Action-centric Polar Representation of Motion Trajectories for Online
Action Recognition
Fabio Mart
, Antoine Manzanera
, Mich
ele Gouiff
and Thanh Phuong Nguyen
LIMSI, CNRS, Universit
e Paris-Saclay, Orsay City, France
U2IS/Robotics-Vision, ENSTA-ParisTech, Universit
e Paris-Saclay, Palaiseau City, France
LSIS, UMR 7296, Universit
e du Sud Toulon Var, Toulon, France
Action Recognition, Semi Dense Trajectories, Motion Shape Context, On-line Action Descriptors.
This work introduces a novel action descriptor that represents activities instantaneously in each frame of a
video sequence for action recognition. The proposed approach first characterizes the video by computing
kinematic primitives along trajectories obtained by semi-dense point tracking in the video. Then, a frame level
characterization is achieved by computing a spatial action-centric polar representation from the computed tra-
jectories. This representation aims at quantifying the image space and grouping the trajectories within radial
and angular regions. Motion histograms are then temporally aggregated in each region to form a kinematic
signature from the current trajectories. Histograms with several time depths can be computed to obtain dif-
ferent motion characterization versions. These motion histograms are updated at each time, to reflect the
kinematic trend of trajectories in each region. The action descriptor is then defined as the collection of motion
histograms from all the regions in a specific frame. Classic support vector machine (SVM) models are used to
carry out the classification according to each time depth. The proposed approach is easy to implement, very
fast and the representation is consistent to code a broad variety of actions thanks to a multi-level representa-
tion of motion primitives. The proposed approach was evaluated on different public action datasets showing
competitive results (94% and 88.7% of accuracy are achieved in KTH and UT datasets, respectively), and an
efficient computation time.
Action recognition is a very active research domain
aimed to automatically segment, detect or recognize
activities from video sequences. This domain plays a
key role in many different applications such as video-
surveillance, biomechanical analysis, human com-
puter interactions, gesture recognition, among others.
Action recognition is however very challenging, be-
cause of the great variability that is intrinsic to the ob-
ject, regarding its shape, appearance and motion. The
uncontrolled acquisition conditions also complicates
the problem, due to illumination changes, different
3d poses, camera movements and object occlusions
(Weinland et al., 2011).
Local spatio-temporal features have been widely
used to recognize actions by coding salient descrip-
tors, designed to be robust to viewpoint and scale
changes. These features have been computed us-
ing different strategies, such as: Hessian salient
features, Haar descriptors with automatic scale se-
lection or by choosing 3D patches with maximum
gradient responses (Ke et al., 2005), (Wang et al.,
2009),(Willems et al., 2008). Such descriptors are
however dependent on the object appearance, requir-
ing thereby an extensive learning step to represent dif-
ferent motion patterns.
Motion-based approaches using optical flow prim-
itives have also been used to characterize action pat-
terns, with the advantages of being relatively indepen-
dent from the visual appearance (Cao et al., 2009),
(Efros et al., 2003),(Scovanner et al., 2007). For in-
stance, Histograms of Oriented Optical Flow (HOOF)
have been proposed as symmetry-invariant motion de-
scriptors, to recognize periodic gestures (Chaudhry
et al., 2009) but with the main limitation of losing
local relationships of articulated objects. In (Ikizler
et al., 2008) a block-based representation that com-
bined HOOF and histograms of contours was pro-
posed to recognize periodic actions. This strategy is
Martinez, F., Manzanera, A., Gouiffès, M. and Nguyen, T.
Action-centric Polar Representation of Motion Trajectories for Online Action Recognition.
DOI: 10.5220/0005730404420448
In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 4: VISAPP, pages 442-448
ISBN: 978-989-758-175-5
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
however dependent of a precise definition of the ob-
ject and requires a complete video description to per-
form the recognition.
Optical flow fields have also been tracked during
the video sequence resulting in local space-time tra-
jectories that describe motion activities over longer
duration. Descriptors based on these trajectories
currently report very good performance to represent
gestures and activities (Kantorov and Laptev, 2014)
(Wang et al., 2011) (Jain et al., 2013). For instance
in (Wang et al., 2011), local descriptors like HOF
(Histograms of Optical Flow), MBH (Motion Bound-
ary Histograms) and HOG (Histograms of Oriented
Gradients) were computed around each trajectory and
then integrated as space-time volumes centered in
each trajectory to describe activities.
