![](bg3.png)
factor multiplies the average gray level when compar-
ing it to the gray level of the pixel.
The algorithm forms the segmentation of image I
by calculating the union of the segmentations result of
using different factors, converting image I into bina-
rized image I
. Each pixel in I
is defined depending
on its counterpart in I:
∀p
i
∈ I
,p
i
= thr(p
i
):p
i
∈ I (2)
with thr(p
i
) defined as:
thr(p
i
)=
1,ifµ(p
i
) ≥ k × f (p
i
)
0, otherwise
(3)
We looked for connected regions after each thresh-
olding and merged the results of each segmentation
with the previous. So, if a set of pixels belonged to
any region for a certain segmentation, they did in the
final segmentation.
2.3 Thresholding
It is the simplest approach to image segmentation.
The input is a gray level image I and the output is a
binary image I
representing the segmentation where
black pixels correspond to background and white pix-
els correspond to foreground (or vice versa). In a sin-
gle pass, each pixel in the image is compared with a
given threshold k which is a gray level. If the pixel’s
intensity f (p
i
) is higher or equal to the threshold k,
the pixel p
i
is set to, say, white in the output. If it is
under k, it is set to black. The segmentations result of
applying each threshold k are joined in a similar way
as in LAT.
2.4 Local Variation
The algorithm we implemented is based on the work
introduced in (Felzenszwalb and Huttenlocher, 1998).
An important feature of this algorithm over the other
three is that it does not need a priori information on
which the colour of the objects is.
Felzenszwalb’s approach consists on considering a
criterion for segmenting images based on intensity
differences between neighbouring pixels. The algo-
rithm is based on the idea of partitioning an image
into regions, such that for each pair of regions the
variation between them is bigger than the variation
within regions. The criterion for determining the sim-
ilarity of image regions is based on measures of im-
age variation. The measure of the internal variation of
a region is an statistic of the intensity differences be-
tween neighbouring pixels in the region. The measure
of the external variation between regions is the mini-
mum intensity difference between neighbouring pix-
els along the border of the two regions. The original
algorithm uses two parameters, the minimum size of
the regions in the final result, and one used to smooth
the image before processing it.
Felzenszwalb starts by creating a graph that rep-
resents the image. Arches in the graph are given a
weight that corresponds to the difference in inten-
sity of pixels represented by their vertices. Arches
join pixels to their 8-connected neighbourhood. To
achieve the fastest ordering, original authors recom-
mend in their paper the bucket sort algorithm (Cor-
men et al., 1990). After this step, all arches are or-
dered by non-decreasing weight. The algorithm then
follows by taking an arch at a time and compare the
regions to which each of its ends belongs to. Both
regions will be merged if they accomplish with the
established criteria. The output of the algorithm is a
set of regions in which the image is segmented.
Formally, the graph G on the image I is defined as
follows. Each pixel p
i
in the image will correspond to
a vertex v
i
in the graph. Arches connect neighbouring
pixels and each arch is assigned with a weight. The
function used to calculate the weight of the arches is
defined as follows:
w(v
i
,v
j
)=
|I(v
i
) − I(v
j
)|,if(v
i
,v
j
) ∈ E
∞, otherwise
(4)
E is the set of all edges defined. As we said, for
each vertex v
i
in the graph exists a pixel p
i
in the im-
age, thus, E is the set of all arches connecting ver-
tices in G for some given distance d (in our case,
d =1, so we only consider immediate neighbours),
E = {(v
i
,v
j
):||p
i
− p
j
|| ≤ d}. The segmentation
S of an image I is then a partition of I with a corre-
sponding set of edges, G ⊆ E, such that each compo-
nent C in the segmentation, C ∈ S, corresponds to a
connected component in the graph G.
We used the mean intensity of the region to decide
whether two regions should merge or not instead of
the variance as in the original algorithm. Following
a similar approach as Felzenszwalb does in his algo-
rithm, we decided that two different regions should
join into one if the mean intensity of both regions is
similar. Another difference is that we didn’t use a
minimum size of region, in fact, regions were merged
until the process reaches a situation in which no more
regions could be merged.
We modified the original algorithm because it was
difficult to find values for its parameters that could
perform well with the variety of images we had. We
used the mean of gray intensity of the region which,
after several tests, proved to perform similar to the
original algorithm. In our case, however, we used one
parameter, the percentage of similarity k. For each
value of k we have a different segmentation, all these
resulting segmentations are then joined as in the pre-
vious algorithms.
SEGMENTATION ALGORITHMS FOR EXTRACTION OF IDENTIFIER CODES IN CONTAINERS
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