populated items for each of the constructs as described next.

As mentioned in the preceding section, we operationalized the high level notion of subjective decision quality through the construct of inter-objective correspondence understanding (i.e., as an antecedent to sensible decision making). This construct is both innovative to this work and related to the particular decision problem domain being explored. As such, no prior measurement scales were available for adoption.

We produced a set of seven items based on our experience with the notion of interobjective trade-offs. Specifically, all items were generated in accordance with the general definition by Purshouse et al. [START_REF] Purshouse | Conflict, harmony, and independence: Relationships in evolutionary multi-criterion optimisation[END_REF] according to which inter-objective trade-off understanding is defined as the degree to which an individual believes he or she were able to understand the 'conflict' between the objective. The 'conflict' is interpreted as a relationship between any two objectives in which as performance in one is improved, performance in the other is seen to deteriorate. Each related question was worded such that its most correct answer corresponds to one of the extreme ends in a 1-to-9 Likert scale [START_REF] Trochim | Research methods knowledge base[END_REF].

To operationalize the high level notion of subjective usage experience associated with the decision making task, we adopted a preliminary set of post-test concrete constructs from prior literature as follows:

(1) Usabilitybeing conventionally used to capture the general appropriateness of an artifact to a particular purpose [START_REF] Brooke | SUS-A quick and dirty usability scale[END_REF]. In our study, the artifact being evaluated corresponds to the various visualization interfaces mentioned earlier. The concrete purpose corresponds to the facilitation of multi-objective decision making. We refined the common 10-item SUS scale [START_REF] Brooke | SUS-A quick and dirty usability scale[END_REF] to match such circumstances. In addition, we eliminated two questions with very similar phrasing to two of the other questions that were intended to measure ease-of-use.

(2) Ease-of-useadopted from Moore and Benbasat [START_REF] Moore | Development of an instrument to measure the perceptions of adopting an information technology innovation[END_REF], originally aimed at measuring the degree to which users believe that using a particular system would be free of physical and mental effort. Correspondingly, we adopted a preliminary set of six items and slightly re-worded the phrasing to match the intended usage purpose.

(3) Cognitive-loadthe actual cognitive capacity required for the decision making task [START_REF] Paas | Cognitive load measurement as a means to advance cognitive load theory[END_REF]. The measurement of the actual cognitive capacity is typically considered a multi-dimensional construct. In our study we adopted a corresponding measurement scale from DeLeeuw and Mayer [START_REF] Deleeuw | A comparison of three measures of cognitive load: Evidence for separable measures of intrinsic, extraneous, and germane load[END_REF], to measure two items reflecting: (a) mentaleffortthe self reported effort subjects indicate as required to reach a certain decision, and (b) task-difficultythe self reported difficulty subjects indicate as being associated with the decision making task. Stemmed from the basic notion of task difficulty, and the particular nature of the task in this work, we added two additional items. These items take into account the capacity of the visualization to assist in the recognition of similar choices (i.e., clusters), and its capacity to gradually narrow down the set of preferred choices until a single choice is identified.

(4) Decision-confidencein its broader sense reflects the subject's confidence in the certainty of estimates or predictions of future performance based on their perceptions of their knowledge and experience. Adopted from the work by Kidwell et al. [START_REF] Kidwell | Emotional calibration effects on consumer choice[END_REF], this construct was measured by a unitary item which we slightly re-worded to reflect the confidence between the choice that is made and subjective preferences.

We operationalized the two remaining construct groups: problem characteristics and participant factors in a more straightforward manner. We incorporated problem characteristic factors into the experimental design by manipulating the problem's domain and the problem's complexity. Its exact levels of manipulation are further explained in the following section. We incorporated participant factors by including three questions on background knowledge: familiarity with the problem domain, pre-vious experience using visual-analytics interfaces, and previous experience in solving multi-objective problems.

The set of all items being produced for the measurement of the main effect (i.e., H1), together with all other items populated for the measurement of the resulting user experience (i.e., H2), were jointly considered as the input pool for the first card sorting round. We fragmented this preliminary set as illustrated in Table 2. To eliminate ambiguous items, we conducted three separate card sorting rounds with 21 independent judges. As noted by Moore et al. [START_REF] Moore | Development of an instrument to measure the perceptions of adopting an information technology innovation[END_REF], this was aimed at increasing construct validity and our confidence in the developed scale. The procedure was an 'open card sort' style, implying that the judges in the first round were not told what the underlying constructs (i.e., item categories) were, rather they were asked to provide their own construct labels and definitions. We used three indicators to identify construct validity and the convergence of the sorting procedure: (1) Inter-rater agreement between the judges for each construct in each round, (2) Hit ratio ("convergent" validity)item-wise portion of true item classifications within its "target" construct, and (3) Missed ratio ("discriminant" validity)construct-wise portion of wrong item classification within each construct. In each round, a "doesn't fit" category was also permitted for items that did not match any of the other clusters. A summary of results is illustrated in Table 3.

After the first sorting round, we observed a significant cross loading between easeof-use and usability. As noted above, this can be traced back to [START_REF] Lewis | The factor structure of the system usability scale[END_REF] having the SUS scale being composed of two sub-factors to measure usability and learn-ability, the former having conceptual overlap with ease-of-use. In addition, two items had poor loading on either ease-of-use or usability. We dropped these items and split the remaining items as being measures of either ease-of-use or learn-ability, considering usability as the combination of both (i.e., a second degree construct). Learn-ability is defined as the degree to which the tool enables the user to learn how to use it. "the degree to which an individual believes that using a particular system would be free of physical and mental effort". Hence, we decided to drop the entire construct, since it was sufficiently captured in the measurements for ease-of-use. Task-difficulty had very poor inter-rater agreement and inconsistent definitions across the judges. Consequently, we concluded that the actual construct being measured should be labeled as decision-making helpfulness. This captured the extent to which the visualization aid helped in the decision making process.

Decision-confidence also had very low hit ratio. Hence, we reworded the item to better reflect the certainty of choice made based on the perception of one's own knowledge and experience. We labeled this construct as choice confidence. This concluded all modifications made according to the results of the first sorting round.

After the second card sorting round, we dropped two additional items due to loading ambiguities. One was originally intended to measure ease-of-use but appeared to load equally on choice-confidence. The second item was originally intended to measure learn-ability and appeared to load equally on ease-of-use. To further increase item loading, we reworded two additional items (7 and 20) to better reflect their intended constructs. This concluded the modifications for the second sorting round.

Finally, after the third sorting round, the only apparent problem was a relatively low discriminant validity for choice confidence. Due to its high convergent validity, and no consistent classification to any of the items wrongly classified as its potential measures, no further actions seemed necessary. All remaining constructs demonstrated reasonable inter-rater agreements, alongside good convergent and discriminant validities. Hence, we decided to keep all items unchanged and concluded sorting rounds with the final loadings as illustrated in Table 4. A summary of all scale items is depicted in Table 5. The developed scale is our first contribution in this paper and can be used to assess any multivariate visualization aimed to promote MCDM. -Final items after the sorting procedure (EOUease-of-use, LBTlearnability, CON 3 conflict understanding, HLPdecision-making helpfulness, CNFchoice confidence)

Item

Item Description EOU1

The visualization aid was cumbersone to use EOU2

Using the visualization aid required a lot of mental effort EOU3 using the visualization aid was often frustrating EOU4 using the visualization aid was clear and understandable EOU5

Overall, I believe that the visualization aid is easy to use EOU6 I found the usage of the visualization aid unnecessarily complex EOU7 I think there was too much inconsistency in the usage of the visualization aid LBT1

Learning how to use the visualization aid was easy for me LBT2 I would imagine that most people would learn to use the visualiztion aid very quickly LBT3 I needed to learn a lot of things before I could start using the visualization aid

CON1

Based on all presented alternatives, an increase in the value of <objective1> requires a decrease in the value of <objective2> CON2

Based on most presented alternatives, an increase in the value of <objective1> requires a decrease in the value of <objective2> CON3

In most presented alternatives, the two objectives <objective1> and <objective2> seem to be conflicting CON4

With regard to the conflict between <objective1> and <objective2>, there are solutions that denote a good compromise between them CON5

With regard to the conflict between <objective1> and <objective2>, there are solutions that denote a good compromise between them CON6 Solutions <1> and <2> are strong indicators to having a conflict between <objective1> and <objective2> CON7 Solution <1> denotes a good compromise between <objective1> and <objective2> HLP1

The visualization aid did not help me find the selection solution HLP2

Using the visualization aid helped me focus the selection to the finding of a preferred solution HLP3

The visualization aid eased the decision making task be helping me identify groups of solutions that have similar characteristics CNF1 I have strong confidence that my choice fits my personal preferences

Experimental Design

We pursued a 4X2 (visualization type, problem domain) mixed experimental design to evaluate our hypotheses. In the laboratory setting, each participant was randomly assigned to one of four visualization interface groups: Tabular, PC, SOMMOS, PC and SOMMOS. The participants were then asked to make two consecutive choices, each corresponding to a different problem domain.