In (Jain et al., 2013) and (Wang and Schmid,
2013) the space-time volumes based on the character-
ization of trajectories were also implemented but us-
ing an improved version of the trajectories that takes
into account the camera motion correction. These de-
scriptors are however largely dependent on the ap-
pearance around the trajectories, which may be sensi-
tive to illumination changes. Additionally, the spatio-
temporal volumes are heuristically cut off from a
fixed temporal length that may be restrictive to rep-
resent non periodic actions in a on-line scheme. Be-
sides, the resulting size of the motion descriptor, com-
posed of many spatio-temporal volumes may be pro-
hibitive in real-time applications.
The main contribution of this work is a com-
pact spatio-temporal action descriptor, based on local
kinematic features captured from semi-dense trajecto-
ries, that is efficient in recognizing motion activities
at each frame. Such features are spatially centered
around the potential motion to be characterized and
coded as an action polar representation. From point
trajectories extracted in each time in the video, po-
tential regions of interest are extracted in each frame
using the centers of mass of the activity. Three differ-
ent types of trajectories are evaluated. Then, around
the center of mass of the current motion, an action-
centric polar representation is built to capture the spa-
tial distribution of kinematics features. For each re-
gion of the polar grid and at each frame, a motion
histogram is stored and updated, to represent the re-
gional temporal distribution of the trajectory kinemat-
ics. Therefore a temporal series of histograms can
be analyzed at different time depths from the current
frame. This collection of histograms forms a descrip-
tor that is mapped to Support Vector Machine classi-
fiers that returns an action label.
Unlike most existing methods that arbitrarily cut
off the temporal support of their motion representa-
tion, the proposed motion descriptor is incrementally
computed, which allows an on-line recognition of the
actions, i.e., for each frame, a label is assigned to the
potential action descriptor. Since the time depth of
the histogram is null at the beginning of the sequence
to be analyzed, the reliability of the label is low at the
beginning and increases with time.
This paper is organized as follows: Section 2 in-
troduces the proposed method, section 3 presents the
results and a quantitative evaluation of the method.
Section 4 concludes and presents prospective works.
Action recognition involves the characterization of
particular events and behaviors, embodied by phys-
ical gestures in the time-space domain. A potential
activity is herein defined as a particular spatial distri-
bution of local motion cues updated along the time.
For doing so, an action-centric polar representation
is first designed to independently analyze motion tra-
jectories within the different polar regions. Then, in
each region are computed local kinematics along the
trajectories, which are used to update a temporal his-
togram in each frame. Finally, the action descriptor
is formed by the set of the motion histograms, which
may be mapped at each time to a previously trained
SVM classifier. A pipeline of the proposed approach
is shown in Figure 1.
2.1 Motion Cue Trajectories
Local cues tracked along trajectories over several
frames have demonstrated outstanding action mod-
elling, thanks to their capability to represent fore-
ground dynamics and interaction history. The pro-
posed approach is aimed to recognize potential ac-
tions in on-line applications and therefore requires a
significant set of trajectories with a suitable trade-off
between accuracy and computation time. In this work
were considered the following methods to compute
Dense Trajectories: are extracted from a dense op-
tical flow field which is tracked by using a me-
dian filter over the displacement information and
using multiple spatial scales. These trajectories
have demonstrated good performance in terms of
accuracy and speed in different scenarios of action
recognition. This method includes a local crite-
rion to remove trajectories with poor motion in-
formation, such as: 1) trajectories being beyond
certain fixed standard deviation boundaries and 2)
trajectories with sudden displacements, defined as
Action-centric Polar Representation of Motion Trajectories for Online Action Recognition
Figure 1: Pipeline of the proposed approach: (a) spatio-temporal representation of the proposed motion descriptor. First,
a set of point trajectories are computed from the video. Then, a polar representation is centered in each frame around the
potential action defined by the end points of the active trajectories. A histogram is computed in each polar region to estimate
the partial distribution of kinematics. The histograms are updated at each time by considering different time intervals, thus
enabling frame-level recognition. (b) recognition process using the SVM. Different histogram versions are built at each time
corresponding to different time depth. Each one of these action descriptors is mapped to its respective SVM and a recognition
label is returned at each frame.
velocity vectors whose magnitude exceeds 70% of
the overall displacement of the trajectory (Wang
et al., 2011).
