Motion Volume: Visualization of Human Motion Manifolds
Masaki Oshita
Kyushu Institute of Technology
Iizuka, Fukuoka,, Japanoshita@ces.kyutech.ac.jp(a) input data (trajectories only)(b) input data (trajectories with orientations)(c) visualization (motion volumes)

Figure 1: Example visualization of the eight motions of a tennis forehand shot. (a)(b) The input data contain the spatial andorientational trajectories of body parts from a set of motions. (c) The output visualization contains the selected poses for key
timings as well as spatial and orientational volumes for the body parts.

ABSTRACTCCS CONCEPTS

The understanding of human motion is important in many areas
such as sports, dance, and animation. In this paper, we propose amethod for visualizing the manifold of human motions. A motion
manifold is defined by a set of motions in a specific motion form.
Our method visualizes the ranges of time-varying positions andorientations of a body part by generating volumetric shapes forrepresenting them. It selects representative keyposes from the keyposes of all input motions to visualize the range of keyposes at eachkey timing. A geometrical volume that contains the trajectories
from all input motions is generated for each body part. In addition,a geometrical volume that contains the orientations from all input
motions is generated for a sample point on the trajectory. The user
can understand the motion manifold by visualizing these motion
volumes. In this paper, we present some experimental examples fora tennis shot form.

• Human-centered computing → Visualization techniques;• Computing methodologies → Motion processing; Volumetricmodels.

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VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ACM ISBN 978-1-4503-7002-8/19/11. . . $15.00
https://doi.org/10.1145/3359997.3365684

KEYWORDS
Visualization, Human Motion, Motion Manifolds, Computational
Geometry
ACM Reference Format:
Masaki Oshita. 2019. Motion Volume: Visualization of Human Motion Manifolds. In The 17th International Conference on Virtual-Reality Continuum
and its Applications in Industry (VRCAI ’19), November 14–16, 2019, Brisbane,
QLD, Australia. ACM, New York, NY, USA, 7 pages. https://doi.org/10.1145/
3359997.3365684

1

INTRODUCTION

The understanding of human motion is important in many areas
such as sports, dance, and animation. In these areas, people often
need to understand the variations in the motions of a specific form
rather than just a single motion. For example, for a tennis trainee
to practice a shot form, he or she needs to understand the manifoldof the good motions rather than a single ideal motion because there
are some variations even in the good motions that are performed byexperts. However, because human motions are high-dimensional
space-time data, it is difficult to visualize them in a way that people
can easily understand. Playing back a motion clip as an animation is
a common way to view a motion. However, because only one pose isdisplayed at a time during animation, it is difficult to understand thecharacteristics of the motion. To solve this problem, many methods

VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia

for depicting a motion as a single image have been developed [Assaet al. 2005; Bouvier-Zappa et al. 2007; Li et al. 2016; Yasuda et al.
2008]. However, these methods are intended for dealing with asingle motion and cannot visualize the manifold of a motion form.
In this paper, we propose a method for visualizing the manifold of
human motions. A motion manifold is defined by a set of motions ina specific motion form. Our method visualizes the ranges of the timevarying positions and orientations of a body part by generating
volumetric shapes for representing them. It selects representative
keyposes from the keyposes of all input motions to visualize therange of keyposes at each key timing. A geometrical volume that
contains the trajectories from all input motions is generated foreach body part. In addition, geometrical volume that contains theorientations from all input motions is generated for a sample pointon the trajectory. The user can understand the motion manifold byvisualizing these motion volumes. The generated three-dimensional(3D) shapes can be rendered as an image. The viewing positionand orientation can be freely chosen by the user. An example ofour results is shown in Figure 1. In this paper, we present someexperimental examples for a tennis shot form.
The remainder of this paper is organized as follows. Section 2
review related work, Section 3 explains the input motion data, andSection 4 describes our method for generating motion volumes.
Section 5 and 6 present the experimental results and discussion,respectively. Finally, Section 7 concludes the paper.

