Summarize each of the research papers in a separate paragraph (e.g., 4 paragraphs total for 4 research papers).? 1. Describ

Common Fate for Animated Transitions in Visualization Amira Chalbi,† Jacob Ritchie,† Deokgun Park, Jungu Choi,

Nicolas Roussel, Niklas Elmqvist, Senior Member, IEEE, and Fanny Chevalier

Abstract—The Law of Common Fate from Gestalt psychology states that visual objects moving with the same velocity along parallel trajectories will be perceived by a human observer as grouped. However, the concept of common fate is much broader than mere velocity; in this paper we explore how common fate results from coordinated changes in luminance and size. We present results from a crowdsourced graphical perception study where we asked workers to make perceptual judgments on a series of trials involving four graphical objects under the influence of conflicting static and dynamic visual factors (position, size and luminance) used in conjunction. Our results yield the following rankings for visual grouping: motion > (dynamic luminance, size, luminance); dynamic size > (dynamic luminance, position); and dynamic luminance > size. We also conducted a follow-up experiment to evaluate the three dynamic visual factors in a more ecologically valid setting, using both a Gapminder-like animated scatterplot and a thematic map of election data. The results indicate that in practice the relative grouping strengths of these factors may depend on various parameters including the visualization characteristics and the underlying data. We discuss design implications for animated transitions in data visualization.

Index Terms—Gestalt laws, common fate, animated transitions, evaluation, motion

1 INTRODUCTION

Animation is commonly used for state changes in HCI and visualiza- tion applications, allowing the viewer to gradually track changes in an interface rather than having to reinterpret a visual representation or in- terface from scratch [4, 46]. However, designing animated transitions so that they convey changes that are smooth and simple to follow is not trivial, and involves issues such as pacing [22], staging [16], and tracking [44, 56] of animated objects. The Gestalt Law of Common Fate (LCF) [38] is an example of a widely known guideline for de- signing animations, where visual elements that move with the same velocity (i.e. same speed and same direction) are said to be perceived as sharing the same “fate”, and thus belong to the same group. The LCF is also the only of the five Gestalt Laws that deals with dynamic (i.e. animated, time-changing) properties; the others all concern static instances of grouping in visual perception [59].

Although the Gestalt Laws—including LCF—were derived from perceptual psychology experiments in the early 1900s at the “Berlin School” of psychology [38], only a few isolated examples of applica- tion to dynamic visualizations have been explored [10, 27, 62]. This presents an opportunity for visualization research to delve deeper into human perception for the purposes of optimizing animated transitions. For example, better knowledge of the automatic grouping of animated objects may suggest ways to structure animated transitions so that their complexity is decreased and they become easier to perceive. Further- more, while most examples of LCF use visual elements with identi- cal trajectories [38], the philosophical meaning of a “common fate” of objects engaged in joint motion is not necessarily restricted to ve- locity [48]. Rather, a general interpretation of “common fate” might

† The first two authors contributed equally to the work. • Amira Chalbi and Nicolas Roussel are with Inria, France. E-mail:

[email protected], [email protected] • Jacob Ritchie and Fanny Chevalier are with the University of Toronto in

Toronto, ON, Canada. E-mail: [email protected], [email protected]

• Deokgun Park is with the University of Texas at Arlington, TX, USA. E-mail: [email protected]

• Jungu Choi is with Purdue University in West Lafayette, IN, USA. E-mail: [email protected]

• Niklas Elmqvist is with the University of Maryland in College Park, MD, USA. E-mail: [email protected]

merely imply shared dynamic behavior between multiple objects that creates a perception that they are under the influence of the same phys- ical process [1]. Such shared behaviors include growth and compres- sion (size) as well as darkening and brightening (luminance). Given this background, it is useful to ask ourselves how the visual group- ing arising from common fate is influenced by such dynamic behav- iors, and how these factors interact with each other. Answering these questions may shed light on potential new ways to add structure to animated transitions in interfaces and visualizations.

