pe 
so 
1e 
d 
le 
d 
st 
Wm N95 — 
2.4.1 Measures 
(1) Mean grey level 
Maxlxi-xl«TO 
where TO is a threshold. 
(2) Texture 
sqri(Z(xi-x)?/m)«T1., or 
H= ZpjlnPj <T2 
G = X(ij)2py <T3 
where H is the entropy, G is the contrast and p is the 
properbility. 
2.4.2 Data structure----doubletree. Doubletree, which 
node consists of the regions from dividing the image 
equally and alternately in x-direction and y-direction, is 
simpler than quadtree. 
  
  
The encoding criteria are 7 
  
  
left :0 
right :1 
up :0 
down : 1 
  
  
  
  
The code of the region on Fig.O is ; 
1001 5 8 Fig. 0 
2.4.3. Separation-merger algorithm. 
(1) scparation. For cach node, if the measure of the 
consistency is false it is divided into left and right (or up 
and down) parts, untill all leaves represnt a consistent 
region. 
(2) merger. For each region, if the consistent measure of 
the region and its neighbor region is true, then the 
neighbor region is merged into it. 
2.4.4 Labling algorithm of neighbor regions. The 
conneclivily of a region is considered in the separalion- 
merger algorithm. So, it can be a labling algorithm of 
neighbor regions. In this case, the consistent measure is 
true, if all pixels in the region are 1, and the region, in 
Which no pixel is 1, do not store in the tree. 
As a special cxmaple, the unconnected curves can be 
separated by separation-merger algorithm, so that the line 
following will be simple. 
The result of image segmentation is a binary or multiple 
value image. It can be used in image analysis. 
3. IMAGE ANALYSIS BASED ON MATHEMATICAL 
MORPHOLOGY 
The human vision is concerned in not only the images or 
objects, but also human thought, knowledge and new 
perception. 
On the basis of this idea, the structuring elements with 
different size and shape can more easily be designed to 
adapt to our task, while the mathematical morphology is 
73 
used in image analysis. The morphological filtering with 
the structuring elements is applied in the extraction of the 
useful imformation and the restraint of the uninterested 
imformation. 
3.1. Back 
1975], [Serra, 1982] 
[Matheron 
The operations of mathematical morphology can be 
divided into set operations and function operations. À 
binary image is a set in which the objects are its subsets. 
A grey-level image is a function on a set. 
If X is a binary image on a plane, it is equivalent to a 
binary function f(x,y), where (xy)€X and xy€R, € 
means belong to. 
Let A KE2R*R K called structuring element is a limited 
set. z=(x0,y0)ER?. 
Difinition 1: the Translate of f(x,y) or A by z is defined as 
Trans([,z) =f(x+x0,y+y0)=[z 
Trans(A,z) = {a+z: aCA} =Az 
Difinition 2: the Reflection of K is defined by 
K = (Ck: kCK ) 
Difinition 3: the Dilation of A and f by K is 
A@K={1Kz A!=9} 
fek(x)- ut n - k(7)} 
Difinition 4: the Frosion 
AGK - (zl Kzc A ) 
fOk(x) 7 sup(f(x-z) + k(z)} 
k 
x-zCF 
Difinition 5: Opening 
AoK = (A©K)@K - U Ky 
KyCA 
Difinition 6: Closing 
; v 
AK - (A6K)GK - f Ky 
{yIkÿNA != 6} 
where Kc={xIx€2R"R, x &K ) 
Difinition 7: Let X be image and T=(T1,T2), where 
T1,T2€2R"R are structuring elements. 
Hitmiss(X,T) » (X0T1) / (X912) = X@T 
where / is the subtract of sets. 
XQ9T - (XOT1)A(X*0T2). 
3.2 Analysis of Edge 
3.2.1. Edge. The edge extraction with mathematical 
morphology is simple for the binary image. The method 1