2

RELATED WORK

Because it is difficult for an observer to understand a motion when
it is played back to him or her, many methods have been developed
for depicting a motion as a single image [Cutting 2002; Li et al.
2016]. Drawing a series of important poses is one approach. Many
methods have been developed for choosing important poses in a
motion and drawing them. Assa et al. [2005] proposed a method for
projecting a motion into a low-dimensional space to find important
poses. Yasuda et al. [2008] proposed a method for drawing important
poses on a timeline. The colors of the poses are determined by the
direction in which they face. Bouvier-Zappa et al. [Bouvier-Zappa
et al. 2007] proposed a method for adding visual cues to posessuch as motion arrows, noise waves, and stroboscopic motion torepresent the movements at each pose. These methods are intended
to visualize one complex motion as an image and cannot be used
to visualize a motion manifold that is defined by a set of motions.
Some methods have been developed for visualizing a large number of different motions [Hu et al. 2010; Jang et al. 2014; Sakamoto
et al. 2004; Shen et al. 2017]. These methods are intended for categorizing the motions into groups and depicting the differences
between them. Recently, Shen et al. [2019] proposed a metric forevaluating the similarity of motions in terms of the interaction between two characters or between a character and an object. Thesemethods are also not suitable for visualizing motion manifolds.
The aim of most previous studies is to generate 2D images. In
contrast, Zhang et al. [2018] proposed the MoSculp system, which
generate 3D shapes for representing the trajectories of body parts
from a motion sequence. They only depict the time-varying positions of body parts and cannot depict their time-varying orientations. Their method focuses on analyzing video for generating

Masaki Oshita

shapes. Moreover, their method is intended for a single motion andcannot be used to visualize motion manifolds. Kazi et al. [2016]
developed a tool for creating 3D shapes that includes poses and visual effects representing movements. However, the 3D shapes must
be authored by the user and they are not considered to represent
motion manifolds. Our method also generates 3D shapes, but it isintended for representing the motion manifold of a set of motions,
including not only the spatial but also the orientational ranges ofbody parts.

3

MOTION DATA

Our method takes a set of motions in a specific motion form as
input. Instead of example motions, a generative statistical model[Lau et al. 2009; Min et al. 2009] that is constructed from a setof motions can also be used. Our method can take a number ofexample motions that are generated from such a statistical model.
Given a human body model, a pose is represented by the positionand orientation of the pelvis as well as the rotations of all joints.
A position is represented by a 3D vector. There are several ways
to represent an orientation or rotation, such as a combination ofrotational angles, 3×3 matrix, or quaternion. Our method works
with any of these representations, so we used a 3×3 matrix in
our implementation. A motion is represented by a series of poses.
The positions and orientations of the body parts in any frame
are computed based on the body model and pose using forward
kinematics. The spatial and orientational trajectories of the bodyparts are represented by a series of positions and orientations, as
shown in Figure 1 (b).
Our method assumes that the same number of key timings are
specified for all the input motions. The key timings represent theimportant moments of the motions. For example, for the tennis
forehand shot in Figure 1, three key timings were used: take-back,impact, and follow-through. These keyposes are commonly usedin the training of tennis shot forms [Oshita et al. 2019]. The key
timings can be either manually specified or automatically detected.
To detect key timings, either some general methods such as [Assaet al. 2005] or motion-specific methods such as [Oshita et al. 2019]can be used. The appropriate number of key timings and method of
detecting them depend on the target motion form and application.
We assume that all input motions are based on the same bodymodel. In theory, motions from different body models can be treated
together by applying a motion retargeting [Baek et al. 2003], aslong as the difference is acceptable. However, motion retargeting is
not explored in this paper.
We use only skeletal motions and do not use a skinned shapemodel. A pose can be drawn by using a stick figure with thickness
parameters. Alternatively, a skinned shape model can be used for
depicting poses, which may improve the visual quality. However,it highly depends on the quality of the skinned shape model, andmaking such a model for each set of motions is time consuming.
Therefore, the use of a skinned shape model is not explored in thispaper.

Motion Volume: Visualization of Human Motion Manifolds

4 MOTION VOLUME GENERATION
4.1 Overview
This section describes our method for generating geometrical model
for a motion manifold. The positions and orientations of bodyparts at each frame of each motion can be computed from thepose of the frame using forward kinematics. Our method generates
shapes to represent the ranges of each keypose as well as the spatial
and orientational ranges of each body part. Although the motion
volumes can be generated for all body parts, in this paper, they
are generated for the primary body parts: the pelvis, chest, head,right and left hands, and right and left feet, as shown in Figure 1. Inpractice, the body parts for which motion volumes are generated
can be chosen depending on the target motion form and application.
Our method generates static shapes for visualizing this information and does not visualize temporal information. Neither thetimes of the sampling poses and points nor the spatial and rotational velocities of the body parts are considered. Although it ispossible to use the colors of shapes for representing the temporal
information, this is not explored in this paper. Because our method
generates geometrical shapes and does not use their colors, thecolors of shapes can be used for any other purpose depending on
the applications and users. For example, the colors can be used for
representing additional information such as temporal properties orfor identifying different keyposes and body parts.
The motion manifold of input motions can be visualized by drawing the keyposes and the shapes of the spatial and orientational
volumes of the body parts. However, drawing the shapes of all bodyparts sometimes makes it harder to see and may not be appropriate,
as shown in Figure 1. The user can choose one or a few key timings
and body parts on which to focus. In addition, the camera position
can also be controlled by the user so that they can choose a pointof focus. This makes our method suitable for interactive visualization because the user can freely change the camera position, key
timings, and body parts. Moreover, the user can observe the generated shapes in a virtual reality environment with a head-mounted
display.