Improved Dense Trajectories: are a new version
of the dense trajectories that takes into account a
camera motion correction to globally filter out the
trajectories. For doing so, the approach assumes
that the background of two consecutive frames are
related by a homography. The matching between
consecutive frames is carried out using SURF de-
scriptors and optical flow. The trajectory filtering
according to speed and standard deviation is also
applied (Wang and Schmid, 2013).
Semi-Dense Trajectories: are key-point trajecto-
ries extracted from a semi-dense point track-
ing. The selected key-points are tracked using a
coarse-to-fine prediction and matching approach
allowing high parallelism and dominant move-
ment estimation. This technique has the advan-
tage to produce high density trajectory beams ro-
bust to large camera accelerations, allowing statis-
tically significant trajectory based representation,
with a good trade-off between accuracy and per-
formance (Garrigues and Manzanera, 2012).
2.2 Kinematic Trajectory
A trajectory of duration n is defined as a set of n co-
at different times t. Each
trajectory contains relevant cues about the dynamic of
a particular activity in the video, which can be charac-
terized by kinematic measures computed using finite
difference approximations.
In this work were considered different kinematic
features like the velocity v(t), depicted by its di-
rection θ(t) = argv(t) and modulus (speed) s(t) =
||v(t)||. The curvature κ was also tested in our rep-
resentation and defined as κ =
+ ¨y
+( ˙x
( ˙x
+ ˙y
where ˙x and ¨x are first and second time derivatives
computed using finite difference approximations on
the trajectories. The features can be used separately
or jointly, and the proposed framework is flexible to
include any kind of local features.
2.3 Action-centric Polar Representation
The motion information naturally available on trajec-
tories and their spatial distribution in the sequence
are two fundamental aspects to represent activities.
Based on this observation, a motion shape analysis
is herein carried out at each frame by measuring kine-
matic statistics distributed in a polar representation.
This spatial representation quantifies the locations of
a potential activity in a polar way. Additionally, a
rotation-independent region analysis can be deduced
to characterize activities and interactions. To obtain
such representation, the center-of-mass of the points
supporting the current trajectories is first calculated,
to center the polar grid with respect to the current ac-
tion location. Then, the distribution of the kinematics
is measured within each relative region of the polar
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
Figure 2: The different time depth histograms allow to enrich the spatio-temporal activity description while remaining efficient
and usable in arbitrarily long sequences. During training, individual SVM models are learned by using different time periods
for the different versions of descriptors. For the recognition step, the histograms are mapped to the corresponding SVM model
according to their time depth. The minimum distance of the combined action descriptors w.r.t the respective hyperplanes
allows to define the current label for the action.
grid u(ρ, θ). Particularly, the kinematics measured in
each polar region u
are coded in motion histograms
which are updated at each time.
Then, for each polar region u
, a purely spatial his-
togram h
(b) = |
x u
; f
(x) = b
| codes the distri-
bution of the kinematic feature f (quantized on N bins
) computed at time t on the current
support point x of the trajectory. Then for every time
(see Fig. 2), a time cumulative version of the
histogram is initialized every
frames to the spatial
(b) = h
when the time index t divides the time depth
. Oth-
erwise it is updated as follows:
(b) =
(b) +
The resulting collection of histograms (see Fig. 2)
finally represents the frame level representation of the
2.4 SVM Recognition at Different
Temporal Scales
Finally, the recognition of each potential activity is
carried out by a Support Vector Machine (SVM) clas-
sifier, using the set of recursive statistics from the
whole polar partition, as a spatio-temporal multiscale
motion descriptor. This classifier is well known for
being successfully applied to many pattern recogni-
tion problems, given its robustness, generalization
aptness and efficient use of machine resources. The
present approach was implemented by using the One
against one SVM multiclass classification with a Ra-
dial Basis Function (RBF) kernel (Chang and Lin,
Firstly, for training step, it was learned individ-
ual SVM models according to the time periods con-
sidered for the different versions of histograms, i.e,
a motion characterization from different time depths
(see Fig. 2). Each SVM then learns a partial ac-
tion representation that takes into account different
history versions of the motion according to the his-
tograms. A (γ,C)-parameter sensitivity analysis was
performed with a grid-search using a cross-validation
scheme and selecting the parameters with the largest
number of true positives for each time-scale.
