The features and objects are various among different im-
ages, so that the similarity measure varies across images, re-
sulting in the variety of scale parameters. On the other hand,
the gap between scale parameters determines the number of
scales in the set, which relates to the coverage of meaningful
segmentation scale directly. For an image, if the gap is small,
it can produce enough segmentation scales as candidates of
meaningful segmentation scales, but too many scales make it
difficult to select the meaningful scales. By contrast, if the gap
is large, it may lead to partial coverage of meaningful scales.
Hence, if the set of scale parameters is assigned ahead of the
segmentation procedure, it is independent with specific im-
ages, which is difficult to capture the variety among different
images and to produce appropriate number of scales to cover
meaningful segmentation scales.
In this study, we focus on automatically setting a set of
gradually increased scale parameters for region growing
method, especially for local-oriented region growing method,
to produce nested multi-scale segmentations. It is an exten-
sion of the step-wise scale parameter (
SWSP
) strategy by Zhang
et al
. (2013). The contributions of this study mainly include
two aspects. First, instead of setting scale parameters inde-
pendently by
SWSP
, we propose the adaptively increased
scale parameter (
AISP
) strategy to determine scale parameters
dynamically during the segmentation procedure, making the
scale parameters adaptive to specific images and segmenta-
tion procedures. Second, the influence on segmentation
accuracy by applying gradually increased scale parameter to
local-oriented region growing is analyzed, which reveals the
importance of changing growing regions.
Methodology
The flow diagram of the proposed multi-scale segmentation
method is presented in Figure 1. First, the region adjacency
graph (
RAG
) is built based on initial segmentation. Then, the
local-oriented region growing is applied under the control of
AISP
. Finally, the segment tree model is used to record and
export nested multi-scale segmentation results.
Region Growing Based on Graph Model
The local-oriented region growing is performed on the basis
of
RAG
, where regions and adjacency between regions are rep-
resented by nodes and arcs, respectively (Trémeau and Col-
antoni, 2000; Felzenszwalb and Huttenlocher, 2004).
RAG
is
built from initial segmentation, which is over-segmented but
has accurate boundaries. The primary region growing method
in (Zhang
et al
., 2013) is used to produce initial segmentation.
Other methods, i.e., watershed transform (Vincent and Soille,
1991), mean-shift based method (Comaniciu and Meer, 2002),
can also be adopted.
The arc weight is calculated according to the merging
criterion (
MC
), indicating the similarity between two adjacent
regions. In this study, a smaller arc weight indicates a greater
similarity between two adjacent regions. The merging crite-
rion includes four features: the region size (
a
), change of stan-
dard variation (
CStd
) and compactness (
CComp
) after a virtual
merging, and edge strength (
ES
). Region size is the number of
pixels in a region, directly relating to segmentation scale.
CStd
and
CComp
reflect the change of region homogeneity and
compactness caused by region merging, which drive to gener-
ate homogeneous and compact segments, respectively (Zhang
et al
., 2013). In terms of
ES
, an adaptive edge penalty function
g
(
ES
) is applied (Yu and Clausi, 2008; Zhang
et al
., 2014).
The effectiveness of
ES
is weak at initial merging iterations
and getting stronger gradually at latter iterations. Finally, the
features are combined to form the merging criterion as below:
MC
= (
a
1
+
a
2
)(
ω
·
CStd
+(1 –
ω
)
CComp
)
g
(
ES
),
(1)
where
a
1
and
a
2
are the size of two adjacent regions, and
ω
is
the spectral weight with default value 0.5. If
ω
is set large,
region growing concentrates on generating homogeneous
regions. Otherwise, it would be driven to generate compact
regions.
The local-mutual best region merging (
LMM
) (Baatz and
Sch pe, 2000) and local best region merging (
LBM
) (Câmara
et al
., 1996; Castilla
et al
., 2008) are selected and applied on
RAG
. In
LMM
, two adjacent regions are allowed to be merged
if they are the best neighbor of each other. However, in
LBM
,
an adjacent region is merged into the growing region if the
adjacent region is the best neighbor of the growing region.
After each merging iteration, the features of the new region
are recalculated, and the adjacency and arc weights in
RAG
are updated. The stopping rule is defined as the threshold of
arc weight, which also serves as the scale parameter. When all
the arc weights in
RAG
are larger than a given threshold, the
region growing procedure stops on the control of this scale
parameter.
Adaptively Increased Scale Parameter
To generate nested multi-scale segmentations by local-orient-
ed region growing, the step-wise scale parameter (
SWSP
) strat-
egy (Zhang
et al
., 2013) was proposed.
SWSP
strategy defines a
set of increased scale parameters, {
S
1
,
S
2
, …,
S
k
, …,
S
max
|
S
1
<
S
2
< … <
S
k
< … <
S
max
}, in which each scale parameter deter-
mines a segmentation scale. Given the target scale parameter
S
k
, the region growing first satisfies the lowest scale parameter
S
1
, and then up to
S
2
, and finally, after the step-wise increas-
ing process, reaches
S
k
. Owing to the gradually increased
scale parameters, the regions at coarse scales are merged from
the ones at fine scales, resulting in nested multi-scale seg-
ments. However, the scale parameters in
SWSP
are defined
prior to segmentation without considering specific image
features and merging procedure. To make the scale parameters
adaptive to specific images, the following two aspects should
be taken into consideration.
Figure 1. Flow diagram of the AISP-based multi-scale segmenta-
tion method.
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June 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
