Visual Servoing and Pose Estimation with Cameras Obeying the Unified Model - Visual Servoing via Advanced Numerical Methods - page 224

The second part of this chapter deals with the pose estimation problem. There
are many applications of pose estimation, where the 6 parameters of the camera
pose have to be calculated from known correspondences with known scene struc-
ture: robot localization using a vision sensor, or PBVS [33]. The pose estimation
is one of most classical problem in vision [7, 16]. This problem is more than 150
years old and there is recent renewed interest because of automated navigation and
model-based vision systems. Numerous methods have been proposed in the litera-
ture and giving an exhaustive list of them is certainly impossible. The pose estima-
tion methods can be divided into several categories according to the used features,
direct methods or iterative methods. The geometric features considered for the esti-
mation of the pose are often points [7], segments [8], contours, conics [25] or image
moments [29]. Another important issue is the registration problem. Purely geomet-
ric [8], or numerical and iterative [7] approaches may be considered. Linear ap-
proaches are suitable for real-time applications and give closed-form solutions free
of initialization [10, 1]. Full-scale nonlinear optimization techniques [17] consist of
minimizing the error between the observation and the projection of the model. The
main advantage of these approaches is their accuracy. The main drawback is that
they may be subject to local minima and, worse, divergence.
The method we propose in this chapter is based on virtual visual servoing (VVS)
using moment invariants as features. In other words, we consider the problem of
the pose computation as similar to the positioning of a virtual camera using features
in the image [26, 20]. This method is equivalent to nonlinear methods that consist
in minimizing a cost function using iterative algorithms. The main idea behind the
method we propose is based on the following fact: the features that can be used for
visual servoing to ensure a large convergence domain and adequate 3D behavior can
be used to obtain a large convergence domain and high convergence speed for pose
estimation using VVS.
As mentioned above, the features we propose are computed from the projection
onto the unit sphere. This means that the proposed method can be applied not only
to conventional cameras but also to all omnidirectional cameras obeying the unified
model [12, 4]. Omnidirectional cameras are usually intended as a vision system pro-
viding a 360 o panoramic view of the scene. Such an enhanced field of view can be
achieved by either using catadioptric systems, obtained by simply combining mir-
rors and conventional cameras, or employing purely dioptric fisheye lenses [3]. In
practice, it is highly desirable that such imaging systems have a single viewpoint
[3, 27]. That is, there exists a single center of projection, so that, every pixel in the
sensed images measures the irradiance of the light passing through the same view-
point in one particular direction. The reason why a single viewpoint is so desirable
is that it permits the extension of several results obtained for conventional cameras.
The pose estimation method we propose is thus valid for catadioptric, conventional
and some fisheye cameras.
This chapter is organized as follows:

• in the next section, the unified camera model is recalled;

• in Section 13.3, the theoretical background of this work is detailed;