The first problem domain was in the area of property rental, and the task was to select an apartment for rent (namely, RENT). We selected this domain because it was an area with which most participants are familiar with. The corresponding visualization of the solution space was composed of 20 apartments to be examined according to 3 objectives: number of roommates, price, and distance from university; all these objectives were intended to be minimized.

The second problem domain was in the area of transportation asset management (namely, TAM). We chose this domain because it was an area of less familiarity. The corresponding visualization of the solution space was composed of 100 possible transportation plans (e.g., a portfolio of transportation projects), to be examined according to 5 objectives: air quality, safety, foreseen economic growth, traffic scarcity, number of pedestrian/cyclist trails; all these objectives were intended to be maximized. The order in which the two problems were presented to each participant was counter balanced across participants.

Method

Procedure. The entire experimental procedure took an hour on average. In the beginning of the experiment, each participant was given a 15 minute computer-based training session, which included: a primer to multi-criteria decision making and a video demonstration of the visualization type corresponding to the participant's group. The students were then given a quiz with 10 questions to determine whether they had understood the concepts and the usage of the tool presented in the training. A passing score of 70% was targeted to ensure all participants understood the visualization presented to them and its operation. Following the quiz, each participant was given a questionnaire booklet designed to facilitate the experimental procedure. The booklet had the following sections: participation consent, a set of questions about the participant's background knowledge and experience, and two question sets, corresponding to the two decision-making problems. In each such set, participants were first instructed to use the visualization aid for the purpose of choosing a single alternative out of the presented set, and then record both their selection, and a short explanation justifying their choice. Next, participants were presented with a randomly shuffled set of questions about usage experience and objective trade-off understanding.

Pilot. We carried out a pilot with 30 undergraduate students to further test the procedure and all corresponding experimental materials. Results indicated a significant effect of the visualizations on the perceptions of ease-of-use (F [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF][START_REF] Green | New Way to Measure Consumers' Judgments[END_REF] =3.94, p=.039) and usability (F [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF][START_REF] Green | New Way to Measure Consumers' Judgments[END_REF] =3.76, p=.044) for the RENT problem domain. Although an impact on conflict understanding was not yet apparent, it was decided to go ahead with the main experiment as the sample size in the pilot was fairly limited. We incorporated some minor re-wording after the research team reviewed the pilot responses.

Participants. A group of 93 undergraduate students volunteered to participate in the main experiment, which followed a similar scheme to the pilot. As an incentive for participation, students were offered 2 bonus points in a related academic course. After eliminating students who failed the quiz (i.e., 3 in total who scored below the 70% score threshold), and questionnaires that had been improperly filled out not adhering to the instructions, 172 useful responses remained in total: 85 for the RENT problem domain and 87 for the TAM problem domain. These responses were analyzed and all results are detailed in the following section.

Results Analysis

Data Preparation. Prior to running the statistical analysis, we explored the data using BOXPLOT to determine extreme responses. We concluded that 5 responses were outliers, scoring more than 1.5 times the inter-quartile range 4 (i.e., 4 in RENT, and 1 in TAM). Correspondingly, we executed all subsequent analyses twice, with and without the outliers. We found that outlier elimination does not affect any of the significant findings. Hence, final results reporting utilized 80 responses for the rental problem domain, and 85 for the transportation problem domain.

Scale Reliability. Our analysis of the results checked the scale reliability for the measurement of usage experience constructs. Item-wise reliability scores for each construct are illustrated in Table 6, showing that the reliability level indicated by Cronbach's alpha met the suggested tolerance (> 0.7, [START_REF] Trochim | Research methods knowledge base[END_REF]). We skipped the reliability check for the scale developed for conflict understanding. Unlike the other constructs that are traditionally considered reflective [START_REF] Freeze | An Assessment of Formative and Reflective Constructs in IS Research[END_REF], the items used to measure conflict understanding were not expected to be correlated to one another (i.e., a formative construct). Indeed, this was corroborated by exploratory factor analysis that has been attempted for each problem-domain question set, yielding 3 different principle components associated with each question set in each problem domain. Furthermore, no conceptual grounds could have been attributed to the underlying components, supporting the irrelevance of this test [START_REF] Freeze | An Assessment of Formative and Reflective Constructs in IS Research[END_REF]. That is, the inherent content validity of the scale developed for conflict understanding is shaped by how the questions complement each other.

Subjective Decision Quality

We conducted a separate one-way ANOVA for each problem domain to examine the effect of the visualization interface (between groups independent variable) on how well participants understood the relationship between objectives (dependent variable).

The results depicted in Table 7 indicate a significant effect of the visualization type only for the case of RENT (F (3,77) =2.86, p=.042). We performed the analysis for each problem domain separately since the actual measurements for correspondence understanding (i.e., items in questionnaire) were different between the two problem domains. Post-hocs. We conducted pair-wise comparisons between the visualization interfaces once the significant main effect was apparent for the case of RENT. Consistent with the ANOVA analysis, LSD post-hoc comparisons indicated a significant difference between the PC visualization (M=7.51, SD=.72) and the plain representation (M=6.85, SD=.82), p=.005. No further significant pair-wise differences were evident.

Subjective Usage Experience

We conducted a two-way (visualization type, problem domain) MANOVA to test the possible effects of the visualization type and problem domain on usage experience. In this case, it was possible to integrate problem domains in the analysis as the questions pertaining to all usage experience factors were the same in both problem domains. The two-way interaction (visualization type*problem domain) was not found to be significant for any of the usage experience factors, allowing us to interpret each of the main effects separately.

Descriptive statistics for the effect of visualization type on the usage experience factors are illustrated in Table 9. The main effect of the visualization type on the perception of ease-of-use was significant (F (3,157) =2.81, p=.04). Similarly, the effect of the visualization type on the perception of usability was also significant (F [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF]157) =2.81,p=.04). The effect of the visualization type on the remaining usage experience factors was not found to be significant. However, it might be worth noting a somewhat moderately significant effect of the visualization type on learn-ability (F [START_REF] Davis | A technology acceptance model for empirically testing new end-user information systems: Theory and results[END_REF]157) , p=.06).

Descriptive statistics for the effect of problem domain on the usage experience factors are illustrated in Table 10. As in the case of visualization type, the main effect of the problem domain was also significant with regard to its impact on the perception of ease-of-use (F (1,157) =9.51, p=.002), and on the perception of usability (F (1,157) =7.66, p=.006). In addition, choice confidence was also significantly affected by the problem domain (F (1,157) =4.64, p=.03). All remaining usage experience factors were not found to be significantly affected by the problem domain.

Post hocs. We conducted pair-wise comparisons between the visualization interfaces following the conclusion of the significant main effects for ease-of-use and usability. With respect to the effect of the visualization type on ease-of-use, LSD post-hoc comparisons indicated two significant differences: between the PC visualization (M=6.13, SD=1.63) and the plain representation (M=7.06, SD=1.36), p=.005, and also between the latter and the combined visualization of PC & SOMMOS (M=6.37, SD=1.47), p=.048. No further significant pair-wise differences were evident.

With respect to the effect of the visualization type on usability, LSD post-hoc comparisons indicated three significant differences: between the PC visualization (M=6.55, SD=1.28) and the plain representation (M=7.32, SD=1.18), p=.008; between the SOMMOS visualization (M=6.74, SD=1.53) and the plain representation, p=0.046; and between the combined visualization of PC & SOMMOS (M=6.67, SD=1.26) and the plain representation, p=0.032. There were no further significant pair-wise differences evident in the effect on usability.

