Model-free visual servoing on complex images based on 3D reconstruction
ABSTRACT We present a way to achieve positioning tasks by model-free visual servoing in the case of planar and motionless objects whose shape is unknown. Emphasize is made on the algorithm of 3D reconstruction which allows to synthesize easily the control law. More precisely, the reconstruction phase is based on the measurement of the 2D displacements in a region of interest and on the measurement of the camera velocity. However, we will show that the proposed algorithm is robust with respect to inaccurate values of this velocity. 2D displacements rather than 2D motions are used to remove the assumption that the acquisition rate has to be high. In addition, a particular attention is paid to the complex case of large displacements to access high camera velocities. Once the parameters of the plane are sufficiently stable, a visual servoing scheme is used to control the orientation of the camera with respect to the object and to ensure that it remains in the camera field of view for any desired orientation. The 3D reconstruction phase is maintained active during the servoing to improve the accuracy of the parameters and, consequently, to obtain a small positioning error. Experimental results validate the proposed approach.
- SourceAvailable from: François Chaumette[show abstract] [hide abstract]
ABSTRACT: This paper concerns the stability analysis of a new class of model-free visual servoing methods. These methods are "model-free" since they are based on the estimation of the relative camera orientation between two views of an object without knowing its 3-D model. The visual servoing is decoupled by controlling the rotation of the camera separately from the rest of the system. The way the remaining degrees of freedom are controlled differentiates the methods within the class. For all the methods of the class, the robustness with respect to both camera and hand-eye calibration errors can be analytically studied. In some cases, necessary and sufficient conditions can be found not only for the local asymptotic stability but also for the global asymptotic stability. In the other cases, simple conditions on the calibration errors are sufficient to ensure the global asymptotic stability of the control law. In addition to the theoretical proof of the stability, the experimental results prove the validity of the control strategy proposed in the paperIEEE Transactions on Robotics and Automation 05/2002;
Model-Free Visual Servoing on Complex Images
Based on 3D Reconstruction
17 Avenue de Cucillé
35 044 Rennes Cedex, France
17 Avenue de Cucillé
35 044 Rennes Cedex, France
IRISA / INRIA Rennes
Campus de Beaulieu
35 042 Rennes Cedex, France
Abstract—We present a way to achieve positioning tasks by
model-free visual servoing in the case of planar and motionless
objects whose shape is unknown. Emphasize is made on the
algorithm of 3d reconstruction which allows to synthetize easily
the control law. More precisely, the reconstruction phase is
based on the measurement of the 2D displacements in a region
of interest and on the measurement of the camera velocity.
However, we will show that the proposed algorithm is robust with
respect to nonaccurate values of this velocity. 2D displacements
rather than 2D motions are used to remove the assumption that
the acquisition rate has to be high. In addition, a particular
attention is paid to the complex case of large displacements
to access high camera velocities. Once the parameters of the
plane are sufficiently stable, a visual servoing scheme is used
to control the orientation of the camera with respect to the
object and to ensure that it remains in the camera field of
view for any desired orientation. The 3D reconstruction phase is
maintained active during the servoing to improve the accuracy of
the parameters and, consequently, to obtain a small positioning
error. Experimental results validate the proposed approach.
This paper addresses the problem of synthetizing robotic
tasks by visual servoing when the observed object is not
known. Indeed, except rigid manufactured goods for which a
model often exists, we rarely have a precise description of
the object or of the desired visual features, either because
these objects can be subject to deformations or simply be-
cause of their natural variability. Such cases can appear for
example in surgical domain, agrifood industry, agriculture or
in unknown environments (underwater, space). Few authors
relate such cases. In , the authors use a specific motion
to perform an alignment task without a precise description
of the desired visual features. Unfortunately, their study is
restricted to planar motions. In , thanks to dynamic visual
features, a positioning task consisting in moving the camera
to a position parallel to a planar object of unknown shape
is achieved. However, such an approach needs an estimation
of the parameters of a model of the 2D motion  currently
leading to a high computation duration and, consequently, to a
low control scheme rate. In addition, this approach cannot be
used for any specified orientation of the camera. This case has
been taken into account in , where geometric features are
used. However, three tasks have to be performed sequentially
yielding, in some cases, to excessive durations of the task.