In this paper, we study these intricacies of the Gestalt Law of Com- mon Fate by means of a large-scale online graphical perception ex- periment involving 100 crowdworkers performing perceptual group- ing tasks. Our experiment was designed to compare three static visual factors (position, size, and luminance) and three dynamic visual fac- tors (velocity, luminance change, and size change). For each trial, four graphical objects were grouped by two properties at a time: two pairs were grouped based on one factor and two other pairs based on another. This enabled us to not only study the individual grouping strength of each visual factor, but also to rank the factors in order of their relative grouping strength. Furthermore, to increase the ecolog- ical validity of our work, we also conducted a follow-up experiment asking participants to perceive dynamic changes in an animated scat- terplot as well as a thematic map. We discuss how these findings can inform the design of animated transitions to reduce cognitive load.

2 BACKGROUND Here we give a general overview of relevant work in perceptual psy- chology, graphical perception, and animation in visualization.

2.1 Perception and Gestalt Psychology Perception comprises the innate sensory components of the human cognitive system that are pre-conscious and used to represent and un- derstand the environment, and visual perception is the perceptual com- ponent dealing with sight. As the most important of the senses, the human visual system has evolved over millions of years to allow indi- viduals to distinguish, identify, and track objects in their vision [34].

Much of the seminal work on visual perception was conducted in the early 1900s by the so-called “Berlin School” of experimental psy- chology. This eventually led to the development of Gestalt psychol- ogy [38], a theory of mind based on a holistic view of human visual perception where the sum of the perceived “gestalt” is qualitatively different than its component parts, and in effect has an identity of its own. One key practical outcome of Gestalt psychology was the devel- opment of the law of prägnanz (German, pithiness) [38], which can be operationalized into the so-called “Gestalt laws” [59]: examples in- clude the Law of Proximity, which states that objects at close distances are perceptually grouped, or the Law of Similarity, which states that

1077-2626 2019 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

Manuscript received 31 Mar. 2019; accepted 1 Aug. 2019. Date of publication 16 Aug. 2019; date of current version 20 Oct. 2019. For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference the Digital Object Identifier below. Digital Object Identifier no. 10.1109/TVCG.2019.2934288

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CHALBI ET AL.: COMMON FATE FOR ANIMATED TRANSITIONS IN VISUALIZATION 387

objects with similar visual appearance are grouped together. Analo- gously, the Law of Common Fate—incidentally, the only Gestalt law dealing with dynamic settings— is commonly understood to state that objects with the same movement are perceptually grouped together. Recent research suggests that the same feature selection mechanism may underlie both similarity and LCF-based grouping [40, 67].

2.2 Motion and Animation Much of visual perception evolved for survival purposes, and few per- ceptual properties have the urgency of rapid movement. As a result, the human visual system is highly sensitive to motion and is capable of tracking multiple objects moving simultaneously [14, 44]. Animation, where the illusion of motion is recreated through the rapid display of a sequence of static images, is thus of interest both for psychology and for entertainment applications in artificial settings.

Animation has long been used in graphical user interfaces to show progress, convey state transitions, and notify the user of changes [4, 33, 17]. Animated transitions have become particularly popular and are used in a variety of applications, ranging from presentation soft- ware and video editors to visualization tools [26]. Perceptual stud- ies suggest that smooth transitions not only improve user decision- making [30], but also facilitate their mental map [7] and recall [49]. Despite much literature praising the merits of animations, Tversky et al. [56] note that there exist several studies showing that they could harm more than they help, but attribute the unpromising conclusions to poor animation design choices and flaws in evaluation protocols.

Animations can be specifically designed to convey data. Cartoonists were the first to investigate how to communicate emotions through motion [35]. Bartram et al. [6] proved the effectiveness of animated icons to notify changes. Ware et al. [63] suggested the use of animation to express causal relationships between entities in visualizations.

Structured animations can be used to reduce visual complexity dur- ing a transition. Heer and Robertson [32] proposed introducing dis- crete stages during transitions between statistical data graphics to help users follow the animations. Chevalier et al. [16] investigated stag- gering—an extreme case of staging—but found no positive impact on user performance. Dragicevic et al. [22] studied how temporal pac- ing for animation can be distorted to improve perception, and Du et al. [24] studied how a spatio-temporal structuring can reduce visual complexity by bundling trajectories of animated objects.

