Three-Dimensional Pose Estimation and Segmentation Methods - 3D Computer Vision: Efficient Methods and Applications - page 88

spondence with points in the image such that the rotation angles and the trans-
lation of the object with respect to the camera can be determined by minimis-
ing a suitable error measure, e.g. the reprojection error of the model points. Ac-
cordingly, pose estimation of rigid objects is equivalent to the problem of deter-
mining the extrinsic camera parameters (cf. Sect. 1.4 ). This is an important in-
sight, since all approaches described in Sect. 1.4 in the context of camera cal-
ibration can in principle be applied to pose estimation as well. Hence, an im-
portant issue in the context of pose estimation is to establish reliable correspon-
dences between model points and points in the image. This section provides an
overview of pose estimation techniques for rigid objects based on point features but
also on edges or lines, and then regards in more detail the edge-based hierarchi-
cal template matching approach to pose estimation introduced by von Bank et al.
( 2003 ).
2.1.1 General Overview
2.1.1.1 Pose Estimation Methods Based on Explicit Feature Matching
A seminal work in the domain of three-dimensional pose estimation is provided by
Haralick et al. ( 1989 ). They introduce several classes of pose estimation problems:
2D-2D pose estimation determines the pose of a two-dimensional object from an
image, while 3D-3D pose estimation deals with three-dimensional data points from
which the pose of a three-dimensional object is inferred. The estimation of the six
pose parameters from a single two-dimensional image of the object, given a ge-
ometry model, or an estimation of the relative camera orientation based on two
or more images of the object without making use of a geometry model of the ob-
ject, corresponds to 2D-3D pose estimation. The solutions proposed by Haralick et
al. ( 1989 ) are based on point correspondences between the images and the object
model. They rely on a minimisation of the distances in three-dimensional space be-
tween the model points and the observed rays to the corresponding scene points.
A linear method based on singular value decomposition is proposed to determine
the rotation angles, and it is demonstrated that using a robust M-estimator technique
instead of least-mean-squares minimisation may increase the performance of the
optimisation procedure, as a reasonable pose estimation result is still obtained when
the rate of outliers is as high as 50 %.
Image features beyond points are examined in the classical work by Lowe
( 1987 ). Linear structures, whose appearance does not change significantly even
with strongly varying camera viewpoints, are grouped according to geometric cri-
teria such as their similarity in orientation or the distances between their end
points, a process termed 'perceptual organisation' by Lowe ( 1987 ). The three-
dimensional model is projected into the image plane. The complexity of the
subsequent step, during which correspondences between the model and the ex-
tracted image features are established, is reduced by prioritising those correspon-
dences which involve features that are known to have a high probability of occur-
rence.