An approach based on robust tracking is proposed in  to
obtain a projective reconstruction required for a hybrid visual
servoing, unfortunately no result concerning robotic tasks is
The approach described in this paper proposes to treat the
same problem, that is the realization of positioning tasks with
respect to a planar and motionless object of unknown shape for
any specified orientation of the camera. Since the shape of the
object is considered as unknown, a 3D reconstruction phase by
dynamic vision is first performed. This computation is based,
contrary to a previous approach , on a discrete approach.
We will see the benefit of using such an approach. In particular,
it does not require the assumption of a high acquisition rate
and provides consequently better results. In addition, higher
camera velocities can be reached. On the other hand, as in
, the use of a reconstruction phase allows more flexibility
to synthetize the control law, in particular to ensure that the
object remains in the camera field of view.
The paper is organized as follows: first, we present in
Section II a brief review on previous works relevant to 3D
reconstruction by dynamic vision. We show how to recover the
structure of the object in Section III and describe how to obtain
the 2D displacement in Section IV. Section V details the way
we synthetize the control law. Experimental results concerning
objects of unknown shape are presented in Section VI, next
we show in Section VII that, under some conditions, a simpler
version of the approach can be used. Section VIII is devoted to
the study of the influence of the camera velocity to the final
orientation error. Finally, Section IX presents a comparative
study with our previous approach .
II. PREVIOUS WORKS
Let us consider a point P of the object described by P =
(X,Y,Z)Tin the camera frame, with the Z axis the camera
optical axis. Assuming without loss of generality a unit focal
length, this point projects in p, described by p = (x,y,1)T,
which yields to the well-known relation 
?−1/Z0x/Z xy−1 − x2
01/Z y/Z 1 + y2
Proceedings of the 2004 IEEE
International Conference on Robotics & Automation
New Orleans, LA • April 2004
0-7803-8232-3/04/$17.00 ©2004 IEEE
where Tc = (VT,ΩT)Tis the camera velocity and V =
(Vx,Vy,Vz)Tand Ω = (Ωx,Ωy,Ωz)Tits translational and
rotational components respectively. In (2), only the depth Z is
unknown if p, ˙ p and Tccan be measured.
Various ways to estimate Z exist, they are based on different
approaches to cope with ˙ p. The most immediate way is to
approximate the velocities ˙ x (˙ y) by
this method does not provide accurate results because of errors
introduced by the discretization. Another approach is based on
the assumption that the brightness of p remains constant during
the motion yielding the well-known additional constraint 
∆t) . However,
˙ xIx+ ˙ yIy+ It= 0
where Ix, Iyand Itrepresent the spatio-temporal derivatives
of the intensity of the considered point in the image. By
substituting ˙ x and ˙ y given by (2) in (3), an expression of Z
can be obtained ,  (note that these works treat the more
general case where Tcis also supposed to be unknown). Such
approaches, known as direct approaches, require accurate
estimations of Ix, Iyand Itand therefore, are not very accurate
in practice. Another way is to locally model the surface of the
object in the neighborhood of P. That provides an expression
of 1/Z in function of the chosen parameterization, which
can be used in (2) to exhibit a parametric model of the 2D
motion. On the other hand, these parameters can be obtained
by a method of computation of the 2D motion. Finally, an
expression of the structure of the object can be extracted 
(here too, by considering a second point, the case where Tcis
unknown is treated). These approaches are known as indirect
approaches since they require an intermediate computation of
the 2D motion. More precisely, they are relevant to continuous
approaches since they use the 2D velocity. Such works,
including our previous one , implicitly assume that the
acquisition rate is high (or the camera velocity low) enough
so that the parameters of the model of the motion can be
considered as constant between two frames.
The main benefit of the present approach is to remove this
assumption as well as for the computation of the structure
of the object as for the computation of the 2D displacement.
Therefore, higher camera velocities can be reached. The ap-
proach is now relevant to discrete approaches. Moreover, using
explicitly parameters obtained by 3D reconstruction allows us
to synthetize easily the control law, in particular to take into
account any desired orientation of the camera.
III. STRUCTURE OF THE OBJECT
Let us assume that the observed object is planar, unless in
a neighborhood of P
Zk= AkXk+ BkYk+ Ck
which, according to (1), can be rewritten in function of pkas
with Θk= (αk,βk,γk)Twhere αk = −Ak/Ck, βk =
−Bk/Ckand γk= 1/Ck.
