Three-Dimensional Pose Estimation and Segmentation Methods - 3D Computer Vision: Efficient Methods and Applications - page 129

Fig. 2.18 ( a ) Relation between edge direction δ and normal velocity φ n .( b ) Definition of the
constraint line in UV space according to Schunck ( 1989 ), representing the configurations (U, V )
which are consistent with the observed normal velocity φ n

gles, which are included in the model as internal degrees of freedom. In the course
of the adaptation process, three-dimensional points not previously determined to
belong to the object may be added to it while others may be rejected, resulting in a
robust behaviour with respect to errors of the preceding clustering stage. The optimi-
sation procedure is implemented as an M-estimator (Rey, 1983 ). It is straightforward
to utilise the result of this three-dimensional pose estimation procedure as an initial-
isation for the appearance-based MOCCD technique described in Sect. 2.2.1.2 .

2.3.3.2 Estimation of the Temporal Pose Derivatives

Both motion components of a scene point parallel to the image plane can only be
recovered from the corresponding local pixel neighbourhood if the intensity pattern
around the pixel is corner-like. Edge-like intensity patterns only allow the determi-
nation of one velocity component, such as the component parallel to the epipolar
lines computed by the spacetime stereo algorithm (cf. Sect. 1.5.2.5 ). This ambiguity
is a consequence of the well-known aperture problem (Horn, 1986 ). Restricting the
stereo and motion analysis to corner-like image features (Franke et al., 2005 )may
result in fairly sparse depth maps. If edge-like image features are evaluated, as is the
case in all image sequences regarded in this study, projecting the determined veloc-
ity component onto a line orthogonal to the local edge direction yields the normal
velocity φ n , as depicted in Fig. 2.18 a. The angle α between the direction of the hor-
izontal epipolar lines and the direction of the normal velocity is given by δ = tan α

with δ as defined by ( 1.121 ) in Sect. 1.5.2.5 .
In the following, the translational velocity components of the object parallel to
the x , y , and z axes are denoted by U obj , V obj , and W obj , respectively, and expressed
in metres per second. A two-dimensional space is spanned by the horizontal and ver-
tical velocity components U and V measured in the scene and expressed in metres
per second. This space is termed UV space. Given the observed normal velocity φ n ,
all consistent configurations (U, V ) are represented by the corresponding constraint
line in UV space as defined by Schunck ( 1989 )(cf.Fig. 2.18 b). Fermüller and Aloi-
monos ( 1994 ) extend the concept of constraint lines towards the analysis of 'image
displacement fields', i.e. optical flow and disparity, that arise from the motion of a