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.