Moderator Analysis

With respect to each of the factor groups proposed as possible moderators to the influence of visualization type on inter-objective correspondence understanding (i.e., H1), we hereby note the following results: Problem Characteristics. We incorporated both problem domain and problem complexity factors into the experimental design, along with the manipulation of the four visualization types. As implied from Table 7, there was an interaction between problem characteristics and the main effect of the visualization interface. This was apparent in having a significant impact only for the case of lower complexity (i.e., RENT). However, since the manipulation of problem-characteristics was simultaneously facilitated by changing the number of alternatives in the solution space (20 vs. 100), the number of objective (3 vs. 5), and the problem domain (RENT vs. TAM), it is impossible to conclude at this point which one (or more) of the three individual factors were responsible for the moderation.

Participant Factors. Background knowledge in any of the two problem domains, and prior experience in using visual interfaces and in solving multi-objective problems were all incorporated as pre-test questions. We statistically tested the potential effect of these factors as possible covariates. Specifically, we incorporated the following factors as potential covariates: knowledge in problem domain, experience in using visual interfaces, and experience in multi-objective decision making. None of the participant factors were found to significantly moderate the main affect of the visualization type on conflict understanding.

Subjective Usage Experience. It is apparent in the results that the manipulation of problem domain also had a significant impact on ease-of-use, choice confidence, and usability as depicted in Table 6. Similar to the moderation of problem characteristics, this impact may have influenced the potential main effect of the visualization interfaces in the case of the more complicated problem domain. Hence, we statistically tested the potential effect of these factors as possible covariates. None of the usage experience factors were found to significantly moderate the main effect of the visualization type on conflict understanding. Correspondingly, we conducted all post-hoc analyses illustrated in the previous section without integrating the covariates.

Conclusions

Based on the results and the research model in Figure 2, we concluded that:

─ The visualization of PC is more effective in terms of inter-objective conflict understanding than a tabular visualization when used in the context of a multi-objective decision problem that is not overly complicated and in a problem domain with which the decision maker has higher familiarity. Beyond a certain complexity threshold and\or when the problem domain is less familiar to the user, the gain from using a visual interface diminishes. This finding is in line with prior research [START_REF] Khatri | Understanding conceptual schemas: Exploring the role of application and IS domain knowledge[END_REF] according to which domain familiarity should be taken into account as a significant background factor that can interact with the effectiveness of treatments in the context of problem solving tasks. Interestingly, this impact is not affected by the decision maker's background knowledge and experience with using multivariate visualizations. ─ The type of the visualization aid has a significant impact on subjective usage experience, supporting H2. Specifically, the perceptions of ease-of-use and usability show that a plain representation typically scores higher than a graphical visualization aid. This may be explained by the widespread use of tabular visualizations. ─ The decision making problem at hand may also facilitate different perceptions of ease-of-use and usability. Further, decision making confidence is also affected by the problem characteristics. This effect should be carefully taken into consideration as it may also indirectly mask the effectiveness of the visualization aid in promoting better inter-objective correspondence understanding. Our experimental design employed a confounded manipulation, simultaneously tweaking problem domain (RENT vs. TAM), and problem complexity in two dimensions: size of solution space (20 vs. 100), and number of objectives (3 vs. 5). Thus, further work is required to determine which of the concrete dimensions may actually be a source for effect moderation.

Aside from the above conclusions inferred directly from the statistical analysis, our research team deduced some qualitative insights while administrating the experimental procedure. The most prominent observations included the following: ─ Despite our expectations regarding the superiority of the combined visualization (PC+SOMMOS) over the individual constituents, it did not appear to have fulfilled this expectation. Observing user actions revealed that most participants who were assigned to this group used each of the two visualization interfaces independent of the other, practicing a fairly limited number of transitions between them. The root cause we observed for this behavior was the mere use of visual 'tabbing' which did not allow participants to simultaneously watch the two visualizations on a single screen. This may also be attributed to the content of the training session presented to this group. ─ It was observed that users do not immediately rush into making a choice. Rather, the decision making process progressed through several phases. This included: high-level visual skimming of the entire solution space, prioritizing between the presented objectives, identification of choice groups that seem to possess similar characteristics, flipping back and forth between the upper and lower bounds for each objective range and observing its effect on the visible solution space while doing so, and gradually iterating through all previous phases while eventually converging on a single choice. Based on this observation our conclusion is twofold: (a) the suitability of concrete visualization means with regard to each of the above phases may vary, and (b) the multi-objective decision making process itself should be further investigated to more diligently learn about its methodological constituents.

Future Work

Different levels of complexity revealed the possible existence of a certain cognitive threshold beyond which the effectiveness of the visualization means is impaired. Our immediate intention is to pursue an experiment aimed at testing the exact complexity parameters that may play a significant role in this regard (e.g., number of objectives, solution space size). As concluded from the observed methodological aspects of the decision making process, and in congruence with [START_REF] Shneiderman | Strategies for evaluating information visualization tools: multi-dimensional in-depth long-term case studies[END_REF], a longitudinal investigation is necessary to fur-ther discover the actual cognitive stages associated with more effective decision making in multi-objective settings.

Our preliminary experiment was focused on the understanding of trade-off as the main outcome variable. Understanding the potential impact of visual interfaces on other outcome variables (e.g., cluster specific trade-off understanding) requires further investigation.

Finally, it is clear that certain features in the visualization interface can promote better decision making performance. For example, the 'filtering' feature allowing users to restrict the accepted range per objective was used extensively, regardless of the actual multi-dimensional visualization type. There are still a handful of additional features that need to be tested for similar impacts, including visual clustering, objective layout shuffling, glyph shapes, visualization layouts, and more.

Fig. 1 .

 1 Fig. 1. -The PC and SOMMOS visual representations evaluated

Fig. 2 .

 2 Fig. 2. -Extended research model

Table 1 .

 1 -Plain representation of the solution space in Figure1

		Roommates (#)	Price ($/tenant)	Distance from University (m)
	a	4	400	700
	b	3	600	1500
	c	2	800	2300

Table 2 .

 2 -Preliminary construct-wise item pool for card-sorting input

	Conflict understanding	7 Usability	8 Ease of use	6
	Mental effort	1 Task difficulty	3 Decision confidence	1

Table 3 .

 3 -Card sorting results

	#	Inter-	Hit	Missed	#	Inter-	Hit	Missed	#	Inter-	Hit	Missed
	items	rater	Ratio	Ratio	items	rater	Ratio	Ratio	items	rater	Ratio	Ratio
		agree				agree				agree

Table 4 .

 4 -Item loading matrix after the sorting procedure

		Choice	Conflict	Decision making
		confidence	understanding	helpfulness	Ease of use	Learn-ability
	EOU 1	0.00%	0.00%	0.00%	100.00%	0.00%
	EOU 2	0.00%	0.00%	14.29%	71.43%	14.29%
	EOU 3	14.29%	0.00%	0.00%	85.71%	0.00%
	EOU 4	0.00%	0.00%	0.00%	85.71%	0.00%
	EOU 5	0.00%	0.00%	0.00%	100.00%	0.00%
	EOU 6	0.00%	0.00%	0.00%	100.00%	0.00%
	EOU 7	0.00%	0.00%	0.00%	71.43%	14.29%
	LBT 8	0.00%	0.00%	0.00%	14.29%	85.71%
	LBT 9	0.00%	0.00%	0.00%	14.29%	85.71%
	LBT 10	0.00%	0.00%	0.00%	14.29%	85.71%
	CON 11	0.00%	85.71%	0.00%	14.29%	0.00%
	CON 12	0.00%	85.71%	0.00%	14.29%	0.00%
	CON 13	0.00%	85.71%	14.29%	0.00%	0.00%
	CON 14	14.29%	71.43%	0.00%	14.29%	0.00%
	CON 15	14.29%	71.43%	0.00%	14.29%	0.00%
	CON 16	14.29%	85.71%	0.00%	0.00%	0.00%
	CON 17	14.29%	71.43%	14.29%	0.00%	0.00%
	HLP 18	0.00%	0.00%	85.71%	0.00%	0.00%
	HLP 19	14.29%	0.00%	85.71%	0.00%	0.00%
	HLP 20	0.00%	14.29%	85.71%	0.00%	0.00%
	CNF 21	85.71%	0.00%	0.00%	0.00%	0.00%

Table 5 .