In the step of on-line recognition, each motion de-
scriptor is mapped to a specific SVM model according
to the time depth. Then, for each one of the K time
depths, the distances of the motion descriptor w.r.t the
hyperplanes formed by the bank of
is stored, with N being the number of action classes.
To combine the different time depth classifiers, the
distances to the hyperplane are summed for each ac-
tivity and then, the activity with minimum sum is cho-
sen as the predicted class.
Action-centric Polar Representation of Motion Trajectories for Online Action Recognition
Table 1: Action classification by using different types of trajectories and computing different kinematic features, correspond-
ing to the norm s or the orientation θ of the velocity, and to the curvature κ.
Trajectory KTH UT-Interaction
θ s κ θ s κ
Semi-dense trajectory 92.24 87.13 87.25 85.0 77.1 85.00
Dense trajectory 91.19 90.26 89.33 85.0 71.6 85.00
Improved Trajectory 94.00 90.96 90.96 88.7 80.0 87.3
2.5 Datasets
The proposed approach has been evaluated on two
well known public human action datasets presenting
different levels of complexity, and different types of
activity and human interaction. Here is a brief de-
scription of these datasets:
KTH: contains six human action classes: walking,
jogging, running, boxing, waving and clapping.
Each action is performed by 25 subjects in four
different scenarios with different scales, clothes
and scene variations. This dataset contains a total
of 2391 video sequences. The proposed approach
was evaluated following the original experimental
setup which specifies training, validation and test
groups (Schuldt et al., 2004) as well as five-fold
cross validation suggested in (Liu et al., 2009).
UT-Interaction: contains six different human inter-
actions between different people: shake-hands,
point, hug, push, kick and punch (Ryoo and Ag-
garwal, 2010). The dataset has a total of 120
videos. Each video has a spatial resolution of
720 ×480 and a frame rate of 30 fps. A ten-fold
leave-one-out cross-validation was performed, as
described in (Ryoo and Aggarwal, 2010).
The experimental evaluation was designed to assess
the different components of the proposed approach,
regarding the classification of video-sequences and
the on-line recognition. The motion characterization
was firstly analyzed according to the three different
versions of trajectories (sec 2.1) and several kinematic
features coded over them (sec 2.2). This evaluation
was carried out to classify complete sequences with
one recorded activity. The second analysis was aimed
to evaluate the proposed motion descriptor in the task
of frame-level recognition. The configuration of the
proposed approach was set with a polar grid represen-
tation of 8 directions and 4 norm divisions. At each
polar grid region, a motion histogram of 32 bins was
computed. The resulting size of the frame-level ac-
tion descriptor was then of 1024 for each considered
time depth. Three different time depths
of 8, 16 and
32 frames were considered. The velocity components
and the curvature of the trajectories were considered
as kinematic features for the local representation of
the trajectories.
Firstly, the proposed motion descriptor was tested
to classify actions in complete video-sequences. The
label for a global video-sequence was defined follow-
ing an occurrence criterion of the labels recovered in
each frame, i.e., the action that is predicted most of-
ten at the frame level is assigned as the sequence la-
bel. The motion histograms were computed for each
kinematic feature individually. Table 1 shows the re-
sults for the different versions of trajectories and for
every kinematic feature. In general, the kinematic
histograms achieve an appropriate characterization of
individual actions and interactions from the datasets,
the orientation of the velocity θ providing the best re-
sults. A concatenation of the three kinematic features
was also tested, but the improvement in accuracy is
only around 1%, while the size of the descriptor may
turn prohibitive for online applications. The weak im-
provement provided by concatenating different kine-
matic histograms is probably due to a strong statistical
dependency of these features.
Table 2: Action recognition results on KTH dataset for
complete video sequences, compared to different state-of-
the-art approaches.