On the other hand, let us assume that the camera is subjected
to the velocity Tc, therefore˙P can be expressed as
˙P + Ω × P = −V .
Thereafter, by integrating this relation with respect to the
time we obtain
Pk+1= RkPk+ Tk
where Rkis a rotation matrix depending on Ω and Tka trans-
lation vector depending on Tc. Finally, by using (5) and (7)
in (1) we recover the well-known result that an homographic
model describes exactly the frame-to-frame displacement of a
point P belonging to a planar surface :
that we will write under a more compact form as a parametric
with µk= (M13,M23,M11,M21,M12,M22,M31,M32). We
will see how to compute this vector in the next Section.
Furthermore, by using explicitely µkin function of Rkand
Tk, one can show that Θksatisfies the following linear system
M11xk+ M12yk+ M13
M31xk+ M32yk+ 1
M21xk+ M22yk+ M23
M31xk+ M32yk+ 1
0 0 T1− M13T3
T2 0 −M21T3
0 0 T2− M23T3
Finally, using a measure of the displacement between the
frames k and k + 1 modeled as an homographic deformation
and the measure of the camera velocity, one can easily obtain
Θkby solving (10)
Let us note that it is usually possible to obtain from (8)
both the structure Θ and the motion (R,T ) , but in
our case of small displacements (because of frame-to-frame
displacements) the results will be not accurate enough to
ensure correctly the realization of the task.
IV. ESTIMATION OF THE FRAME-TO-FRAME
Let us consider two consecutive frames f and g and assume
that the brightness of pkremains unchanged during the motion,
so we can write
f(p) = g(δ(p,µ)).
Because of the noise, (13) is generally not satisfied. There-
fore, the solution is to move the problem to an optimization
one to find the parameters which have to minimize the
where W is a window of interest centered in pk.
To carry out the optimization, the classical approach ,
 is to assume that the acquisition rate and the displace-
ments are sufficiently small. If so, a Taylor expansion of g
can be performed. However, if we want to access high camera
velocities this way to proceed cannot be used. To cope with
this problem multi-scale  or multi-resolution approaches
,  can be used. Nevertheless, these solutions remain
Here, since Tccan be approximately known it can be used
to provide an estimation ? µ of µ according to (9) (note that
? µ, otherwise a coarse approximation of Θ is used). This way
motion, i.e. visual servoing or active vision.
Thereafter, it is now possible to perform a first order Taylor
expansion of g(δ(x,µ)) in a neighborhood of ? µ such that µ =
g(δ(x,µ)) = g(δ(x,? µ)) + ∇gT(δ(x,? µ)).Jδµ.ς
Therefore, using (15) in (14) and derivating with respect to ς
leads to a linear system in ς. As usually, this system is inverted
by using an iterative Newton-Raphson style algorithm to take
into account the error introduced by the Taylor expansion.
After some manipulations we obtain
where η is a positive scalar and Ψ the vector given by
?f(x) − g(δ(x,µ)?2
once?Θ is known, it can also be introduced in (9) to improve
to proceed can be used in applications involving controlled
? µ + ς:
where Jδµrepresents the Jacobian matrix of δ with respect to
ςk+1= ςk+ η
f(pk) − g(δ(xk),µk)
Ψ = (Jµ
In the case of a homographic model, one can show that Ψ
can be expressed as follows
Ψ = (Gx,Gy,xGx,xGy,yGx,yGy,xSx,ySy)T
and gythe coordinates of ∇g(δ(x,µ)) and Sx= −(? xk+1Gx+
V. CONTROL LAW
First, let us remember the task to achieve. The goal is to
ensure a given final orientation of the camera with respect to
plane π described by (4) and, also to ensure that P will still
remain in the camera field of view.
Once Θ is estimated, the unit normal n of plane π in P
in the camera frame can be derived. However, in the case of
any orientation we rather have to consider n∗= Rn where R
is the rotation matrix computed from the desired orientation
(see Figure 1). Therefore, we have to move the camera so that
Z = ncwith Z the unit vector carried by the optical axis and
nc= −n∗. This rotation to perform can be expressed under
the form uθ where u represents the rotation axis and θ the
rotation angle around this axis
Z ∧ nc
? Z ∧ nc?
θ = arccos(Z.nc)
The camera orientation being known, it is possible to
compute the control law. We used the one described in .