 5

Table 6 .

 6 -Reliability scores (Cronbach's alpha)

	Variable Ease of use Helpfulness Learnability Usability Confidence
	Alpha	0.87	0.71	0.70	0.88 Single-item

Table 7 .

 7 -Inter-objective correspondence understanding (scores ranged from 1 = least understanding to 9 = highest level of understanding)

	PC	SOMMOS PC+SOMMOS	Table	ANOVA
	Case M SD n M SD n M SD n M SD n df	F	Sig.
	Rent 7.51 0.72 22 7.06 0.85 22 7.13 0.56 16 6.85 0.82 21 (3,77) 2.86 0.042*
	TAM 6.51 0.76 23 6.65 0.97 22 6.41 0.85 20 6.30 0.88 21 (3,82) 0.636 0.594

Table 8 .

 8 -Usage experience -between problem domains and between visualization types

	Effect	Dependent	(df,157) F	Sig.
	source	Variable
		Ease of use	3	2.81 0.04*
		Learnability	3	2.49 0.06
	VisualType	Helpfulness Choice	3	0.73 0.54
		confidence	3	0.29 0.83
		Usability	3	2.81 0.04*
		Ease of use	1	9.51 0.002*
		Learnability	1	0.97 0.33
	Problem	Helpfulness	1	2.09 0.15
	domain	Choice
		confidence	1	4.64 0.03*
		Usability	1	7.66 0.006*
		Ease of use	3	0.10 0.96
	VisualType *	Helpfulness	3	0.46 0.71
	Problem	HLP-AVG	3	0.25 0.86
	domain	Choice
		confidence	3	0.04 0.99
		Usability	3	0.17 0.92

Table 9 .

 9 -Descriptive statistics for usage experience factor per visualization type (1-9 scale)

		PC	SOMMOS	PC+SOMMOS	Table
	Variable	M SD n M SD n M SD n M SD n
		6.13 1.63 45 6.53 1.65 43 6.37 1.47 36 7.06 1.36 41
	Ease of use
		7.17 1.34 45 7.35 1.30 43 7.57 1.41 36 7.26 1.21 41
	Helpfulness
		7.53 .99 45 7.24 1.56 43 7.37 1.15 36 7.93 1.14 41
	Learnability
		6.55 1.28 45 6.74 1.53 43 6.67 1.26 36 7.32 1.18 41
	Usability
		7.56 1.25 45 7.40 1.76 43 7.33 1.47 36 7.61 1.39 41
	Confidence

Table 10 .

 10 -Descriptive statistics for usage experience factor per problem domain (1-9 scale)

		Rent	TAM
	Variable	M SD n M SD n
		6.90 1.48 80 6.16 1.56 85
	Ease of use
		7.48 1.10 80 7.19 1.47 85
	Helpfulness
		7.63 1.17 80 7.42 1.30 85
	Learnability
		7.12 1.29 80 6.54 1.34 85
	Usability
		7.74 1.25 80 7.24 1.62 85
	Confidence

p=.186 and p=.144 for the two experimental tasks RENT and TAM.

We used OptimalSort by OptimalWorkshop.com as a platform for card sorting.

Note that in all CON items, the phrases appearing in brackets were populated by concrete objectives/solutions in the context of the concrete problem domain.

The inter-quartile range (IQR) contains the middle

percent of the distribution. If the data is normally distributed, a range that is 1.5 times the IQR covers ~99.3% of the distribution.

Acknowledgements. Our thanks go to Dr. Ofer M. Shir for the insights and help in the field experiment.

The single item measuring mental-effort had a significantly stronger load on easeof-use than on itself. This was also explained by the definition of ease-of-use being:


Damien Marchal
email: damien.marchal@lifl.fr

Clément Moerman
email: clement.moerman@lifl.fr

Géry Casiez
email: gery.casiez@lifl.fr

Nicolas Roussel
email: nicolas.roussel@inria.fr

Designing Intuitive Multi-touch 3D Navigation Techniques

Keywords: 3D navigation, multi-touch, interaction technique, design rationale 1

Multi-touch displays have become commonplace over recent years. Numerous applications take advantage of this to support interactions that build on users' knowledge and correspond to daily practices within the real world. 3D applications are also becoming more common on these platforms, but the multi-touch techniques for 3D operations often lag behind 2D ones in terms of intuitiveness and ease of use. Intuitive navigation techniques are particularly needed to make multi-touch 3D applications more useful, and systematic approaches are direly needed to inform their design: existing techniques are still too often designed in ad-hoc ways. In this paper, we propose a methodology based on cognitive principles to address this problem. The methodology combines standard usercentered design practices with optical flow analysis to determine the mappings between navigation controls and multi-touch input. It was used to design the navigation technique of a specific application. This technique proved to be more efficient and preferred by users when compared to existing ones, which provides a first validation of the approach.

INTRODUCTION

Multi-touch displays have become commonplace over the recent years. Smartphones, tablets, interactive kiosks and systems of other sorts can now detect and react to the presence of two or more contact points on the screen surface. Numerous applications take advantage of this to support reality-based interactions [START_REF] Jacob | Reality-based interaction: a framework for post-wimp interfaces[END_REF] that build on users' knowledge and correspond to daily practices within the real world. 3D applications are also becoming more common on these platforms, including games, virtual tours, and CAD applications for both specific, e.g. interior design, and general purposes. But the multi-touch techniques for 3D operations often lag behind the 2D ones in terms of intuitiveness and ease of use. Navigation particularly seems to be the Achilles heel of multi-touch 3D applications. Existing techniques are still too often designed in ad-hoc ways. Intuitive techniques are direly needed to make the applications more useful, and systematic approaches direly needed to inform their design.

The Merriam-Webster Dictionary defines intuitive as "attaining to direct knowledge or cognition without evident rational thought and inference". Based on an extensive review of the relevant literature, Ingram et al. also identify direct manipulation as the most influential factor determining the intuitiveness of multi-touch systems [START_REF] Ingram | Towards the establishment of a framework for intuitive multi-touch interaction design[END_REF]. Direct manipulation is commonly supported by 2D multi-touch applications, due to the trivial mapping between 2D tasks and the multi-touch input space. However, finding a direct mapping between 3D tasks and this 2D input space is much more difficult. To clarify the requirements for intuitive 3D navigation techniques, we propose to turn first to cognitive accounts of the feeling of directness.

Hutchins et al. identify two underlying phenomena that give rise to this feeling: a small cognitive distance, and direct engagement [START_REF] Hutchins | Direct manipulation interfaces[END_REF]. The cognitive distance is the one "between the user's intentions and the facilities provided by the machine". It encompasses the semantic distance, concerned with the meaning of available interactions, and the articulatory one, concerned about their form. For the semantic distance to be small, the system should provide users with adequate commands to concisely express what they want to do. For the articulatory distance to be small, the system should provide an adequate mapping between user actions and the commands. This mapping should not be arbitrary, but should rather favor similarities between user action and command meaning. Lastly, for direct engagement, the system should provide continuous representations of the objects of interest and promptly react to user actions on them. Ultimately, the degree of directness relates to the one to which the system supports skill-based rather than rule-or knowledge-based behaviors [START_REF] Rasmussen | Skills, rules, and knowledge; signals, signs, and symbols, and other distinctions in human performance models[END_REF].

