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Fig. 2.16 Two-stage
mean-shift procedure.
Projected search region ( left ),
three-dimensional probability
grid ( middle ), final result
( right )
to the pixel resolution at the current depth. Every three-dimensional point on the
surface grid of the ellipsoid is projected into the images of all three cameras. The
histogram bin of a three-dimensional point p is obtained with the look-up function
iBin( p ) =
+ I C 3
1
3 (I C 1
+ I C 2
uv ) , where I C c
uv is the greyscale value in the image from
camera c at the projected position (u, v) of the three-dimensional point p .Using
all three-dimensional points on the surface grid of the ellipsoid, a one-dimensional
histogram of the object appearance is computed. A normalisation of the histogram
yields the relative frequency of each greyscale value on the ellipsoid surface, which
is interpreted as a probability.
uv
uv
2.3.2.3 Image-Based Mean-Shift
In the first stage, the mean-shift procedure is applied to a search region, a three-
dimensional plane parallel to the image plane centred at the last object position.
Similar to the method of Bradski ( 1998 ) in two dimensions, the target model
q (id)
is used as a look-up table to compute the probability value for all three-dimensional
points in the search region. The look-up function iBin is used to obtain a probability
value for each three-dimensional point on the grid. Figure 2.16 (left) depicts the
projected search region in the image of one camera and Fig. 2.16 (middle) shows
the inferred three-dimensional probability grid. The three-dimensional centre point
c is estimated with the mean-shift procedure using a geometric ellipse model. The
ellipse orientation β is computed similarly as in Bradski ( 1998 ). This mean-shift
stage allows only for an update of the lateral pose of the tracked ellipsoid, since the
probability grid is parallel to the image plane. No information from the scene flow
field is used; thus a pose update of the ellipsoid is computed even if there is no new
three-dimensional information available.
2.3.2.4 Point Cloud-Based Mean-Shift
In this stage all moving three-dimensional points of the scene flow field are used
to update the three-dimensional pose of the tracked ellipsoid. At the first iteration
j
=
1 of the mean-shift procedure, the ellipsoid centre c j = 1 is initialised with the
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