Online Event Segmentation in Active
Perception using Adaptive Strong
Anticipation
• Bruno Nery
Rodrigo Ventura
•
RT-701-10
arXiv:1006.5829v1  [cs.RO]  30 Jun 2010
Instituto de Sistemas e Robótica
Pólo de Lisboa
Online Event Segmentation in Active
Perception using Adaptive Strong
Anticipation
Bruno Nery
Rodrigo Ventura
June 2010
RT-701-10
ISR — Torre Norte
Av. Rovisco Pais, 1
1049-001 Lisboa
PORTUGAL
This work was supported by the FCT (ISR/IST plurianual funding) through the PID-
DAC Program funds. Partially funded with grant SFRH/BD/60853/2009, from Funda¸c˜ao
para a Ciˆencia e a Tecnologia
Abstract
Most cognitive architectures rely on discrete representation, both in space
(e.g., objects) and in time (e.g., events). However, a robot interaction with
the world is inherently continuous, both in space and in time. The segmen-
tation of the stream of perceptual inputs a robot receives into discrete and
meaningful events poses as a challenge in bridging the gap between inter-
nal cognitive representations, and the external world. Event Segmentation
Theory, recently proposed in the context of cognitive systems research, sus-
tains that humans segment time into events based on matching perceptual
input with predictions. In this work we propose a framework for online event
segmentation, targeting robots endowed with active perception. Moreover,
sensory processing systems have an intrinsic latency, resulting from many
factors such as sampling rate, and computational processing, and which
is seldom accounted for. This framework is founded on the theory of dy-
namical systems synchronization, where the system considered includes both
the robot and the world coupled (strong anticipation). An adaption rule is
used to perform simultaneous system identification and synchronization, and
anticipating synchronization is employed to predict the short-term system
evolution.
This prediction allows for an appropriate control of the robot
actuation. Event boundaries are detected once synchronization is lost (sud-
den increase of the prediction error). An experimental proof of concept of
the proposed framework is presented, together with some preliminary results
corroborating the approach.
Keywords: Event segmentation, anticipative systems, active perception,
cognitive robotics.
Contents
1
Introduction
2
2
Related work
4
3
Strong anticipation
4
4
Adaptive synchronization
6
5
Event segmentation
7
6
Experimental results
10
7
Conclusions and future work
15
1
1
Introduction
The perception of a robot is grounded on the physical world. Its sensors
receive a continuous stream of information, as for instance the light pat-
terns hitting the CCD sensor of a video camera. Cognitive representations,
however, are often discrete, as in the case of events and objects. Although
the usage of digital computers demand that all sensory information is dis-
cretized, this discretization is commonly performed in fixed, not always ad-
justable, discretization step (e.g, the frame rate and the pixel resolution of
a video camera). The detection of meaningful events from a stream of sen-
sory information is an important challenge, from the point of view of the
design of a cognitive architecture for robots, contributing to bridge the gap
between a continuous time world and discrete time, event-based cognitive
representations.
The segmentation of a continuous stream of information into events is
often overlooked, being commonly performed in an ad-hoc manner, either
recurring to threshold values over heuristic functions, or fixed time triggers,
for instance. But these methods are mostly sensor modality dependent, as
well as task specific. This work addresses the problem of bridging the gap
between the time continuous stream of sensory/actuation information, and
the discrete time sequence of cognitive representations, proposing a modality
and task independent framework for event segmentation.
This problem is addressed using a biologically inspired approach. Under
this paradigm, our goal is not to faithfully model any aspect of the human
brain, but rather to employ findings from neuroscience capable of providing
guidance on how to engineer better systems.
The Event Segmentation Theory (EST) provides a model of how the hu-
man brain segments perception into a sequence of events [18, 7]. This model
sustains that event segmentation is based on the detection of prediction er-
rors in the sensory stream. Prediction is a commonplace mechanism found in
many brain systems. In particular, the human brain is permanently making
predictions and comparing them with the actual outcome [12]. Events are
detected whenever a significant disparity between prediction and outcome is
encountered. An event segmentation mechanism can be built following this
principle, but the problem of how to make predictions about perceptions has
to be addressed first.
Dubois distinguishes between strong and weak anticipation [3, 13]: the
latter is based on an explicit model of the world, where the physics is encoded
in analytical constructs, that can be mathematically solved given an initial
condition. On the contrary, strong anticipation does not rely on a model,
but rather on the dynamical evolution of the interaction of the agent with
2