Navigation concerns viewpoint control and is the aggregate of wayfinding (cognitive planning of one's route), travel (the motor aspects) and inspection (for particular proximal views of objects). The importance of each sub-task depends on the considered application. We did not consider wayfinding sub-tasks in this work. We rather focused on multi-touch support for traveling and, to a lesser extent, inspection. Travel techniques support the motor aspects of 3D navigation, allowing users to control the position and orientation of their viewpoint [START_REF] Bowman | 3D user interfaces: theory and practice[END_REF]. Viewpoints are typically modeled using seven parameters: the camera's field of view, three Cartesian coordinates (its position) and three Euler angles (its orientation). Controlling these parameters requires a rich command vocabulary because of their number and the different ways to use them. Turning around is pretty straightforward, for example, as it requires the control of a single viewpoint parameter (Figure 1, ). Wandering around a horizontal space requires the control of three parameters at the same time (

). But some navigation tasks require quite a complex coordination of controls, especially when the desired motion is conceptually tied to other reference points. Orbiting around an object, for example, couples planar circular motions with a rotation around an orthogonal axis, both centered on the object ( for ; for ). Temporary transformations can also be useful, such as adjusting the field of view ( ) of the camera to remotely inspect a distant place or have a closer look at a nearby detail. To reduce semantic distance, multi-touch navigation techniques should support not only elementary viewpoint controls, but also coordinated ones, including the complex coordination required by externally referenced tasks and temporary ones. To reduce articulatory distance, they should be based on a mapping favoring similarities between user gestures and commands meaning. To support direct engagement, they should provide a close and continuous visual-motor loop. In this paper, we present a methodology for designing multi-touch 3D navigation techniques that meet all these requirements. After discussing related work, we describe our methodology and explain how it was used to design the navigation technique of a particular application. We then provide some implementation details for that application. We finally report on a study that compared this technique with existing ones and provides a first validation of the approach.

RELATED WORK

Navigation in virtual 3D worlds has been extensively studied in immersive and desktop environments. Bowman et al. [START_REF] Bowman | 3D user interfaces: theory and practice[END_REF] and Christie et al. [START_REF] Christie | Camera control in computer graphics: models, techniques and applications[END_REF] provide detailed reviews of the relevant concepts and techniques in these contexts, many of which are also relevant to multi-touch environments. Navigation techniques map user actions on one or more input devices to viewpoint controls such as those of Figure 1. Theoretically, a technique could allow users to operate all controls at once. However, it is rarely the case since few input devices (or device combinations) have enough degrees of freedom, and their control properties seldom match the perceptual structure of the navigation tasks [START_REF] Jacob | Integrality and separability of input devices[END_REF]. Viewpoint controls thus tend to be organized in groups, which can raise issues about consistency and mode switching. The following review focuses on input-to-control mappings for multi-touch systems, but also discusses pen or mousebased navigation techniques that could easily be adapted to these systems.

Basic viewpoint control

Different techniques have been proposed to freely and precisely control the viewpoint. These are typically used when navigation is a primary task of the application, one without which it would not be the same. They most often provide only elementary input-to-control mappings to move and orient the viewpoint. Games using a first-person perspective are probably the most popular 3D applications supporting this kind of navigation on multi-touch platforms. A common practice is to use one or two on-screen joysticks for moving and turning ( or ). Virtual joysticks make control grouping explicit and make it possible to use non-linear transfer functions for a trade-off between speed and control. They can also be complemented by buttons, sliders or other widgets for discrete or continuous actions on other controls (e.g.

). Coordinating interactions on multiple screen locations is not necessarily easy, though, especially without haptic feedback. Compound controls such as orbiting are thus usually difficult in these settings. Instead of spreading controls across the screen, some techniques combine them using modes. In the RealMyst1 game, for example, touching the screen and moving horizontally or vertically changes the orientation of the viewpoint while holding still moves forward. Such an approach is of course only practical for a small number of modes.

Multi-touch devices can be used to interact with a 3D scene displayed elsewhere. The ability to use a different view of the scene, a different orientation, or a different physical shape offers new interesting possibilities. The Finger Walking in Place (FWIP) technique allows to navigate in a CAVE by mimicking walking movements with fingers on a horizontal multi-touch device [START_REF] Kim | iPhone/iPod Touch as input devices for navigation in immersive virtual environments[END_REF][START_REF] Kim | Finger Walking in Place (FWIP): A traveling technique in virtual environments[END_REF]: repeated single-touch sliding gestures move the viewpoint forward or backward ( ), while multi-touch turn gestures rotate it left or right ( ). The Follow my Finger (FmF) technique uses a horizontal multi-touch table to navigate in a scene shown on a vertical screen [START_REF] Ajaj | Follow my finger navigation[END_REF]. The table shows a 2D bird's-eye view of the scene with a camera icon that users can move (

) and orient ( ) using the 2D Rotate'N Translate technique [START_REF] Kruger | Fluid integration of rotation and translation[END_REF]. The Cub-Tile [START_REF] De La Rivière | CubTile: a multi-touch cubic interface[END_REF] takes the idea of aligning the perceptual structure of the tasks with the input device in the opposite direction. This device combines 5 multi-touch surfaces arranged as a cube so that gestures performed on multiples sides at the same time define a 3D gesture that can be used for 3D interaction. Although designed for object manipulation, the CubTile may well be suitable for navigation tasks.

Viewpoint control facilitation

It might well be the case that the 3D environment in which a user wants to navigate is extremely large [START_REF] Mccrae | Multiscale 3D navigation[END_REF]. Or the user might be willing to quickly get a glimpse of the scene from different perspectives. Or (s)he might be engaged in repeated tasks requiring frequent switches between two or more viewpoints. In these situations, navigation is just a mean and not an end. One wants to transition between viewpoints but does not necessarily care about all the details of the transition. Even with sophisticated transfer functions, basic viewpoint controls are not enough: one needs faster and integrated techniques to move and orient the viewpoint. The Point Of Interest (POI) desktop technique was precisely designed for rapid controlled movement through a 3D space [START_REF] Mackinlay | Rapid controlled movement through a virtual 3D workspace[END_REF]. After selecting a POI with the mouse, it allows to quickly move there by simply pressing a key, the system taking care of the transition with an animation adjusting the viewpoint position (using a logarithmic function of the remaining distance) and reorienting it to face the POI. UniCam [START_REF] Zeleznik | UniCam -2D gestural camera controls for 3D environments[END_REF] is a mouse or stylus-based system that uses simple gesture recognition to facilitate a variety of complex navigation tasks including orbiting around specific points, clickto-focus on points and edges, and region zooming. Navidget [START_REF] Hachet | Navidget for easy 3D camera positioning from 2D inputs[END_REF] expands on these ideas by allowing the user to not only specify a point of interest but also control the final position and orientation of the viewpoint, rather than inferring them. The system uses single-stroke symbolic gestures and animations in constant time to combine travel and inspection with the ability to go back to a previous viewpoint configuration.

A difficulty when trying to control the viewpoint without any external representation (as in FmF) is that by definition, it cannot be seen. As a consequence, it can only be indirectly manipulated. There is, however, a way to change this: by giving users the impression they can grab the whole scene and manipulate it. Instead of indirectly moving the viewpoint to a particular place, for example, they would thus manipulate the whole scene so that the place comes into the viewpoint. To support this, one needs to make sure that any object touched by a finger remains under it as long as it stays in contact with the surface. This approach has its roots in Gleicher & Witkin's early work on through-the-lens camera control [START_REF] Gleicher | Through-the-lens camera control[END_REF] and recently received renewed attention after Reisman et al. adapted it to the interactive manipulation of 3D content on 2D multi-touch systems under the name screen-space [START_REF] Reisman | A screen-space formulation for 2D and 3D direct manipulation[END_REF]. The DabR system [START_REF] Edelmann | The DabR -a multitouch system for intuitive 3D scene navigation[END_REF] uses it in a strict way to support the direct manipulation of basic viewpoint controls, for example. A drawback of the screen-space approach is that its output (viewpoint transformation) is not always predictable due to ambiguities in potential mappings between points in screen space and the 3D scene. To avoid these ambiguities, the Drag'n Go technique [START_REF] Moerman | Drag'n Go: Simple and fast navigation in virtual environment[END_REF] assigns viewpoint controls to input gestures based on kinematic correspondence, i.e. the similarity of the input and output paths [START_REF] Britton | Making nested rotations convenient for the user[END_REF].

Fu et al. assembled an impressive set of viewpoint control facilitation techniques more or less inspired by the above ones for exploring large-scale 3D astrophysical simulations [START_REF] Fu | Multi-touch techniques for exploring large-scale 3D astrophysical simulations[END_REF]. Yet this assemblage seems quite ad-hoc. The fact is that designers have little information to rely on when creating a new application.