Animated transitions are also increasingly used in information vi- sualization to support various operations such as filtering, sorting, zooming, or changing visual representations. Bartram and Ware were among the first to study them in this context for brushing [5]. Van Wijk and Nuij [58] proposed a mathematically optimized animation scheme for panning and zooming so that the visual flow is invariant. The Scat- terDice [25] and GraphDice [9] techniques leverage shape transitions between scatterplots and node-link diagrams, respectively.

2.3 Gestalt Laws in Visualization The Gestalt Laws are an important component of visual perception that researchers have attempted to leverage for more efficient visual communication. Early work in cartographic animation assumes that common fate is more generally valid for objects that change together, e.g., by blinking, though no formal evaluation is reported [10]. Ware and Bobrow used motion as a mechanism to highlight a subgraph of interest in a larger graph. While they initially found that motion dom- inates hue for highlighting [61], their most recent studies suggest that motion and hue can be used in conjunction for the highlighting of two different entities simultaneously [62]. Finally, Romat et al. [47] can be said to leverage the notion of common fate by animating the link lines in a node-link diagrams to indicate direction, rate, and speed.

Friedrich and colleagues [27, 43] successfully applied the Law of Common Fate to make subgraphs apparent when transitioning from one layout to another to preserve the viewer’s mental map. The goal was to find an animation of the subgraph of interest that would be in- terpreted by the brain as movement of three-dimensional objects, using affine transforms to decompose the motion into a series of translations, rotations, scalings, and shears. They found that the Law of Common

Fate not only holds for objects moving in the same direction, but also for objects which move in any structured way. However, none of these studies are empirical, and, more importantly, few prior efforts have directly studied common fate for visualization.

3 THE GESTALT LAW OF COMMON FATE

The predominant interpretation of the Gestalt Law of Common Fate (LCF) is that the concept of “common fate” solely refers to the visual grouping of elements moving in a coherent motion, i.e. with the same speed and direction. One way to intuitively explain this phenomenon is that the moving objects that are visually grouped are under the influ- ence of a single factor causing them to move along the same trajectory.

However, this simplistic interpretation is not the only one. Wertheimer, one of the founders of Gestalt psychology, used moving objects with identical velocity as an illustrating example in his original German manuscript [64]. However, as noted by Sekuler and Bennett in 2001 [48], he also included a passage on broader interpretations of the concept of common fate that never appeared in the English tran- script: “The principle [of common fate] applies to a wide range of conditions; how wide, is not discussed here.”

Biased by the belief that Gestaltists only had motion in mind when developing LCF, subsequent studies in psychology have mostly fo- cused on investigating the limits of figure-ground segmentation under variations of motion coherence [39, 51, 57], which may explain why the simplified and incomplete version of the law has become preva- lent. Exceptions include studies on dynamic luminance [1, 48] and its informal application to cartographic animation [10] and graph visual- ization [43, 62]. As stated by Brooks in a recent survey on perceptual grouping: “Although common fate grouping is often considered to be very strong, to my knowledge, there are no quantitative comparisons of its strength with other grouping principles.”(p. 60, [12])

Given this background, we formulate two distinct research ques- tions that we focus on in this work:

RQ1 Does the Law of Common Fate extend to other dynamic vi- sual variables, such as dynamic luminance or size? While past work [1, 48] has proved this for luminance, we want to study this more broadly for other visual variables.

RQ2 What is the relation between the (extended) Law of Common Fate and other Gestalt Laws? As the only Gestalt law dealing with animation, and given the perceptual urgency of motion [56], we are interested in the relation between LCF and other Gestalt laws.

To answer these, we discuss criteria that may have an impact on perceptual grouping and identify visual variables that obey them.

