The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
In this paper, a multi-scale segmentation method based on
Statistical Region Merging (SRM) and Minimum Heterogeneity
Rule (MHR) is presented. The choice of SRM depends on both
the ability to cope with significant noise corruption, handle
occlusions and the consideration of spectral, shape, scale
information. The application of MHR relies on both the
effectiveness local quality and global quality and its
consideration of shape and spectral features. We take the
advantages of them by applying SRM for initial fine
segmentation and MHR for region merging.
2. MULTI-SCALE SEGMENTATION BASED ON SRM
AND MHR
2.1 Statistical Region Merging
The SRM algorithm belongs to the family of region growing
techniques with statistical test for region fusion, and it is based
on a model of image generation who captures the idea that
grouping is an inference problem, namely, the observation
imagery comes from the original imagery by sampling, and the
segmentation imagery comes from the observation imagery by
regenerating, the homogeneity region boundary may defined by
simple theorem (Nielsen and Nock,2003; Nock and Nielsen,
2004).The two key steps of the algorithm are as follows:
(1) Ascertain a sort function, by which the adjacent regions
are sorted according to the size of the function;
(2) Ascertain a merging predicate, which confirms whether
the adjacent regions are merged or not. It is obvious that
sort function and merging predicate are basis of the
algorithm and they are interactive with each other.
Supposing I is an image with 11 | pixels each containing three
values (R,G,B) belonging to the set {l,2,...,g} . The observed
imagery/' is generated by sampling, in particular, every colour
level of each pixel of /' is described by a set of Q independent
random variables with values in [0,glQ] . In /' the optimal
regions satisfy the following homogeneity properties:
(1) A homogeneity property: inside any statistical region and
for any channel, statistical pixels have the same
expectation value for each channel;
(2) A separability property: the expectation value of adjacent
regions is different for at least one channel (Nock, 2001).
Nielsen and Nock consider a sort function / defined as follows:
(1)
Where, p a , ^7 stand for pixel values of a pair of adjacent pixels
of the channel a . From the Nielsen and Nock model obtains
the following merging predicate:
P(RR') = \ true - (AVa e{R,G,B},\R a -R a \<jb 2 (R) + b 2 (R') (2)
[ false. otherwise
Where,
b(R) = g
1
(ln l^ } , R a denotes the observed
2Q\R\ S
average for channel a in region R , R ri stands for the set of
regions with R pixels. More sort functions and merging
predicates could be used to define, which could improve the
speed and quality of segmentation.
In conclusion, the SRM algorithm is able to capture the main
structural components of imagery using a simple but effective
statistical analysis, and it has the ability to cope with significant
noise corruption, handle occlusions with the sort function, and
perform multi-scale segmentation(Nielsen and Nock,2003;
Nock and Nielsen, 2004; Nock and Nielsen, 2005). However, it
has the disadvantage of over-merging, and is not applied in
remote sensing imagery. In this paper, we optimize and apply it
in HR imagery for initial fine segmentation.
2.2 Minimum Heterogeneity Rule
In order to implement the multi-scale segmentation, the MHR is
introduced to merge two adjacent regions from the initial
segmentation.
A MHR not only considering the colour heterogeneity (hcoi or )
but also shape heterogeneity ( hshape) is defined as follows:
+ w.h. (3)
h = KolorKolor
Where, W a;/or , W $hape are weight values about colour
heterogeneity and shape heterogeneity respectively, and
Kotor ^ ] ]’Khape e[0,l]> Kotor + Khape =1'
The colour heterogeneity hobr is defined as follows:
(4)
h color ^c(^ merge ^ c. merge (^obj _\ ^ c .obj _ 1 ^obj_ 2 ^c ,obj ,2))
Where, VV, indicates weight value of every channel.
a c,obj_i ’ a c,obj_2 > G C,merge are the deviation of the two region
and the merged region respectively. tl obj J , H obj _2 » n merge are
the numbers of the two adjacent regions and the merged region.
This value indicates the similar degree of the two adjacent
regions.
The shape heterogeneity ( hshape ) describes the changes of
compact degree (hcomp,) and smooth degree ( hsmoch ) before and
after two adjacent regions are merged, hshape , hcomp, , hsmooth are
defined as follows:
(5)
^shape ^compt^compt Wsmooth^smooth
h = n
compt merge
=
L
obj _ 1
obj _ 1
+ n
obj _ 2
I ' ”obj_ 2 I-
\l n objJ yjn
obj _ 2
/
-(«
obj _ 1
obj _ 1
■ + n.
obj _ 2
0
/7 ' °bj 2 rr
"merge \J U obj _l °obj _2
Where, W compt , w smoot h are weight values about compact
heterogeneity and smooth heterogeneity respectively. And
Komp, ^ [0,1],
smooth
t 0 » 1 ]. Ko mp , + w ,
smooth
= 1.
n obj ,, n obj 2 > n merge are the numbers of the two adjacent regions
and the merged region respectively. / ^ ] , / ^ ^, l merge are the
boundary length of the adjacent regions and the merged region
respectively, b , > b, > b are the perimeter of the
obj _ 1 obj _2 merge
bounding box of the two adjacent regions and the merged
region respectively.
The value of hcomp, represents the cluster degree of the pixels in
the region. Smaller the value is, more compact the pixels in the
region. The value of hsmoo,h represents the smoothness degree of
the region boundary. Smaller the value is, Smoother the region
boundary is.