the world, seen as a single system. An example of strong anticipation can be
found on the behavior of an outfield baseball player when catching a well-
struck ball1: weak anticipation of the ball landing position requires modeling
the physics of the ball, encoding the initial state of the system (initial veloc-
ity, mass, friction coefficient, etc), and then predicting the landing position
by solving the analytical model; in contrast, strong anticipation views the
outfielder and the ball as a single system with new dynamics, as the outfielder
moves itself driven by the projection of the ball on his retina. Empirical ev-
idence suggest that this is the way an human outfield player functions [13].
In the context of robotics, a model based approach to anticipation may be
appropriate for passive sensors, but when designing systems that actively
engage in interactions with the world, as in the case of active perception, the
world can no longer be modeled as an independent, self-contained system.
Stepp proposes an approach to strong anticipation based on the work de-
veloped in the field of chaotic systems concerning synchronization of dynam-
ical systems [13]. Consider two systems, denoted D (drive) and R (response),
connected by a unidirectional flow of information from D to R. It is possible
to design the system R such that its dynamic evolution synchronizes with
the one of D, regardless of the initial condition of each system. One way of
doing this is for the R system to compare its state with the one of the D,
and bias its dynamics accordingly, i.e., system R is controlled by a feedback
loop, where the error results from this comparison. More interestingly, if this
feedback loop contains a delay, system R is capable, under certain conditions,
to anticipate system D [14]. Considering that system D includes both the
robot and the world, and system R to be a model internal to the robot, this
approach suggests an interesting mechanism to perform strong anticipation
of the dynamical evolution of the world-robot system.
One problem remains to be solved: how to design system R? No system
model is assumed a priori, since it depends on the coupling involving the
robot and the world. A possible approach is to adapt system R during in-
teraction. A solution to the adaptation of response systems in the context
of dynamical systems synchronization has been proposed by Chen [1], where
the convergence to the solution has been proved using the Lyapunov sta-
bility theory. This result does not directly apply, however, to anticipating
synchronization.
The contributions of this work are:
• An event segmentation method based on Stepp’s strong anticipation
concept [13], cast as an anticipating system synchronization framework;
1Example from [13].
3
• The application of Chen’s parameter identification method [1] to an-
ticipating synchronization;
• A proof-of-concept implementation of an architecture for event segmen-
tation and active perception, employing these methods.
This report is organized as follows: after a short section surveying related
work, two sections on the theoretical background behind strong anticipation
and the adaptation method to learn the response system R follow. Then, the
proposed architecture for event segmentation is described, followed by some
experimental results of a proof of concept implementation of these ideas. A
section presenting some conclusions and open questions closes the report.
2
Related work
The problem of event segmentation has been studied in the past. See [10] for
a review of recent techniques for the formation of event memories in robots.
Ramoni et al. proposed a method to cluster robot activities using Markov
chain models [11]. In [4] a batch maximum likelihood estimator is used to
fit a sequence of time-indexed models to raw data. The incremental ver-
sion of this algorithm is based on thresholding the likelihood of the current
model along time.
The spatio-temporal segmentation of video have been
researched in [16], applying motion model clustering, and in [2] using hier-
archical clustering of the 3D space-time video stream. Gesture segmentation
and recognition has been addressed in [6] employing hidden-Markov models
(HMM).
3
Strong anticipation
In [13] strong anticipation is modeled using a dynamical system synchroniza-
tion framework. Consider two continuous dynamical state vectors x(t), y(t) ∈
Rn with the following coupled dynamics:
˙x = f(x)
˙y = f(y) + k(x −yτ)
(1)
where yτ = y(t −τ), i.e., a feedback loop with a constant delay τ, and k
is a scalar gain. The first system is called the drive (D) while the second
the response (R). This delayed feedback loop in the response system is a
fundamental aspect, and is responsible for the response system capability of
anticipating the trajectory of the drive.
4
This delayed feedback loop is neurophysiologically supported by the dis-
covery of forward models in the brain, which predict sensory consequences
of motor commands [8, 17, 5]. These models receive as input a copy of the
subject motor action, and produce a prediction of future perceptions. For
instance, when performing an arm movement, these models predict the tra-
jectory followed by the arm, as perceived by the subject. One important
