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

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

1. Describe the motivation the authors had for their work. What makes their work so important? (You may find it useful to provide some background and context here.)

2. Who would be interested in reading this paper (domain experts, GVSU departments, outside organizations, etc.)?

3. What are the paper’s main research hypotheses or contributions?

4. What did the researchers do to test their hypotheses or achieve their research contributions?

5. What are the long-term contributions that will still be relevant 10, 20, 30, … years from now?

6. Which of its citations appear to be the most relevant resources for exploring this topic further? 

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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:

amira.chalbi.ihm@gmail.com, nicolas.roussel@inria.fr.
• Jacob Ritchie and Fanny Chevalier are with the University of Toronto in

Toronto, ON, Canada. E-mail: jritchie@dgp.toronto.edu,
fanny@cs.toronto.edu.

• Deokgun Park is with the University of Texas at Arlington, TX, USA.
E-mail: deokgun.park@uta.edu.

• Jungu Choi is with Purdue University in West Lafayette, IN, USA. E-mail:
monsieur.choix@gmail.com.

• Niklas Elmqvist is with the University of Maryland in College Park, MD,
USA. E-mail: elm@umd.edu.

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

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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:
reprints@ieee.org, 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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388 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 26, NO. 1, JANUARY 2020

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). …

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