4.2

Selection of Keyposes

Keypose visualization is a common and useful approach to understanding motion [Assa et al. 2005; Yasuda et al. 2008]. However,
especially when there are many input motions, displaying all the
keyposes of all motions makes it hard to see them. The range of
poses at each key timing should be shown by drawing the minimum
number of poses, as shown in Figure 2.
To solve this issue, our method chooses a few keyposes fromthe keyposes of all input motions for each keypose timing. Morespecifically, one primary keypose pp and a few secondary keyposes
psi are chosen from the keyposes pi ∈ Ps from all input motions.
The selected keyposes can be drawn as stick figures, as explainedin Section 3.
The primary keypose should be the center pose of the all keyposes. Therefore, the keypose for which the sum of distances toother keyposes is the smallest is chosen as the primary keypose.
That is,Õ
pp = argminpp
D(pp , pi ),
(1)
pi ∈K

VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia

where pi is one keypose in the set of all keyposes K and D(pi , pi ) is
the distance function between two poses. The distance is computed
as the average distance between all the body parts of the two poses
after the position and orientation of the poses are aligned by atransformation matrix T. It is calculated as
1 Õ kD(pi , pj ) =|pi − Tpkj |,
(2)
n
k ∈B

where B is the set of all n body parts and pki and pkj denote thepositions k-th body part in the two poses.
The secondary keyposes should show the boundaries of the
keyposes. Therefore, we choose the combination of keyposes S =ps1 , · · · , psm for which the sum of distances to the primary keypose
as well as the distances to each other is the largest as the secondary
poses.
ÕS = argmaxS ∈K {D(pi , pp ) +D(pi , pj )}(3)
pi ,p j ∈S

Finding such a combination of secondary poses S ∈ K is considered to be a NP-hard problem. However, as long as the numbers ofn and m are small (particularly m), the computational speed is not
a problem in our experiments, even with a brute-force approach. If
the numbers n and m become large, some approximation and/or optimization algorithms can be introduced for facilitating the process,although this is not explored in this paper.
The number of secondary poses m can be either specified by theuser or determined based on a specified threshold for the sum of
distances in Equation 3. In our experiments, we took the former
approach and used m = 2, because determining an appropriate
threshold is not straightforward. As a result, three poses werechosen for each of the three key timings in our results (Figures 1
and 2).

4.3

Generation of Spatial Volumes

A series of time-varying positions of a body part in a motion can be
represented by a trajectory. However, drawing the trajectories fromall input motions makes it hard to see the range of all trajectories,
as shown in Figure 3 (a). To solve this issue, our method generates
a geometrical shape that contains the trajectories from all input
motions for each body part, as shown in Figure 3 (b).
It generates a surface such that the distance to the closest trajectory is a constant value. The distance function is defined by theminimum distance to the closest sample points on all the trajectories. That is,
V (p) = minpi j ∈P |p − pi j |,(4)
where p is an arbitrary point in the space and pi j is j-th point ofi-th trajectory in all sample points P.
To generate a surface, we employ the marching cubes method[Lorensen and Cline 1987], which is a conventional method forsurface generation defined by a distance function. It generates asurface by connecting the faces generated for each small voxel in a
3D grid. In our experiments, the size of voxel is set to 0.05 m andthe surface distance is set to 0.05 m.
Because the trajectories are represented by a series of positions,the generated surface may become bumpy, especially when the distances between adjacent sample points are large. As postprocessing,VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia(a) all key poses

Masaki Oshita(b) selected key poses

Figure 2: Selection of keyposes. (a) Input: all example poses for three key timings. (b) Output: selected poses for three key
timings.

(a) spatial trajectories(b) spatial volumes and center trajectories

Figure 3: Spatial volumes. (a) Input: trajectories for the body parts from all motions. (b) Output: geometrical shapes for the
body parts.
we apply a Laplacian smoothing [Sorkine et al. 2004] to make thegenerated shape smoother.
Although it is possible to use a meta-ball [Blinn 1982] instead of
the simple distance function for generating a smoother surface, it
is difficult to adjust the distances between adjacent sample points.
Therefore, we chose to use a combination of the marching cubes
method and Laplacian smoothing.