function of this mechanism is to overcome the sensory processing latency in
the brain, when the subject is performing controlled, quick movements.
To understand how the response system can anticipate the drive, consider
that τ = 0 and that the systems are synchronized at time t0, i.e., x(t0) =
y(t0). Under these conditions, the systems will remain synchronized, since
x −yτ = 0 and thus there is null feedback in the response. In this case, the
concatenated state z = (x, y) ∈R2n evolves in the x = y hyperplane, called
the synchronization manifold [9]. The response system synchronizes with
the drive if the error system with state e = y −x, also called the transversal
system
˙e = f(y) −f(x) −k e
(2)
is able to reject the perturbation e, driving it to zero. For f(y) ≃f(x),
system (2) behaves like a first-order system with an exponential decay to
zero. Anticipation is realized once τ > 0, as synchronization implies x(t) =
yτ = y(t−τ) and thus y(t) = x(t+τ), meaning that the response anticipates
the driver. This is called anticipating synchronization [14], where x = yτ
defines the anticipatory manifold [15].
Successful synchronization from an arbitrary initial condition is not guar-
anteed in general (unless for simple cases), and strongly depends on the values
of k and τ. However, for any delay value τ, e(t) = 0 is a fixed point of the
transversal system (2), meaning that once synchronized, the system will re-
main so. Voss conjectures that, if e(t) = 0 is a stable fixed point for τ = 0,
then there is a τ0 > 0 such that, for any 0 < τ < τ0, the transversal system
has a stable fixed point at e(t) = 0. This conjecture has been backed up by
numerical simulations [15].
In general, for sufficiently small τ, stability of the transversal system
can be expected. In the case of this work, since τ models the delay of the
perceptual system (e.g., the latency from a change in the environment up to
its detection by the computer vision algorithm), this delay can be assumed
smaller than the time scale of the events being perceived.
5
4
Adaptive synchronization
In the previous section it was assumed that the dynamics of the drive and
response systems are equal. If the drive system corresponds to the world-
robot coupled system, its dynamics is not known a priori. One way of tackling
this problem is to adapt the response system, online, during synchronization.
Chen proposes in [1] an approach to adapt response systems in the context
of dynamical system synchronization. It does not account, however, for a
delayed feedback.
Consider that the drive system has the form
˙x = f(x) + F(x)θ
(3)
where θ ∈Rm is a vector of (constant) parameters, f(x) ∈Rn and F(x) ∈
Rn×m. The response system is identical, except for the parameter vector that
is unknown, and for the synchronization feedback loop
˙y = f(y) + F(y)α + U(y, x, t, α)
(4)
where α is the response parameter vector, and U(y, x, t, α) is called the con-
troller of the response. Chen et al. proved in [1] that, under certain con-
ditions, not only the response system synchronizes with the drive, but also
that the response parameters α converge to the ones of the drive θ, i.e.,
lim
t→+∞||α(t) −θ|| = 0.
(5)
These conditions consist of the existence of a smooth controller U(y, x, t, θ)
and of a scalar (Lyapunov) function V (e), where e = y −x, such that:
1. c1||e||2 ≤V (e) ≤c2||e||2,
2. the derivative of V (e) along the solution of the coupled system
˙x = f(x) + F(x)θ
˙y = f(y) + F(y)θ + U(x, y, t, θ)
(6)
satisfies ˙V (e) ≤−W(e), and
3. the parameter vector α is adapted according to the learning rule
˙α(t) = −F T(x) [∇V (e)]T
(7)
for ∇V (e) denoting the gradient (row) vector of V with respect to e,
6
where c1 and c2 are two positive constants, W(e) is a positive definite func-
tion2, and U(y, y, t, θ) = 0.
This result has two important consequences: first, it proves convergence,
provided that the response system is capable of synchronizing with the driver
if α = θ (i.e., if the true parameters were known), and second, it provides a
learning law, in the form of the gradient of α. However, in order to use this
result, one has to find a controller U and a function V satisfying the premises
of the theorem. Chen shows that the controller
U(y, x, t, θ) = −e + f(x) −f(y) + [F(x) −F(y)] θ
(8)
and the Lyapunov function
V (e) = 1
2eTe
(9)
satisfy the premises for any F and f.
The practical application of these results raises three practical issues.
One is the assumption that functions F and f are known, meaning that
one should have a prior knowledge of the structure of the dynamics of the
system. One can reverse this argument, stating that, given functions f and
F sufficiently generic, this method allows the adaptation to any dynamical
system that can be modeled by (3) for some parameter vector θ. Second,
this result was proved for continuous time systems. The discretization of ˙α
raises the issue of the choice of a learning rate (hidden in a proportionality
constant of V , since the theorem is invariant to a change of scale of this
Lyapunov function). Finally, the third issue concerns hidden state variables:
if there is a state variable that is hidden, i.e., the Lyapunov function V (e)
does not depend on its error, then this function is no longer positive definite.