3.1 Criteria for Perceptual Grouping

As is clear from the above treatment of Gestalt psychology, percep- tual grouping of visual objects arises from relations between visual variables. Identifying (and ranking) such visual variables was one of the fundamental advances of early work in visualization; for example, Bertin [8] lists seven visual variables, and Cleveland and McGill [18] list ten. However, it is not feasible for us to study all of these visual variables, and besides, not all of them have the same potential for ex- hibiting perceptual grouping. Here we describe our selection criteria.

3.1.1 Associativity

Visual variables that support grouping are often described as associa- tive in the literature. It is worth noting, however, that this term has often been misunderstood by the community. As Carpendale points out [13], there are discrepancies between the notion of associativity as defined by Bertin [8, p. 48] and that which is usually understood [45]. For Bertin, a variable is associative if objects can be grouped across other variables despite changes in that one. In contrast, Carpendale’s definition of associativity refers to perceptual grouping power.

Since we focus on grouping, we adopted Carpendale’s definition, yielding one dynamic (motion) and eight static (position, size, shape, luminance, color, orientation, grain, texture) associative variables.

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3.1.2 Ordered Transitions Since our focus is on common fate, our second criterion of selection pertains to the dynamic aspects of the above listed associative vari- ables. Among these variables, there are several for which it is difficult to describe a dynamic behavior and specify a transition. For instance, working with shapes, textures or color hue, we would have many op- tions to choose from as people (including us) have no clear intuition of how one should transition from one value to another.

Thus, in the spirit of keeping the study as simple as possible, we focused on variables that, in addition to being associative, are ordered, i.e. a change in these variable can be perceptually interpreted as in- creasing or decreasing. This allows for deterministically interpolating between values for both increasing transitions (the value of the visual variable grows), or decreasing transitions (the value becomes smaller). From the list of associative variables given by Carpendale [13], only position, luminance, and size are ordered.

3.2 Visual Variables with Grouping We focus on the static and dynamic versions of the three visual vari- ables satisfying our criteria as follows:

3.2.1 Static Variables Static visual variables are invariant over time and thus do not create the perception of common fate. However, including these factors allows us to answer RQ2 on the relation between LCF and other laws.

• Static position (SP): Visual elements in close proximity are per- ceived as grouped, a phenomenon known as the Law of Prox- imity. Geometric position is also generally ranked as the most perceptually accurate visual variable [8, 18].

• Static size (SS): According to the Law of Similarity, elements with the same size will be grouped together. Bertin [8] names size as the second most perceptually accurate visual variable, whereas Cleveland and McGill [18] rank area as number five.

• Static luminance (SL): By the same Law of Similarity, elements with the same color are grouped. Bertin ranks it at number five, and Cleveland and McGill rank it as “color saturation” at six.

3.2.2 Dynamic Variables Dynamic visual properties represent behavior that changes over time, which means that they may exhibit common fate effects. These fac- tors allow us to answer RQ1 on whether the concept of common fate extends beyond mere object motion.

• Dynamic position (DP): The canonical example of the Law of Common Fate: objects moving with the same speed and direc- tion are perceived as belonging to the same group.

• Dynamic size (DS): Are visual objects that grow or shrink in the same manner perceived as belonging to the same group?

• Dynamic luminance (DL): As shown by prior studies, visual ob- jects becoming brighter or darker in the same way are perceived as belonging to the same group [48, 59, 62]. However, these ex- periments did not allow for investigation of the relation of DL to other visual variables, both static and dynamic.

4 STUDY RATIONALE Our goals are to (i) determine whether the LCF extends to visual variables beyond motion, and to (ii) determine the relative grouping strength of LCF and other Gestalt laws. Here we present our rationale.

4.1 Task Rationale In our study, we chose to give participants perceptual tasks where four graphical objects were grouped by two properties at a time so as to create two orthogonal possible groupings, and ask participants which emergent groups they perceive. In other words, we make two visual variables compete, and record which one—if any—coincides with the participant’s answer, and hence influenced their grouping perception.

From a visual variable’s grouping power perspective, any answer to the above question falls into one of the three following categories:

(i) the participant’s grouping coincides with that dictated by the first visual property, and we can assume that the corresponding visual vari- able thus has the highest grouping strength for this task; (ii) they grouped the objects based on the second, competing property, so we assume that the other visual variable has the highest grouping strength for this task; or (iii) none of the above (i.e., they grouped differently), in which case none of the two variables can be said to have a grouping power for this task.