A lack of systematic approach

Intuitive navigation techniques are needed to make multi-touch 3D applications useful. Different techniques have been proposed to support basic viewpoint controls and facilitate more complex ones. But comparing these techniques is hard, considering the little information available on their design process and performances. Although the initial design motivation is usually clearly stated in the corresponding papers, the design rationale is largely undocumented. Which decisions were made during the design process, and why, for example? How did the authors come up with the proposed mapping between user actions and viewpoint controls? Why did they decide to group them this way? Without these explanations, one might wonder if there was actually a design process. The authors of UniCam somehow acknowledge this problem: "Our choice of how to gesturally map the 3 DOFs of camera translation to 2D mouse movements involves some apparently arbitrary choices. (...) In lieu of an ex-planation, we note that from our experience with gestural interaction, the most reliable technique for insuring usable interactions is through empirical evaluations." [START_REF] Zeleznik | UniCam -2D gestural camera controls for 3D environments[END_REF].

We collectively need more explanations on the design of these techniques. Evaluations are also important and need to be properly reported. As illustrated by Table 1, few of the techniques we reviewed have been evaluated and even less have been compared to others. We definitely need more comparative evaluations. Without explanations of what is being done and comparisons with existing solutions, there can be no progress in the understanding of the problems and their solutions. Systematic approaches are direly needed to inform the design of new techniques.

Technique or system

Design motivation

Reported Evaluation

*FWIP [START_REF] Kim | iPhone/iPod Touch as input devices for navigation in immersive virtual environments[END_REF][START_REF] Kim | Finger Walking in Place (FWIP): A traveling technique in virtual environments[END_REF] walking metaphor comparative (vs. joystick) & usability testing *FmF [START_REF] Ajaj | Follow my finger navigation[END_REF] 2D directness None POI [START_REF] Mackinlay | Rapid controlled movement through a virtual 3D workspace[END_REF] speed and control none UniCam [START_REF] Zeleznik | UniCam -2D gestural camera controls for 3D environments[END_REF] integrated suite empirical?

Navidget [START_REF] Hachet | Navidget for easy 3D camera positioning from 2D inputs[END_REF] ease of use and control comparative (vs. standard 3D viewer) *Screen-space [START_REF] Reisman | A screen-space formulation for 2D and 3D direct manipulation[END_REF] 3D directness none *DabR [START_REF] Edelmann | The DabR -a multitouch system for intuitive 3D scene navigation[END_REF] 3D directness none *Drag'n Go [START_REF] Moerman | Drag'n Go: Simple and fast navigation in virtual environment[END_REF] multi-scale navigation comparative (vs. POI, DabR, keyboard+mouse) *Fu et al [START_REF] Fu | Multi-touch techniques for exploring large-scale 3D astrophysical simulations[END_REF] large scale navigation usability testing Table 1. Summary of the characteristics of the most relevant techniques and systems discussed in this section. Rows prefixed with a star correspond to those specifically designed for multitouch interaction.

DESIGN METHODOLOGY

Considering a set of application-specific tasks, how can one map the associated viewpoint controls to the input handles provided by a multi-touch system? In this section, we report on the design of such a mapping for a particular application. Although the resulting technique is specific to that application, we believe our design methodology should be of general interest. The application we worked on is one for reviewing interior designs (Figure 2) that typically runs on computers equipped with a multi-touch screen. Our goal was to design an intuitive navigation technique for this application, as defined earlier, i.e. one with reduced semantic and articulatory distances and a close and continuous visual-motor loop. In the following, we explain how standard user-centered practices and optical flow analysis helped us identify application controls and input handles and define the mappings between them.

Identifying navigation tasks and associated controls

A way to reduce the semantic distance by design is to work with users to define the navigation commands from their perspective, rather than the application developers'. Developers usually think of viewpoint control in terms of parametric modifications of the camera model, as these are ultimately the only controls available. But they typically have little insight into the ways these should be grouped. Users, on the other hand, typically think in terms of high-level situated tasks (i.e. context-specific) that can help structure the design space. To provide users with adequate commands to concisely express what they want to do, application designers must identify these tasks. Based on our specific application context (Figure 2), the related work we previously described and interviews of potential users, we decided to focus on the following tasks, in decreasing order of importance:

 Move around -Users need to be able to move around the virtual interior the way they do in the real world, i.e. mostly by moving forward or backward ( ) while possibly turning left or right ( ). Although commonly supported by video games, sidestepping (or strafing, ) is rarely used in real world situations and thus of lesser importance. Altitude control ( ) is also pretty limited in the real world without assistance, and thus also of lesser importance.  Look around -Adjusting the viewpoint orientation is another important task that must be supported by the considered application. Users need to be able to look left and right ( ) as well as up and down ( ). The third rotation of the camera ( ) does not seem necessary as people have limited control on it in the real world and it does not change what they see but only how they see it.  Circle around -When focusing on a particular object or area, users need to be able to look at it from different sides. This is typically achieved by orbiting around a previously specified point ( ) in the horizontal plane ( ).  Scrutinize -Looking at a particular point of interest ( ) from different sides might not be enough. One might want to have a closer look at it. In real-life, one can bend over or use optical tools such as a magnifying glass or binoculars to temporarily modify one's field of view ( ).

Table 2 summarizes the viewpoint controls of Figure 1 associated with the above four tasks to be supported by our particular application. Having identified the viewpoint model's degrees of freedom we want to control and taken a few first steps into their organization, we must now turn to the input device (the multi-touch screen) and examine the handles it provides for that control.

T x T y T x R x R y FOV O y

Move around

◐ ◐ • ○ • ○ ○ Look around ○ ○ ○ • • ○ ○ Circle around ○ ○ ○ ○ ○ ○ • Scrutinize ○ ○ ○ ○ ○ • ○ Table 2.
Relevance of viewpoint controls to high-level navigation tasks, by decreasing order of importance.•: relevant,◐: partially relevant, ○: not relevant.

Identifying input handles

Although some touch sensing technologies provide rich information about contact regions, including their shape or the applied force, most multi-touch APIs only expose the 2D coordinates of their centroid. One might thus think that using fingers, users should be able to control degrees of freedom. But in reality, it is never the case. Multi-touch systems can't distinguish between fingers, so degrees of freedom cannot be univocally associated to them. The order of appearance of contacts or hit-testing with specific on-screen areas can be used for these associations. But in the end, interaction will always be constrained by limited finger individuation: it is quite difficult to move one finger without some degree of involuntary movement at one or more of the others [START_REF] Ingram | The statistics of natural hand movements[END_REF].

Instead of considering contacts individually, one can group them using different methods (e.g. hit-testing, proximity, hand identification) and extract from the collated movement information global parameters to be associated with degrees of freedom to control. A common practice is to consider multi-touch gestures on objects as Rotate-Scale-Translate (RST) manipulations and to determine and characterize the principal transformation involved -e.g. for a turn gesture, for a pinch or a spread, and for a swipe 2 . Figure 3 shows a simplified view of the state machine we used, based on this approach. The machine differentiates four interaction states (shown in gray): one for single-touch interaction, and three differentiating multi-touch interactions based on the first principal transformation detected.

Having described the desirable viewpoint controls for our application (Table 2) and the different handles provided by a multi-touch screen, i.e.

for single-touch interactions and , & for multi-touch ones, we will now examine the mappings between them.

Figure 3.

Simplified view of a multi-touch state machine based on an RST classifier. +1 and -1 transitions are triggered by contact addition and removal. The R, S and T transitions are triggered based on the first principal transformation detected. Note that once in mode #1, #2 or #3, multi-touch interaction does not have to be restricted to the transformation initially detected.

Choosing the right mappings

A way to reduce the articulatory distance and ensure tight coupling between perception and action is to choose the mappings between viewpoint controls and multi-touch gestures so that contact trajectories match the scene transformations caused by viewpoint modifications. To achieve this, we created video clips illustrating the effect of the 7 viewpoint controls of Table 2 on a particular scene. We used OpenCV to compute and visualize the optical flow of each of these videos (Figure 4). We then compared these flows to those corresponding to multi-touch RST manipulations, i.e. when using a single finger and , , otherwise. 2 (arrows could all point in the opposite direction).