This requires that all drive state variables have to be fed to the response
system controller. This is mostly true3 once the state variables considered
are all obtained from perception (as in the case of the outfield baseball player
example above).
5
Event segmentation
The event segmentation framework we propose in this work, depicted in
Figure 1, consists of a pair of response systems, one performing adaptation
(labeled adaptive response), and the other anticipation (labeled anticipating
2W(0) = 0 and W(e) > 0 for any e ̸= 0.
3Occlusion of objects by others have to be accounted for.
7
drive
adaptive 
response
anticipating 
response
controller
delay
u
x
α
y*
yτ
y
delay
delay
xτ
uτ
world
Figure 1: System architecture, consisting of the drive system and the percep-
tual delay (world), and the double response system formed by the adaptive
and the anticipating responses. The anticipating response uses the param-
eters α obtained by the adaptive response. The control input u is obtained
by a controller fed with the anticipated state y.
response). The adaptive response learns the parameter vector α as described
in the Adaptive synchronization section, while anticipating response performs
anticipating synchronization as explained in the Strong anticipation section.
The robot-world coupled system is modeled by the controlled drive system.
Note that the access of the architecture to the world state is subject to
a delay, modeling for instance the latency of the perceptual channel (image
acquisition, processing, and tracking). The controller computes the actuation
vector u based on the anticipated world state y.
The drive system, together with the perceptual delay, is modeled by the
dynamical system
˙x = f(x) + F(x)θ + u
(10)
where u is the control input, modeling the actuation of the robot in the
world. Shifting this equation by a delay of τ one obtains
˙xτ = f(xτ) + F(xτ)θ + uτ
(11)
where uτ(t) = u(t −τ). This model can be put in the form of (3) defining a
time varying function
fτ(xτ, t) = f(xτ) + uτ
(12)
8
from which ˙xτ = fτ(xτ, t) + F(xτ)θ.
The adaptive response receives the
delayed state xτ, together with the delayed control input uτ
˙y∗= f(y∗) + F(y∗)α + uτ + U(y∗, xτ, t, α)
(13)
Once fτ(y∗, t) = f(y∗) + uτ, this equation can be put in the form of (4). The
anticipating response is described by
˙y = f(y) + F(y)α + u + k(yτ −xτ)
(14)
where yτ = y(t−τ) as before, and the parameter vector α equals the one ob-
tained by the adaptive response. The anticipatory synchronization manifold
is defined by yτ = xτ. Thus, y = x, meaning that the anticipating response
is synchronized with the drive system, which is the same to say that it is
anticipating the delayed perception xτ. By shifting (12) in time one can get
fτ(y, t + τ) = f(y) + u, allowing us to write (11) and (14) as
˙xτ = fτ(xτ, t) + F(xτ)θ
˙y = fτ(y, t + τ) + F(y)α + k(yτ −xτ)
(15)
thus matching (1) (except for the time varying dynamics, which do not affect
the previous considerations on anticipating synchronization) when α = θ.
According to the theory of Event Segmentation
[18], perceptual sys-
tems continuously make predictions about perceptual input, and perceive
event boundaries when transient errors in prediction arise. On the adaptive
synchronization framework, the Lyapunov function V (e) defined in (9), for
e = y∗−xτ provides a solid estimate of the prediction error. Considering
the function values in a time window, we can associate the obtained samples
with a random variable with Normal distribution of mean µV and variance
σ2
V . Under this assumption, the normalized metric
bV = V −µV
σV
(16)
is normally distributed with zero mean and unit variance. When |bV | ex-
ceeds a threshold bevent, an event boundary is detected. If bV is normally
distributed with zero mean and unit variance, the cumulative probability of
the distribution tails for |bV | > bevent is the probability of false positive detec-
tion. Thus, bevent should be sufficiently high so that false positive detection
is minimized, but low enough in order to detect the prediction error increase
due to a sudden change in the dynamics of the system.
9
β1
β3
v1
v2
β2=0
Figure 2: Simulated scenario, where β1 = β3 = π/12.
6
Experimental results
As a proof of concept for the ideas presented here, a simple scenario was
simulated: a ball rolling free on a series of inclined planes, with different
slopes, is observed by a robot camera which aims to follow it, in order to
center it on the image, as depicted in Figure 2. The camera moves parallel
to the plane, for simplicity sake.
Denoting the ball coordinates by v = [v1 v2]T and the camera coordinates
by c = [c1 c2]T, the ball projection x = [x1 x2]T in the image plane is assumed
orthographic: x = v −c. Assuming that there is no ground friction, the
dynamics of the ball is a double integrator
¨v1 = −g sin β cos β
¨v2 = −g sin2 β
(17)
Considering that the camera support is frictionless and that its movement is
controlled in acceleration (i.e., force control), the resulting drive system, in
state space form, is given by
¨x1 = −g sin β cos β −¨c1
¨x2 = −g sin2 β −¨c2
˙x1 = ˙x1
˙x2 = ˙x2
(18)
considering the state vector x = [ ˙x1 ˙x2 x1 x2]T. This system can be put in
10
the form (10) once
f(x) =