Our focus being on common fate, we are primarily interested in tasks where dynamic variables are involved, and hence on animated transitions implementing these dynamic behaviors. However, for the sake of experimental completeness, we also tested static variables against each other, and our trials also included static visualizations.

By making a dynamic visual variable compete against any of the static variables whose grouping power is established (i.e., by the Law of Proximity or the Law of Similarity), we can quantitatively mea- sure the grouping power of the Law of Common Fate—in our case, restricted to motion, dynamic luminance, or dynamic size. The more cases where participants deviate from the Laws of Proximity and Sim- ilarity in favor of the dynamic property, the stronger the evidence that the associated dynamic visual variable has perceptual grouping power, and subsequently the stronger the evidence that the Law of Common Fate applies to this variable (RQ1). The relative grouping strength be- tween each variable is directly measurable from tasks comparing pairs of non-conflicting visual variables (RQ2).

4.2 Summary of Tasks Table 1 summarizes all of the possible pairwise comparisons for our six visual variables. Out of the 36 cells, we do not consider self- comparisons (diagonal), nor do we count duplicates (i.e. SP vs. DL is the same as DL vs. SP); these are grayed out. We also discard any pairwise comparison where a dynamic visual variable competes against its static counterpart (e.g. SS vs. DS). The reason is to avoid conflicts: having orthogonal groups bound to the same visual variable would necessarily break the notion of similarity at a point during the animation, making such cases difficult to interpret.1

This leaves 12 distinct pairwise comparisons that form our set of tasks for the study: DP-DS, DP-DL, DP-SS, DP-SL, DS-DL, DS-SP, DS- SL, DL-SP, DL-SS, SP-SS, SP-SL, and SS-SL.

Table 1: Comparison Tasks Generated from the Six Visual Variables.

DP DS DL SP SS SL

DP — DS-DP DP-DL — DP-SS DP-SL DS DP-DS — DS-DL DS-SP — DS-SL DL DP-DL DS-DL — DL-SP DL-SS — SP — DS-SP DL-SP — SP-SS SP-SL SS DP-SS — DL-SS SP-SS — SS-SL SL DP-SL DS-SL — SP-SL SS-SL —

4.3 Manipulation of Visual Variables Let visual property henceforth denote a specific value for a visual vari- able. To create the above tasks, where objects are grouped by similar visual properties, we manipulate static properties (i.e. position, size, and luminance) as well as dynamic behaviors (i.e. changes in position, changes in size, and changes in luminance). Through these manipula- tions across objects, we can manipulate the relation of similarity—in the most general sense of the term—between objects to create distinct groups of objects sharing similar visual properties.

Here, we propose a generalization of similarity in a particular visual variable’s definition space for both the static and dynamic aspects.

4.3.1 General Notation In the following, we use S to refer to the set of visual objects in a task. For a given object A in S , VA(t) refers to the value of a visual

1For example, comparing SP and DP would mean that two objects grouped

by static position would only be in proximity during a single point in the trial,

e.g. at the beginning or end; they would become separated (and thus no longer

near) by varied dynamic positions (velocities) during the rest of the trial.

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CHALBI ET AL.: COMMON FATE FOR ANIMATED TRANSITIONS IN VISUALIZATION 389

variable at time t, and ΔVA(ti−1,ti) denotes the difference of values for A between time ti−1 and ti (i.e. ΔVA(ti−1,ti) = VA(ti) − VA(ti−1)), where the increment between times ti−1 and ti corresponds to one step at the finest observable temporal resolution.

Let PA(t), SA(t) and LA(t) refer to the position, size, and luminance of the object A at time t of the animation. Object luminance is normal- ized to [0,1], where 0 is black and 1 is white, for a given display.