Table 3 summarizes the compatibility between gesture flows and optical flows using a three-level scale. Starting from this table, we applied the following heuristics to choose between alternative mappings:  As MT-is the most compatible gesture with , we decided to map the two.  and are compatible with the same gestures, MT-and ST-. Since is one of the most important controls, we wanted to keep it as simple as possible and thus preferred a single-touch gesture for it. Moving forward/backward seemed better matched with a vertical movement rather than a horizontal one, so we chose ST-. For , we chose MT-.  For ST-, we were left with , and , the first two being more important than the third one. We decided to map ST-to so that single-touch interaction would support both Move around (with and ) and Look around (with ).  For MT-, we were left with and . We chose the latter, as looking up/down was considered more important than controlling one's altitude.  For MT-, we were left with and . Informal tests convinced us that the latter was preferable, considering our previous choice of for MT-. 6) ○ Table 3. Compatibility between gesture flows (rows) and optical flows (columns): ○ incompatible, • compatible, ◐ compatible under one of the conditions below. A dot in place of or indicates that this component is ignored. The gray cells correspond to the chosen mapping.

T x T y T z R x R y FOV O y ST • ○ • ○ ◐ (1) • ◐ (2) ○ • • ◐ (3) ○ • ○ MT ○ ○ ○ ◐ (4) ◐ (5) ○ • MT ○ ○ • ○ ○ • ○ MT • ○ ◐ (6) ○ ◐ (1) ◐ (6) ◐ (2) ○ • ◐ (6) ◐ (3) ○ ◐ (
(1) compatibility is inversely proportional to the vertical distance to the center of the screen (2) the point of interest ( ) must have been previously specified (3) compatibility is inversely proportional to the horizontal distance to the center of the screen (4) must be in the middle of a vertical border of the screen, i.e. left or right (5) must be in the middle of a horizontal border of the screen, i.e. top or bottom (6) contacts must be "close enough", i.e. within a certain radius, so they can be reduced to singletouch interaction

IMPLEMENTATION: THE MOVE&LOOK TECHNIQUE

A close look at Table 2 and the chosen mapping in Table 3 shows that STcorresponds to Move around while MT-corresponds to Circle around, MTto Scrutinize and MT-to Look around. As illustrated by Figure 5, each of our 4 high-level navigation tasks can thus be associated to an interaction state of the machine shown in Figure 3. This section details the implementation of the resulting navigation technique, which we called Move&Look.

Single-touch interaction: move around

When a single contact is detected, subsequent finger movements are mapped to camera movements to support the move around task. When touch is detected, a ray is casted in the 3D scene from the camera center through the contact point in the camera plane. The intersection with the scene ( ) defines the point of interest, and the ray a path towards it. Progression along the path is controlled through finger movements in the following way:

 Lateral movements (
) do not affect the camera position. Proximal finger movements translate the camera towards and distal movements translate it backwards along the path (

).  The distance between the initial contact point and the bottom of the display is mapped to the entire path length: the destination is reached when the finger reaches the bottom of the display.  Distal finger movements past the initial contact point (i.e. above it) continue moving the camera backwards along the path. For consistency, the scale factor remains the same as when closing in on .

Users can turn the camera left and right ) through lateral finger movements. The camera orientation is computed so as to always keep the projection of under the finger.

is computed either analytically [START_REF] Gleicher | Through-the-lens camera control[END_REF] or numerically [START_REF] Reisman | A screen-space formulation for 2D and 3D direct manipulation[END_REF] to minimize the distance between the previous projection of and the current finger position (we used the minimizer from ALGLIB to solve the different minimization problems).

Multi-touch interaction switch: RST classifier

When multiple contacts are detected, their movement is analyzed to determine whether the state machine should switch to circle around, scrutinize or look around. The movement of the contact points is interpreted as a rigid transformation combining a rotation , an homogeneous scaling , and a translation . The initial position of the contact points is noted and their current position . The and transformations correspond to the minimization of the cost function defined by Equation 1.

is first computed from the centroids of the initial set of contact points ( and the current one ( according to equations 2, 3 and 4. The rotation angle is the one that minimizes the cost function of Equation 5 and is computed using Equation 6where and . The scale factor is similarly the one that minimizes the cost function of Equation 7and is computed using Equation 8 where :

∑ ‖ ‖ ∑ = ∑ = = ∑ ‖ ‖ = ( ∑ ∑ ) = ∑ ‖ ‖ =
The only rotations considered in these equations are those centered on the centroid of the contact points. Although we perceive it as an elementary rotation, moving one's index finger around one's thumb while keeping this one steady will thus be interpreted as a combination of a centroid-centered rotation and a translation. To tackle this problem, we weight all contact positions by the inverse of their traveled distance when computing , the center of both the rotation and the homogeneous scaling is also adjusted by removing the displacement possibly introduced by . The and parameters resulting from the above computations are used to determine the prominent gesture among Rotate, Swipe and Pinch. Our classifier considers one model for each gesture type and returns the one that better fits the observations (highest value). The models map the initial configuration to an estimated state ̃ (Equation 9). The estimated error (the residual sum of squares) and the coefficient of determination are then computed using Equations 10, 11 and 12.

̃ = ∑ ‖ ̃‖ ∑ ‖ ‖
Our classifying method is similar to the GestureMatching method used by Nacenta et al. [START_REF] Nacenta | Separability of spatial manipulations in multi-touch interfaces[END_REF], but instead of classifying the combined contribution of Rotate, Swipe and Pinch gestures, ours allows to classify the contribution of individual gesture types. Our method requires enough information to properly work. The classifier is thus enabled only when the summed distance covered by the contact points is beyond a given threshold. Based on preliminary tests, we found that a value of 10 pixels on a 90PPI display (around 2.8 mm) provides a good trade-off between latency and success rate, which is in agreement with other thresholds reported in the literature for similar applications [START_REF] Zeleznik | UniCam -2D gestural camera controls for 3D environments[END_REF].

Multi-touch gestures: circle around, look around and scrutinize

When the classifier detects a prominent Rotate gesture, the technique enters the circle around state of Figure 5 until all contacts are lost. provides the pivot point to rotate the scene and the angle of rotation (the center of the 3D rotation is computed from the projection of in the 3D scene).

When a Swipe gesture is detected, the technique enters the look-around state until all contacts are lost.

is then used to rotate the camera ) in a way similar to move around, but with two degrees of freedom instead of one.

When a Pinch gesture is detected, the technique enters the scrutinize state until all contacts are lost. The scale factor of is used to adjust the of the camera. To ensure smooth camera movements, its look-at point remains fixed while contacts are moving. The is restored to its initial value when all contacts are lost. This state further supports remote inspection by using to rotate the camera ( ), as in the look-around state.

EXPERIMENT

Our main motivation in this experiment was to assess our design choices by comparing Move&Look to other techniques from the literature (Screen-space [START_REF] Reisman | A screen-space formulation for 2D and 3D direct manipulation[END_REF], DabR [START_REF] Edelmann | The DabR -a multitouch system for intuitive 3D scene navigation[END_REF] and Drag'n Go [START_REF] Moerman | Drag'n Go: Simple and fast navigation in virtual environment[END_REF]) or available in commercial products (Virtual joysticks and the RealMyst technique described above), most of which have never been evaluated nor compared.

Task

Informal user testing with Move&Look suggested the technique was particularly efficient for interior designs mainly consisting of flat orthogonal surfaces. Encouraged by this, we wanted to assess the effectiveness of the technique in a more demanding environment. The task we chose consisted in collecting spheres placed inside boxes in an outdoor environment, and dropping them in a fountain at the center of the scene (Figure 6). To provide a fair comparison between multi-scale navigation techniques (Drag'n Go and Move&Look) and the others and focus on the evaluation of camera movements, the boxes were not positioned far away from each other but close to the central drop zone. Participants had to find the boxes in the scene. For each box, they had to position the camera in front of its only open face to pick up the sphere it contained. A sphere would turn from red to green when the camera was close enough to indicate one could touch it to pick it up. Participants could carry only one sphere at a time, and it was automatically dropped once in the drop zone. Collision detection prevented participants from moving through objects, and a trial was considered as fully completed after all the spheres had been dropped. Participants were instructed to perform this as quickly as possible. They could ask the experimenter to reset the camera to its initial position or withdraw a trial if they felt unable to complete it. They were not encouraged to do so, however. The experimenter rather encouraged them to finish a trial if he felt they could succeed.