Indeed, it ensures that P remains in the camera field of view
since the trajectory of p is a straight line between the current
position p and the desired position p∗(which has been chosen
as the principal point of the image). We describe here briefly
this approach known as hybrid visual servoing .
First, pris defined as follows
with Z∗the desired depth for P in final position.
In few words, this approach is based on the regulation to
zero of the following task function
yielding to the camera velocity
λ being a positive gain and?L an approximation of the
interaction matrix given by 
where the notation [v]× denotes the antisymmetric matrix
associated to v and
with sinc(θ) = sin(θ)/θ.
Let us note that the value of Z required for the computation
of pris obtained thanks to (5).
VI. EXPERIMENTAL RESULTS
In order to validate the proposed algorithm, we present here
experimental results for two different desired orientations. The
experimental system is described in , except the PC is now
a Pentium at 2 Ghz.
The object consists of a photograph of a raw ham fixed
on a planar support. To evaluate the positioning accuracy of
our method, this support makes possible to express precisely
LΩ(u,θ) = I3−θ
Fig. 1.Rotation to perform by the camera.
the transformation matrix between the camera frame and
the object one with the method used in . This matrix is
characterized by the Euler’s angles denoted φX,φY,φZwhich
respectively represent the angles of the X, Y and Z rotations.
Furthermore, since the object is motionless, one can improve
the accuracy on Θ. Indeed, in a fixed frame, one can express
a value Θfthat can be filtered since a fixed value has to
be obtained. Thereafter, this value is expressed in the camera
frame to be used in the control law. Moreover, proceeding
this way allows to know when Θfis stable enough to be used
in the control law (typically five acquisitions are sufficient).
Thus, a preliminary phase is required.
Finally, the algorithm consists of three phases, a first phase
at constant velocity, a second phase when both reconstruction
and servoing are performed, and a last phase where only the
servoing operates. This last phase occurs when the camera
translation velocities are too small, in practice when ? V ?<
1 cm/s. Note that during this phase the camera velocity can
be increased since W can be fixed to a lower value, p is
therefore tracked by taking into account only the rigid terms
of the model of displacement. This is done by considering
Ψ = (gx,gy)Tin (16).
The following values have been used for all the experiments:
Z∗= 65 cm, for the first and second phases λ = 0.3 (0.1
for the second experiment), W = 171 × 171 pixels. The
acquisition rate ∆t is not constant, it varies from 200 ms to
720 ms. For the last phase W = 11 × 11 pixels, ∆t = 40 ms
and λ = 1.
The first experiment consists in positioning the camera
parallel to π. Figures 2.a depicts respectively the behavior
of parameters A, B and C (filtered and nonfiltered) in a
fixed frame; Figures 2.b the components of nc; Figures 2.c
the components of the camera velocity; Figure 2.d the norm
of e; Figure 2.e the parameters M13 and M23 (in pixel);
Figure 2.f the estimated depth. Finally, the initial and final
images are reported respectively on Figures 2.g-h. Note that
the unit of x axes is second. First, Figure 2.d confirms that
the control law converges since ? e ? tends towards zero,
as well as?Z towards Z∗(Figure 2.f). One can also remark
last phase begins near 8.5 s when the camera velocity is too
on Figures 2.a and 2.c the three phases of the algorithm, the
low to provide accurate estimations of Θ as shown clearly
on Figure 2.a. One can also remark the benefit of using an
estimation of pk+1in the algorithm of computation of the
displacement since high values are observed in Figure 2.e.
For this experiment, the initial orientation of the camera was
φX = 3.3◦, φY = 12.6◦and φZ = −2.5◦, the orientation
after the servoing was φX = 2.94◦and φY = 0.0◦(let us
recall that φZis not controlled). Consequently, the orientation
error is around 3◦.
The second experiment consists in positioning the camera
so that φX= 10◦and φY = −20◦. Figures 3.a-h describe the
behavior of the same variables as for the previous experiment.
The same comments can be made, in particular concerning
the convergence of the control law and the benefit of using an
estimation of pk+1. The initial orientation of the camera was
the same as for the first experiment, the final orientation was
φX = 13.1◦and φY = −21.9◦. Here again the orientation
error is around 3◦.