0
0
˙x1
˙x2


θ =
 −g sin β cos β
−g sin2 β

F(x) =


1
0
0
1
0
0
0
0


u =


−¨c1
−¨c2
0
0


(19)
For this proof of concept, we set the response system to be structurally
identical, thus employing the same functions f and F, and control input u.
The vector α = [α1 α2]T is the parameter vector to be adapted according to
Chen’s learning rule (7).
When the anticipating response is synchronized with the drive, we have
x = y, and thus the dynamics of the anticipating response becomes
¨y = α −¨c.
(20)
The camera motion controller considered has the form
¨c = kpy + kd ˙y + α
(21)
where kp and kd are the proportional and the derivative gains of the controller.
Thus, the closed loop dynamics becomes
¨y = −kpy −kd ˙y
(22)
The design of the controller gains kp and kd can be performed by pole place-
ment (in the experiments we set k2
d = 4kp, yielding a smooth response with
a double pole at −kd/2).
The experiments were conducted after discretizing the above equations
using a simple approximation ˙z(t) ≃[z(t + T) −z(t)]/T.
The sampling
rate was 100Hz, kp = 1, kd = 2, k = 1, and the Lyapunov function used
was (9). The delay considered was τ = 0.65s (65 samples). Event boundaries
are detected using a 10-second window and a bevent = 3.
The system is
initialized with the ball starting on the top left position of the ramp, and
as the ball transverses the scenario there are two events, corresponding to
the two changes of the ramp slope. Each simulation takes 100s of simulated
time.
Figure 3 attests the performance of the adaptive response system, in
terms of the evolution of the parameters α, compared with the ground truth
11
0
10
20
30
40
50
60
70
80
90
100
−4
−2
0
2
4
t
 
