3.2 Robust Region Representation
Our segmentation algorithm produces a set of disjoint
regions. Each of them, in turn, consists of a set of
runs. For subsequent object detection steps, however,
the pixel precise image data representation in terms of
runs is inappropriate. In addition, pixel precise repre-
sentation is prone to stochastic errors such as image
noise. For that reason, we interpret a region and its
associated pixels as two-dimensional Gaussian distri-
bution in the image plane. Based on (Hu, 1962), the
distribution is described by two moments m
10
and m
01
of first order (corresponding to mean values m
x
and
m
y
) and three centralized moments µ
20
, µ
02
, and µ
11
of second order (corresponding to variances σ
2
x
and
σ
2
y
and covariance σ
xy
). We already showed in (Jung-
mann et al., 2012) how to efficiently compute these
moments by directly using the intermediate run-based
representation and how to derive additional attributes
such as center of mass or an equivalent elliptical disk.
Although assuming that pixels of a region are
Gaussian distributed, the true distribution may be
of arbitrary shape (like, e.g., the red region in Fig-
ure 2(h)). One approach for better approximating the
true distribution might be the incorporation of mo-
ments of higher order. In our work, however, we cur-
rently consider only moments up to second order.
4 EVALUATION FRAMEWORK
For evaluating the robustness of our segmentation ap-
proach in combination with different color spaces, we
set up the evaluation framework depicted in Figure 3.
The entire framework is divided into two main sec-
tions: the actual image segmentation process and the
evaluation process of the segmentation result.
The main component within the image segmenta-
tion section is our segmentation algorithm (cf. Sec-
tion 3). It consumes a single RGB image and pro-
duces a set of regions, each of them described in terms
of moments. The color space, in which the segmen-
tation process should take place, is selected in ad-
vance. For each selectable color space, a heuristic
for determining whether color values are similar, as
well as a calculation specification for averaging color
values are predefined. Each heuristic can be individu-
ally parametrized by means of thresholds. The nec-
essary color space transformation from the original
RGB color space into the selected color space is done
on-the-fly during the segmentation process by means
of an additional calculation specification.
The subsequent evaluation process can be divided
into two branches. Both of them use the regions pro-
duced by the segmentation process to evaluate the ro-
bustness of the current segmentation setting. The first
branch incorporates a tracking mechanism for eval-
uating relative robustness across consecutive images.
The second branch uses ground truth data to evaluate
absolute robustness for each frame individually.
4.1 Relative Robustness
Evaluating relative robustness of our segmentation al-
gorithm in combination with a selected color space
corresponds to evaluating how stable regions are de-
tected among consecutive frames without moving the
camera and without changes within the environment
(except of illumination changes). By doing so, we
want to estimate how good the different color spaces
can deal with image noise as well as different illumi-
nation conditions.
4.1.1 Region Tracking
We apply a deterministic tracking approach that es-
tablishes correspondences between regions of consec-
utive frames. The amount of established correspon-
dences is subsequently compared with the amount of
regions that were originally extracted by the segmen-
tation algorithm. The tracking algorithm was origi-
nally introduced in (Jungmann et al., 2010).
The main idea of the approach is to gradually re-
duce the amount of valid correspondences between
a region extracted from image I
t
and all regions ex-
tracted from image I
t−i
by applying heuristics with
respect to position, motion, size, and shape.
4.1.2 Evaluation
Let R
S
denote the set of regions extracted by the seg-
mentation algorithm. Furthermore, let R
T
denote the
set of successfully tracked regions detected by the
tracking algorithm. We define the relative robustness
κ
i
for a framework iteration i as
κ
i
=
|R
T
i
|
|R
S
i
|
. (4)
In order to get a meaningful value for the relative ro-
bustness, we consider a sliding window comprising
the last n framework iterations, and take the arith-
metic mean
κ =
1
n
n
∑
i=1
κ
i
=
1
n
n
∑
i=1
|R
T
i
|
|R
S
i
|
. (5)
If κ = 1, the current setting can be considered as
highly robust, since corresponding regions were de-
tected in each of the last n − 1 images. If κ = 0,
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