VII. A SIMPLER VERSION OF THE ALGORITHM
In the case of a planar object and when the desired values for
φXand φY are small, the parameters M31and M32involved
in (8) are very close to zero. In this case, we rather have to
consider them direclty as zero in (8) leading to
The computation of the frame-to-frame displacements be-
comes also simpler since δ(.) describes an affine deformation,
consequently we have to consider in (16)
0 0 T1− M13T3
0 0 T2− M23T3
Ψ = (gx,gy,xgx,xgy,ygx,ygy)T
and µ = (M13,M23,M11,M21,M12,M22).
We performed an experiment consisting in moving the
camera in front of the object. The behavior of the algorithm
is depicted on figure 4 where the same variables as previously
For this experiment we used the same parameters as for the
previous experiments except W is now 101 ×101 pixels. The
acquisition rate varies now from 120 ms to 200 ms. The initial
orientation was φX= 8.8◦and φY = −14.6◦. Here again, the
final orientation error is small, since we have φX= 1.5◦and
φY = −1.3◦.
To conclude, similar results can be obtained with this
approach by comparison with the complete model defined
by (8) when an affine model is valid1. However, the image
processing is less time consuming since W and?ΨkΨT
1That is essentially when the desired orientation is close to zero and the
desired depth is high.
smaller, that leads globally to a better dynamic behavior of
the robot. Note that in the case of an high initial orientation
error the control law converges even if?Θk=0is not accurate
VIII. INFLUENCE OF THE ESTIMATION OF THE CAMERA
Since M and Γ given by (11) depend on R and T which
both depend on the camera velocity Tc, Θ also depends on
the camera velocity. To measure the influence of Tc on the
estimation of the structure of the object we have to compute
∂Θ/∂Tc. However, it leads to very complicated expressions in
the case of any values for the components of Tc. Nevertheless,
since in practice Θ is filtered (see VI and VII), the perturba-
tions due to the noise introduced by an error of Tcwill be also
filtered. Figure 5 show simulations results of the behavior of
the parameters A, B and C involved in (4) when Tcis given
by (23). More precisely, the figure 5.a compares the filtered
values of A, B and C with the measured one; the figure 5.b
compares the filtered values of A, B and C with the real one.
Figures 5.c-d represent the same variables but when a random
noise of 20 % has been added to Tc. As we can see, filtering
dicreases highly the noise introduced by Tc.
since?Θkrefines during the motion.
IX. COMPARISON BETWEEN THE CONTINUOUS AND THE
First, let us recall the continuous approach , . By
substituting (5) in (2), one can show that the 2D motion is
exactly modeled by a parametric model with 8 parameters
. By neglecting the second order terms, we obtain
Consequently, if the parameters involved in (28) and the
camera velocity can be measured, Θ can be obtained.
In continuous approaches the problem is to obtain precisely
the ai’s. They can be obtained by measuring the displacement
between two frames by considering the ai’s constant during
∆t. In fact it is not true since Θ is not constant during the
motion. Thus, with such approaches, we have to consider high
acquisition rates or small displacements.
On the other hand, once (29) has been integrated, we obtain
an affine relation between pk+1 and pk that can be used to
express the ai’s by substituting ˙ x = (xk+1− xk)/∆t and
˙ y = (yk+1− yk)/∆t in (29). Here again, these relations hold
only for small values of ∆t.
Note that the discrete approaches presented in Sections
III and VII do not depend at all of ∆t regardless of the
reconstruction of the structure or of the estimation of the
frame-to-frame displacement since we have an estimation
a0+ a1x + a2y
a3+ a4x + a5y
−Ωy − γVx
−αVx + γVz
Ωz − βVx
Ωx − γVy
−Ωz − αVy
−βVy + γVz
of µ. Moreover, recall that we can use with these discrete
approaches high camera velocities in order to decrease the
duration of the task. The drawback of using such velocities is
that we have less values to filter leading to similar positioning
errors than with our previous approach .
X. CONCLUSION AND FUTURE WORKS
We have presented a way to achieve positioning tasks by
visual servoing when the desired image of the object cannot
be precisely described and for any desired orientation of the
camera assuming the object to be planar and motionless.
The approach is based on a 3D reconstruction allowing the
estimation of the current orientation of the object with respect
to the camera, and thereafter on the elaboration of the control
law. The special case of high camera velocities has been
studied. Experimental results validated our algorithm, low
orientation errors were observed (≈ 3o). We also showed the
robustness of the approach with respect to a coarse estimation
of the camera velocity.
Future works will concern the realization of positioning
tasks in the case of unknown and nonplanar objects.