Participants

Twelve unpaid male participants with a mean age of 35 (SD=14) served in the experiment. Five of them used a computer on a daily basis, played 3D video games and were familiar with touch-screens through mobile phones or tablets. Seven of them had a low experience with video games and were novice with touch interfaces.

Apparatus, design and procedure

Participants were seated in front of a 22" 3M multi-touch screen orientated at an angle of about from a horizontal desk. The experiment was implemented using Unity 3.5 3 . A repeated measures within-subjects design was used. The independent variable was the interaction technique (TECH) with six levels: DabR, Screen-space, Drag'n Go, RealMyst (a custom implementation of the RealMyst technique), Virtual joysticks (a standard combination of two Unity virtual joysticks displayed at fixed positions) and Move&Look. A trial consisted in collecting 4 spheres and each technique was evaluated with 3 successive trials (TRIAL). In summary the experimental design was: 12 participants 6 TECH 3 TRIAL = 212 total trials.

The presentation order for TECH was counter-balanced across participants using a balanced Latin Square design. To favor expert usage and a fair comparison between techniques, each was first introduced by the experimenter with a demo and then a training session. Participants could also use a cheat sheet throughout the experiment. After each technique, participants filled a questionnaire inspired by the Nasa TLX test and at the end of the experiment, they were asked to rank the techniques and give additional feedback.

Results

The dependent variables were the completion time, the number of give-ups and camera resets, and the qualitative results. Numbers of give-ups and camera resetsof trials were aborted for Screen-space, for RealMyst, for Virtual joysticks and for Drag'n Go, DabR and Move&Look. The camera was reseted in of all trials for Screenspace, for Virtual joysticks, for RealMyst, for DabR and Move&Look, and for Drag'n Go. Task completion time -Task completion time is defined as the time needed to successfully collect the four spheres and drop them in the fountain. Trials where participants gave up were removed for the analysis. Trials at least three standard deviations away from the mean for each TECH condition were considered as outliers and also removed. A repeated measures ANOVA showed a significant effect of TECH (

). Subsequent pairwise comparison showed significant differences (

) between Drag'n Go and Screen-space, Drag'n Go and RealMyst, Move&Look and Screen-space, and Move&Look and RealMyst. No significant difference was found between Drag'n Go and Move&Look. Completion times were for DabR, for Screen-space, for Drag'n Go, for RealMyst, for Virtual joysticks and for Move&Look. User ranking and questionnaire -The participants ranked the techniques in decreasing order of preference. Overall, Move&Look came first (10 participants ranked it first and 2 ranked it second) followed by Drag'n Go, DabR, Virtual joysticks, RealMyst and Screen-space. The participants who ranked Move&Look first explained it nicely complements Drag'n Go as it allows to control more degrees of freedom while keeping the navigation intuitive: it does not require focusing on the gestures to execute nor does it require planning a trajectory in the scene to reach a target. Screenspace was ranked last considering its lack of intuitiveness: in spite of the frequent use of the cheat sheet the participants did not understand how to effectively use the technique to navigate the way they wanted (we believe the important semantic distance explains this gap between users' intentions and the system's behaviours). These subjective results are in agreement with the quantitative results found for completion time and the numbers of give-ups up and camera resets.

After each technique, the participants answered questions related to the following six criteria on a 5 point Likert scale: mental demand, physical demand, performance, effort, frustration and satisfaction. The questions asked were similar to the ones available in the Nasa TLX test. We ran a Friedman analysis with Bonferroni-corrected Wilcoxon post-hoc analyses. This analysis shows significant differences between the techniques for all criteria, especially for the techniques at the bottom of the participants' ranking. Table 5 summarizes the significant differences that were found.

Mental demand

Physical demand

Performance

Effort

Frustration

Satisfaction

Move&Look-Screen-space

• • • • • • Move&Look-RealMyst • • • ○ • • Drag'n Go-Screen-space • • • • ○ • Drag'n Go-RealMyst • • • ○ ○ ○ Drag'n Go-DabR ○ • ○ ○ ○ ○ RealMyst-Virtual joysticks ○ • ○ ○ ○ ○ RealMyst-DabR ○ ○ ○ ○ • ○ Screen-space-DabR • ○ ○ ○ • • Screen-space-Virtual joystick • • ○ ○ ○ •
Table 5. Details of the post-hoc analysis for cases where one or more significant differences were found (•: significant difference, ○: non significant difference).

User feedback and observations -During the experiment we encouraged the participants to "think aloud" and freely comment on the interaction techniques. Comments were overall in agreement with the user ranking.

Screen-space received the most negative critics. All participants repeatedly reported their frustration with this technique. They felt out of control and found the mappings between fingers and camera movements inconsistent. The finger movements corresponding to different screen-space controls can indeed be quite similar, as illustrated by the optical flows of Figure 4 (e.g. and ). The output of the screenspace solver is also strongly influenced by the picked point in the 3D scene, and thus by the geometrical shape of the underlying objects. Lastly, the movements to execute in order to move forward ( ) and to zoom ( ) depend on whether the initial contact point is above or below the invisible horizon (in the former case, one has to move up, in the latter, one has to move down). All these reasons probably contribute to the fact that users were not able to anticipate camera motions. The comparison of Screenspace to other interaction techniques in 3D manipulation tasks corroborates these observations [START_REF] Martinet | Integrality and separability of multitouch interaction techniques in 3D manipulation tasks[END_REF].

Participants found DabR, Virtual joysticks and RealMyst either too slow or too fast. We hypothesize this was caused by the use of transfer functions not specifically tuned for the particular 3D environment we used: long distances took too much time to travel while participants traveled too fast on short distances. Participants found the Virtual joysticks to be less fatiguing. We hypothesize this was due to the use of rate control, which reduces physical movements. Participants reported an important fatigue when using DabR and complained they had to pay attention to the number of fingers they used. They complained about the delay introduced by the time-based mode switch used by RealMyst and the fact that the traveling direction is not towards the selected point but along the axis of the camera. Drag'n Go was particularly appreciated for its ability to quickly reach distant targets, but moving to a box while orienting the viewpoint in order to pick the sphere was found more difficult and required some planning. This was not reported as a problem with Move&Look.

Conclusion and future work

In this paper, we proposed an original methodology based on user-centered practices and optical flow analysis to address the problem of designing intuitive multi-touch navigation techniques for 3D environments. User-centered practices allow to define the navigation commands from the user's perspective while the optical flow analysis provides guidelines for defining intuitive multi-touch gestures to perform these commands. We instantiated this methodology for tasks articulated around the review of interior designs, which led to the design of a new interaction technique, Move&Look. The comparison of this technique to state of the art ones in a controlled experiment showed its overall superiority and revealed usability problems with the others. These results provide a first validation of the proposed design methodology. The methodology should be applied in other navigation contexts in order to further assess its effectiveness. The robustness of the proposed RST classifier should be formally evaluated, and it can certainly be improved. Even if participants did not complain about it, we observed them flattening their rotation gestures for the circle around command, probably because they unconsciously followed the corresponding optical flow. Our classifier could be modified to better take into account this oval shape, for example.

Figure 1 .

 1 Figure 1. Typical viewpoint controls: dolly, sidestep and fly ( and ), tilt, pan and roll ( and ), zoom ( ) and orbit ( and ).

Figure 2 .

 2 Figure 2. Sample interior design.Reviewing such a scene requires the ability to quickly navigate through it (including moving from one floor to the other), to orient the viewpoint in a precise way (e.g. to check the view from the couch) and to inspect particular objects (e.g. the ones on the table).

Figure 4 .

 4 Figure 4. Top image: optical flow computed over time with OpenCV when circling the viewpoint along the vertical axis ( ). Bottom images: stylized renderings of the flows corresponding to the 7 viewpoint controls of Table2(arrows could all point in the opposite direction).

Figure 5 .

 5 Figure 5. The Move&Look technique, instanciated from Figure 3.

Figure 6 .

 6 Figure 6. Left: overview of the 3D environment used in the experiment. Right: detailed view showing a box containing a sphere to pick up and drop in the fountain.

http://www.cyanworlds.com/iOS_realMyst/

The parameters associated to each transformation will be explained in the next section.

http://unity3d.com/unity/whats-new/unity-3.5