Method Acc
Wang et. al. (Wang et al., 2011) 94.2
Proposed approach 94.00
Laptev et. al. (Laptev et al., 2008) 91.8
Motion context (Zhang et al., 2008) 91.33
Polar flow histogram (Tabia et al., 2012) 82.33
In Table 2 and Table 3 are summarized the average
accuracies of different state-of-the-art approaches for
automatic classification in KTH and UT-interaction
datasets. The proposed approach achieves a good per-
formance for different motion activities under very
different scenarios, and a wide spectrum of human
motion activities. Furthermore, it has the determining
advantage to compute frame level action descriptors
VISAPP 2016 - International Conference on Computer Vision Theory and Applications
Figure 3: On-line action recognition for different videos recording several human motion activities. The frame-level recog-
nition is carried out by mapping the motion histograms to the different SVM models at each time. Then action label with
minimal distance to the hyperplanes is assigned to the motion descriptor.
Table 3: Action recognition results on UT-interaction
dataset for complete video sequences, compared to differ-
ent state-of-the-art approaches.
Method Acc
Proposed approach 88.7
Laptev et. al. (Kantorov and Laptev, 2014) 87.6
Yu et. al. (Yu et al., 2010) 83.3
Daysy (Cao et al., 2014) 71
with fixed size, allowing the action label prediction of
partial sequences in a computationally efficient way.
In contrast, the approach proposed by Wang et. al.
(Wang et al., 2011) uses complete video sequences
to compute the motion descriptor. It characterizes in
average 30 000 trajectories for each video with de-
scriptors of size 426 for each trajectory. Afterwards, a
bag of features is applied to reduce the feature space.
Nevertheless, this approach remains limited to off-
line applications. Other approaches like (Tabia et al.,
2012) and (Zhang et al., 2008) use polar space rep-
resentations to characterize activities. However they
compute their descriptors on entire sequences, thus do
not explicitly provide on-line recognition capabilities.
Likewise, the local features coded in their descriptors
are in most cases appearance-dependent and do not
provide a kinematic description.
Regarding the spatial representation, we also
tested a log-polar representation that focuses the at-
tention in regions located near the center of mass.
This representation is not convenient for actions that
are more discriminant in peripheral regions, like wav-
ing or pointing. In average, for the orientation of ve-
locity, the log-polar representation achieves an accu-
racy of 91.19%, and 83% for KTH and UT datasets,
Figure 3 illustrates the typical action recognition
of the proposed method at the frame-level and for dif-
ferent videos-sequences. The proposed approach rec-
ognizes activities in partial video sequences, taking in
general around of 30 frames to stabilize on a proper
label. This motion descriptor achieves a stable recog-
nition thanks to the integration of the different time
depth versions of the histograms, that allows a con-
sistent multiscale spatio-temporal description of the
The proposed approach achieves both fast compu-
tation and low memory footprint, thus allowing effi-
cient on-line frame-level recognition. The implemen-
tation of the proposed approach was not particularly
optimized for these experiments. However the com-
putation of the motion descriptor is very fast, taking
in average 0.15 milliseconds for each frame. Addi-
tionally, the mapping of each motion descriptor to the
SVM model at each time takes in average 8 millisec-
onds. The experiments were carried out on a single
core i3-3240 CPU @3.40GHz.
This paper presented a motion descriptor for the on-
line recognition of human actions based on the spatio-
temporal characterization of semi-dense trajectories.
The proposed approach achieved competitive results
on different public datasets while being intrinsically
computationally efficient. A polar grid designed over
each frame allows to code spatial regions of the activ-
ity. In each region, motion histograms are updated at
each frame according to the dynamic of the trajecto-
ries. These histograms form a motion descriptor that
is capable of recognition at each frame and then for
partial video sequences. Integrated at different time
depths, such descriptors represent multi-scale statis-
tics of kinematics features from the trajectories, and
they are relatively independent on the visual appear-
ance of the objects. The proposed approach can be
Action-centric Polar Representation of Motion Trajectories for Online Action Recognition
extended to multiple actions by computing several po-
lar regions of interest and then characterizing each of
them individually.
This research is funded by the RTRA Digiteo project
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