 
0
10
20
30
40
50
60
70
80
90
100
−5
0
5
10
15
t
 
 
α1
θ1
α2
θ2
Figure 3: Parameters α evolution (solid line) in comparison with the true
values (dashed line).
(θ, that changes with the slope). As can be seen, the parameter vector α
converges to the true parameters θ after some time.
Figure 4 shows the evolution of the ball position in the camera without
an anticipating response system, i.e., the camera motion controller is fed by
y∗instead of y. As expected, the delay introduced by the latency of the
perceptual channel jeopardizes the control of the camera. Also, the adaptive
response follows the drive with a delay of τ.
Figure 5 compares the ball position in the camera with its anticipated
response. In this case, both are synchronized, since the ball coordinates in
the image converge to zero (except for a brief time after each slope change,
while the adaptive system learns the new parameters). Also, the anticipating
response makes it possible to control the drive system satisfactorily.
Figure 6 pictures the evolution of the prediction error estimate V (e). Its
value approaches zero as the drive and response system become synchronized.
Finally, Figure 7 shows the event segmentation results obtained using the
normalized metric (16), with a window of 10s. As expected, each change of
plane is detected as an event boundary by the framework. Interestingly, the
peak of this metric, at the event boundary, increases with the window size,
without any loss of temporal resolution.
These results show that the proposed system is capable of correctly (1) de-
tecting the event boundaries that correspond to the change of ramp slope
12
0
10
20
30
40
50
60
70
80
90
100
−10
−5
0
5
10
t
 
 
0
10
20
30
40
50
60
70
80
90
100
−100
−50
0
50
100
t
 
 
x1
y*
1
x2
y*
2
Figure 4: System response without anticipation.
0
10
20
30
40
50
60
70
80
90
100
−10
−5
0
5
10
t
 
 
0
10
20
30
40
50
60
70
80
90
100
−40
−20
0
20
40
t
 
 
x1
y1
x2
y2
Figure 5: System response using the full architecture.
13
0
1
2
3
4
5
6
7
8
9
10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
V(e)
Figure 6: Prediction error V for the first 10 seconds of the simulation.
0
10
20
30
40
50
60
70
80
90
100
−200
−100
0
100
200
300
400
t
 
 
32
33
34
35
36
37
38
39
−60
−40
−20
0
20
40
60
t
 
 
v2
Event boundary
v2
Event boundary
Figure 7: The ball v2 coordinate evolution along the experiment: top plot
shows the detected events, and the bottom plot a zoom around the first
detected event. The delay observed in this second plot corresponds to the
perceptual delay τ.
14
by the ball, (2) controlling the camera movement using anticipation, and
(3) learning the correct system parameters.
7
Conclusions and future work
This report describes an event segmentation framework, targeting active per-
ception in robots, based on the concept of strong anticipation proposed by
Stepp et al. in [13]. A dynamical system synchronization paradigm is used as
theoretical foundation of the proposed architecture, where the robot-world
coupled system is identified using a parametric method for adaptation pro-
posed by Chen et al. in [1], and the actuation is performed using anticipation.
This anticipation accommodates for the net delay of the perceptual channel.
The capability of the architecture to anticipate perception allows the robot
to control its actuation based on the prediction of the robot-world state,
instead of relying on the delayed perceptual data.
Having the described proof of concept experiments shown that the pro-
posed architecture behaves as expected, future work includes scaling this
approach to more complex domains. This involves tackling the issues of the
learning rate, which is hidden in the proportionality constant of the Lyapunov
function, used in the Chen’s learning rule, as well as the automatic design
of the controller, given the adapted parameters. Other open questions in-
clude dealing with hidden state variables, as well as complex relations among
objects (e.g., grasping, occlusion, and so on).
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