4.3.2 Similarity and Similar Behavior Visual objects A and B are similar with respect to a visual variable V at time t if their difference is below a threshold: |VA(t)−VB(t)|≤ τV

In the static case, the notion of similarity for two objects A and B directly refers to the Law of Proximity for position, and the Law of Similarity for size and luminance. In other words, these static situ- ations correspond to the special cases in the above definition where PA(t) and PB(t), SA(t) and SB(t), LA(t) and LB(t) are constant over time (i.e., static position, size, and luminance).

What the Law of Common Fate suggests, is that even if objects are not similar at any time t, the fact that they behave similarly is a factor for perceptual grouping. Put differently, this means that the difference in their variations across time is below a certain threshold. Formally, visual objects A and B behave similarly between ti−1 and ti if:

|ΔVA(ti−1,ti)− ΔVB(ti−1,ti)|≤ θV Applying the above definitions in the context of our visual variables

during an animated transition, we have:

A and B are SP-similar (resp. SS-similar; SL-similar) if: A and B are similar in position (size; luminance), ∀t of transition; A and B are DP-similar (resp. DS-similar; DL-similar) if: A and B behave similarly in position (size; luminance), ∀t of transition.

We can operationalize these rules to create groupings for any of the above visual variables by ensuring both that (1) objects that are to be grouped are indeed similar (within some tolerance), and that (2) there exist no other object in S that is similar to the objects in the group. We note that these rules do not apply generally across all situations, but only in the context of our controlled experiment; in general, sim- ilarity is highly contextual. For example, two objects with identical luminance will not be perceived as similar if one is placed on a darker background and the other on a lighter background.

4.3.3 Neutrality To control for perceptual processes and confounding effects, all ob- jects in S should be theoretically neutral, i.e. they should all be sim- ilar in all aspects (both static and dynamic). For simplicity and to guarantee perceptual grouping neutrality, we use a set of static and identical visual objects as a default set. It is only when testing the effect of visual variables on grouping that we modify these specific object properties to create distinct groups, as described above.

The only exception for neutrality is position, since it does not make sense to have objects overlap. Perfect position similarity (i.e. τP = 0) would entail all objects sharing the exact same position. In fact, we also cannot enforce equidistance between all possible pairs of objects for sets of more than three objects. Dot lattices are commonly used in psychology experiments that study proximity grouping [12]; however, we chose to avoid too much regularity in object arrangement since this can also lead to grouping by proximity [50].

Any positioning strategy deviating from the above rules will neces- sarily introduce a small bias for a set of more than three objects. To minimize the spatial proximity that may occur by uniform random po- sitioning, we used a similar approach to Poisson-disc sampling [11], which results in a balanced spatial distribution by adding a constraint on the spatial position of each object relative to the closest neighbor: each object must be located within a distance range [dmin,dmax] from its closest neighbor (measured from the objects’ centers). The smaller this distance range is, the more regular the objects’ arrangement.

4.4 Design Decisions We made several design decisions when designing our experiment, based on extensive pilot testing and the above theoretical framework.

4.4.1 Choice of Animation Because we primarily study the impact of dynamic changes on percep- tual grouping, our main focus when testing dynamic variables lies in what happens during the animated transition itself, and nothing more. We want to prevent any bias that may be caused by the exposure to the first frame (i.e. the initial static state) or the end frame (i.e. the final static state). …

CourtTime: Generating Actionable Insights into Tennis Matches Using Visual Analytics

Tom Polk, Dominik Jäckle, Johannes Häußler, and Jing Yang

Fig. 1. CourtTime visual analytics system. CourtTime provides an overview of the match score (A) and lets the user switch seamlessly between high-level overview of played points (B) and a detailed view on the shot level (C) that displays the serve, return, and last three shots in the point from each player. To facilitate access to the analysis, we provide a rich set of different spatio-temporal encodings, as well as ordering and aggregation capabilities (not shown). An interconnected filter list (D) provides a multi-faceted means to effectively drill-down to specific points. We enable shot-specific, spatial feature-driven re-orderings (E) to aid in finding shot patterns. A 1-D Space-Time Chart displaying the left/right dimension of a point over time is shown in the inset in (B). Solid circles are forehands and hollow

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