4.4

Representation of an Orientation

In addition to the positions of a body part, its orientations arealso important for understanding its motion. Visualizing a set oforientations is more difficult than visualizing a set of positions.
Displaying poses is not enough to show the orientations of the
body parts, especially with stick figures, which do not show therotations of body parts.
Various methods have been used to depict orientations. An arrow(Figure 4 (b)) is a common way to represent an orientation. However,it cannot represent 3D orientation, because the rotation along thedirection of arrow cannot be represented. Using three perpendicular

arrows to indicate the local coordinates (Figure 4 (c)) is also acommon way for representing a 3D orientation. However, thisis not suitable for representing many orientations and requires
different colors for the three arrows. Although it is also possible torepresent a orientational trajectory using a color coded trajectory[Pȩszor et al. 2014], this is not very intuitive. Moreover, because
the colors often indicate additional information, as mentioned in
Section 4.1, using color coding for orientations is not desirable.
To solve the problems of these previous approaches, we introduce
flat arrows to represent a 3D orientation in a simple form (Figure
4 (a)). The rotation along the direction of an arrow can also be
represented using this flat arrow. Although we can use two different
colors for the front and back of a flat arrow to represent 360-degree
rotations around the direction of arrow, this is not necessary when
only 180 degrees of rotation is sufficient.
To draw a flat arrow, the local coordinates (i.e., the forwardfacing axis and upward axis) must be defined for each body part.

Motion Volume: Visualization of Human Motion Manifolds

VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia(a) flat arrow representing orientation (our method)(b) arrow representing one direction(c) three arrows representing the local coordinates

Figure 4: Visualization of an orientation. (a) Using flat arrows, our method represents 3D orientation in a simple form. (b) An
arrow represents only one direction. (c) Three arrows represent the local coordinates (a 3D orientation).

(a) orientations and trajectories(b) selected orientations and center trajectories(c) orientatoinal volume and center trajectories

Figure 5: Orientational volumes. (a) Input: all trajectories with orientations. (b) Center trajectories with orientations. (c) Center
trajectories with orientational volumes.
In our experiments, we assigned these axes based on the forwardfacing and upward directions of the body parts in an initial T-stance
pose.

4.5

Generation of Orientational Volumes

Time-varying orientations can be displayed by drawing the flatarrows on the trajectory at certain intervals, as shown in Figures 5(a) and (b). Figure 5 (a) shows all trajectories and their orientations,whereas Figure 5 (b) shows the center trajectory and its orientations.
The center trajectory for a body part is determined by choosing
one trajectory from the trajectories of all input motions. We choose
the trajectory with the minimum distance to the position of the
body part of the primary keypose over all key frames.
Visualizing a range of orientations is more difficult than visualizing a range of positions. Our method generates a convex hull for theorientations to represent their range. A convex hull is a geometricalshape that contains all sample points, and many algorithms havebeen developed for computing the convex hull [Berg et al. 2008].
Because the convex hull of a flat arrow contains four vertices, as
shown in Figure 4 (a), a convex hull is generated from all the vertices of the flat arrows for the orientations that are collected fromall trajectories and associated with the sample point, as shown in
Figure 5 (c).
A generated convex hull represents the variation in 3D orientation in a simple form. Our approach works well as long as thevariation in orientation is not too large. When it becomes too large,
the convex hull also increases, which makes it difficult to present
the orientations.

5

EXPERIMENTAL RESULTS

In this section, we present some experimental results of our visualization. We applied our method to tennis shot forms. Our method
visualizes the manifold of a set of motions, and it can be used tocompare the manifold of a set of motions and the manifold of asingle motion. It can also be used to compare the manifold of a setof motions and the manifold of another set of motions.

5.1

Training of Tennis Motion Forms

As mentioned in Section 1, when a trainee would like to practice aform in sport or dance, he or she needs to understand the manifoldof the motion form and the differences between this form andVRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia(a) motion volumes of whole body

Masaki Oshita(b) motion volumes of the right hand(c) motion volumes of the right footFigure 6: Comparison of the motion volumes of a skilled player (blue poses and orange volumes) and with the motion volumesof a trainee (white poses and gray volumes).

