Three-Dimensional Pose Estimation and Segmentation Methods - 3D Computer Vision: Efficient Methods and Applications - page 116

N t time steps only. With the SF algorithm it is possible to estimate the velocity along
the depth axis, which is not possible with the motion analysis module described
in Sect. 2.3.3 , as the regarded scene flow vectors provide no information about the
velocity of the three-dimensional points along the depth axis.
The SF algorithm is a temporal extension of the MOCCD algorithm and fits a
three-dimensional spatio-temporal contour model to multiocular images ( N c cam-
eras) at N t time steps. The input values of the SF algorithm are N c images at N t time
steps and the Gaussian a priori distribution p( T ) ≈ p( T

m T , Σ T ) of the model pa-
rameters T , which define the spatio-temporal three-dimensional object model. To
achieve a more robust segmentation, the input image I c,t of the SF algorithm is
computed using ( 2.11 ). Here, the SF algorithm is used to estimate the temporal pose
derivative T only. Before the first iteration, the SF algorithm is initialised by setting
the mean vector and covariance matrix ( m T ,Σ T ) to be optimised to a priori density
parameters (

|

m T , Σ T ) which may e.g. be provided by the motion analysis module
described in Sect. 2.3.3 . The SF algorithm consists of three steps.

Step 1: Projection of the Spatio-Temporal Three-Dimensional Contour
Model Based on the motion model, e.g. with constant velocity, the three-
dimensional contour model for all time steps N t is computed and camera param-
eters are used to project the extracted outline of the three-dimensional model to
each camera image I c,t . The SF algorithm extends the MOCCD algorithm to the
temporal dimension by using a spatio-temporal three-dimensional model, defined
by the parameter vector and an underlying motion model, e.g. constant velocity.
In this step the observed boundary of the spatio-temporal three-dimensional model
is computed for all time steps N t and projected into each camera image I c,t .The
outline of our three-dimensional model is extracted and projected as described in
step 1 of the MOCCD algorithm.
Now we describe the applied motion model and the computation of the spatio-
temporal three-dimensional model. Note that the optimised parameter vector in the
SF algorithm consists only of the temporal derivative T (t) . We assume that the
forearm radius r 1 and the hand radius r 4 (cf. Sect. 2.2.3.1 ) are constant over short
periods of time corresponding to a few frames; therefore these radii are not part
of the temporal pose derivative T . However, the radii r 1 and r 4 are only excluded
from the estimation of the temporal pose derivative T , not from the estimation of
the pose T itself. Hence, the algorithm is able to adapt itself to short-term changes
of the radii within a sequence; only their temporal derivatives are not estimated
directly.
The three-dimensional pose T (t) at time step t is computed at time step t with
the MOCCD algorithm or with the fusion module described in Sect. 7.4.3 .The
temporal pose derivative T (t) at time step t is determined with the SF algorithm
and the image triples at the time steps (t + t) and (t − t) . The spatio-temporal

three-dimensional curve model at the time steps (t ± t) is computed according

± T (t) to T (t) t , thus assuming constant motion. Figure 2.11 depicts the pro-

jected contour model for camera 1 (the one which defines the coordinate system) and
the spatio-temporal three-dimensional pose estimation result (a model-based dense

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