 B. Yoshimi and P. K. Allen, “Active uncalibrated visual servoing,” in
IEEE Int. Conf. on Robotics and Automation, ICRA’94, San Diego, May
1994, pp. 156–161.
 A. Crétual and F. Chaumette, “Visual servoing based on image motion,”
Int. Journal of Robotics Research, vol. 20, no. 11, pp. 857–877,
 J. Odobez and P. Bouthemy, “Robust multiresolution estimation of
parametric motion models,” Journal of Visual Communication and Image
Representation, vol. 6, no. 4, pp. 348–365, December 1995.
 C. Collewet and F. Chaumette, “Positioning a camera with respect to
planar objects of unknown shape by coupling 2-d visual servoing and 3-
d estimations,” IEEE Trans. on Robotics and Automation, vol. 18, no. 3,
pp. 322–333, June 2002.
 F. Espiau, E. Malis, and P. Rives, “Robust features tracking for robotic
applications: towards 2d1/2 visual servoing with natural,” in IEEE Int.
Conf. on Robotics and Automation, ICRA’2002, Washington, USA, May
 A. Alhaj, C. Collewet, and F. Chaumette, “Visual servoing based on
dynamic vision,” in IEEE Int. Conf. on Robotics and Automation,
ICRA’2003, Taipei, Taiwan, September 14-19, 2003.
 B. Horn and B. Schunck, “Determining optical flow,” Artificial Intelli-
gence, vol. 16, no. 1–3, pp. 185–203, August 1981.
 P. Rives and M. Xie, “Towards dynamic vision,” in Proc. IEEE Workshop
on Interpretation of 3D scenes, Austin, Texas, November 1989.
 B. K. P. Horn and E. J. Weldon, “Direct methods for recovering motion,”
Int. Journal of Computer Vision, vol. 2, no. 1, pp. 51–76, June 1988.
 S. Negahdaripour and B. K. P. Horn, “Direct passive navigation,” IEEE
Trans. on Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp.
168–176, January 1987.
 S. Negahdaripour and S. Lee, “Motion recovery from image sequences
using only first order optical flow information,” Int. Journal of Computer
Vision, vol. 9, no. 3, pp. 163–184, 1992.
 O. Faugeras, Three-dimensional computer vision: a geometric viewpoint.
Boston: MIT Press, 1993.
 T. Huang and A. Netravali, “Motion and structure from feature corre-
spondences: A review,” Proceedings of IEEE, vol. 82, no. 2, pp. 252–
268, February 1994.
 J. Shi and C. Tomasi, “Good features to track,” in IEEE Int. Conf. on
Computer Vision and Pattern Recognition, CVPR’94, Seattle, USA, June
1994, pp. 593–600.
 G. D. Hager and P. N. Belhumeur, “Efficient region tracking with
parametric models of geometry and illumination,” IEEE Trans. on
Pattern Analysis and Machine Intelligence, vol. 20, no. 10, pp. 1025–
02468 10 12
02468 10 12
a fixed frame (filtered and nonfiltered). (b) Components of nc. (c) Kinematic
screw (m/s or rad./s). (d) Error defined as ? e ?. (e) Rigid terms of the 2D
displacement model (pixel). (f) Desired depth (meter). (g) Initial image. (h)
1stexperiment (x axes in seconds) : (a) Parameters of the plane in
1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10(d)
0 1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10(f)
Fig. 4.Case of an affine deformation.
Fig. 5.Influence of the accuracy of the estimation of the camera velocity.
 M. Irani, B. Rousso, and S. Peleg, “Recovery of ego-motion using
image stabilization,” IEEE Int. Conf. on Computer Vision and Pattern
Recognition, CVPR’94, vol. 19, pp. 454–460, June 1994.
 G. Hager and K. Toyama, “Incremental focus of attention for robust
visual tracking,” International Journal of Computer Vision, vol. 35,
no. 1, pp. 45–63, November 1999.
 E. Malis and F. Chaumette, “Theoretical improvements in the stability
analysis of a new class of model-free visual servoing methods,” IEEE
Trans. on Robotics and Automation, vol. 18, no. 2, pp. 176–186, April
 G. Adiv, “Determining 3d motion and structure from optical flow
generated by several moving objects,” IEEE Trans. on Pattern Analysis
and Machine Intelligence, vol. 7, no. 4, pp. 384–401, July 1985.