(a) motion volumes of whole body(b) motion volumes of the right hand(c) motion volumes of the right footFigure 7: Comparison of the motion volumes of two different skilled players. First player (blue poses and orange volumes) andsecond player (green poses and pink volumes).
their own motions. To evaluate our method in such a scenario,
we visualized the manifold of a tennis forehand shot form andcompared it with a trainee’s motion. We asked a skilled tennis player
to perform forehand shots and captured them using an opticalmotion-capture system with 12 cameras [Natural Point 2013]. The
manifold of the forehand shot was constructed using eight captured
motions. We asked a novice trainee with a physique similar to thatof the skilled player to perform the forehand shots by mimicking
the motion of the skilled player, which was shown as a reference.
A comparison between the motion volumes of the skilled player
and that of the trainee is shown in Figure 6. The motion volumes
were generated for seven body parts including the pelvis, chest,
head, right and left hands, and right and left feet. In Figure 6 (a), thetwo manifolds are placed at different positions in parallel, because
placing them at the same position makes it difficult to see all motion
volumes. The trainee’s motion is visualized by the keyposes as wellas the spatial and orientational trajectories of the body parts. In
Figures 6 (b) and (c), they are placed in the same position and the
motion volumes of a selected body part are visualized. We cansee some deviations of the trainee’s motion from the range of thetarget motion. For example, the trajectory the right hand of the

trainee’s motion deviated substantially from the spatial volumesof the skilled player in the take-back (initial) and follow-through(terminal) parts of the forehand shots, whereas they are close to eachother in the impact (middle) part of the motion. There is a deviationin the orientation of the right hand throughout the entire motion.
In addition, the movements of the trainee’s right foot are very shortcompared with the foot movements of the skilled player. In fact,taking a large step is important in the forehand shot form. Thisvisualization shows the problems in the trainee’s motion. Thesefindings would help a trainee to understand the problems with hisor her motion and fix them.

5.2

Comparison of Tennis Motion Forms

Our method can also be used to compare the manifold of one set of
motions with the manifold of another set of motions. We collected
11 motions of the same forehand shots from another skilled player
and compare the two sets of motion volumes in Figure 7.
Although they are basically similar, we can see some differences
between them. For example, there are difference between the rangesof the right hand in the take-back (initial) and follow-through (terminal) parts of the forehand shots. These findings would be helpfulMotion Volume: Visualization of Human Motion Manifolds

for understanding the characteristics of the forms of individual
players and analyzing them.

5.3

Computational Efficiency

Although our method includes some computationally expensive
processes such as computational geometry and combinatorial optimization, in practice, the computational efficiency is not a problem
as long as the number of input motions is adequate. In our experiments, all motion volumes of seven body parts for each setof motions were generated within a few seconds on a standard
desktop PC (Intel Core i7-8700 3.2 GHz CPU and 16 GB memory). It
took 0.16 s for the set of eight motions presented in Section 5.1 and3.57 s for the set of 11 motions presented in Section 5.2. A further
analysis of the computational efficiency in different cases and the
optimization of our algorithm are future tasks.

6

DISCUSSION

In this session, we discuss the limitations of our method and future
work. One of the limitations is that our method does not visualize
temporal information, as mentioned in Section 4.1. Although it ispossible to visualize spatial or rotational velocity using additional
arrows, the ranges of spatial and/or rotational velocities are difficult to depict in a way that people can easily grasp. Adding avisualization of temporal information is a future task.
Because our method generates a shape that contains all examples, it may be affected by noise, i.e. some motions that deviate
from the manifold. If the input dataset contains such noise, some
preprocessing for removing noisy samples or post-processing forsmoothing the generated geometry may be necessary.
Another limitation is that motion volumes and keyposes may
overlap and make it difficult to see when the motions are performedin place and have small translations, because these shapes andkeyposes are placed based on their positions with respect to theoriginal motions. This issue can be solved by deforming shapes andplacing keyposes in translated positions by scaling them according
to the sample times.
Our method does not control the viewing point and direction;
they are defined by the user, as mentioned in Section 4.1. Finding theimportant points in motion volumes where the difference between
two manifolds is large and suggesting appropriate viewing points
for them may be helpful. This is also future work.

7

CONCLUSION

In this paper, we proposed a method for visualizing the manifold of
human motions. Our method visualizes the ranges of time-varying
positions and orientations of a body part by generating volumetric shapes for representing them. Our method can help a user tounderstand the motion manifold of a set of motions as well as thedifference between two manifolds. Our future work includes theextension of our method to visualizing temporal information, preprocessing and postprocessing for handling noisy samples, warping
shapes and keyposes for avoiding overlaps, and suggesting appropriate viewing points. The application of our method to various
kinds of motion forms will also be investigated.

VRCAI ’19, November 14–16, 2019, Brisbane, QLD, Australia

ACKNOWLEDGMENTS
This work was supported in part by Grant-in-Aid for Scientific
Research (No. 15H02704) from the Japan Society for the Promotionof Science (JSPS).

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