IMAGE ANALYSIS BASED ON MATHEMATICAL MORPHOLOY* 
prof. Zhang Jianqing, Mr. Fan Qingshong 
Wuhan Technical University of Surveying and Mapping 
P.R.China 
Commission III of ISPRS 
ABSTRACT 
Basic information of objects (regions) in digital image is obtained by image segmentation. More precise information 
about the object (regions) is extracted based on image analysis, includeing edge extracting , thinning , configuration 
fitting and shape decompositing, which are mainly based on mathematical morphology. The primitives of structural 
features can be produced by means of the methods. At last, the polygons and the primitives of structure features can be 
acquired for further image matching or understanding. 
key words: Image segmentation, Mathematical morphology, Edge extraction, Thinning, Region decomposition. 
1.INTRODUCTION 
The reliability of image matching and the image 
interpretation are the problems that many 
photogrammetrists and informatics scientists are studying. 
Solving these problems should be based on image 
processing in higher level than in grey level. Vision is a 
complex procedure of imformation processing. The task 
of elementary vision is constructing the proper 
description of local geometric structure on the image from 
the variation of grey levels. To this end, the primitives of 
objects ought to be organized in different level, in order 
to acquire the structure features and carry out the structure 
matching and shape recognition. 
An important sort of the primitive employed in structure 
matching and shape recognition is based on the surfaces 
of objecs. Its acquisition can be by two ways. One is 
from the edges. The other is from the regions. In this 
paper, the information of edges and regions are obtained 
by image segmentation. Then, more precise information 
about the objects (regions) is extracted based on image 
analyses, including edge thinning, configuration fitting 
and region decomposition with method of mathematical 
morpholog . 
2.IMAGE SEGMENTATION 
The purpose of segmentation is to partition the image 
space into meaningful regions with certain consistency of 
grey level, texture, color, gradient or other properties. For 
given image Image 
Image = {X=f(ij) | i=0,1,2,...,.M-1, j=0,1,2,...,N-1} 
and consistency measure P(), the segmentation of Image 
is a decomposition (X1, X2, ..., Xn) of Image satified 
(1) Xj 28, 
Q) XiXi-5, i'-j 
(3) Xiis connected 
(4) P(X;) = True and P(X;UX;U...) = False 
In this section the thresholding clustering and separation- 
merger algorithm are introduced. 
where "!=" means "Be not equal” 
2.1 preprocessing 
For eliminating the noise degradation, the image 
smoothing is performed, and image enhancement is also 
completed in order to sharping thc cdges. 
22^ Thresholdine aleorif [i ; 
22.1 Method of searching valley. ^ The threshold is 
obtained by simply searching the valley along the 
distribution curve in the histogram, which is smoothed 
with 3-order spline or moving average. 
2.22 Polynomial threshold. The intensity on a 
image is not even sometimes. In this case, only one 
threshold on entire image is not suitable. The threshold 
should be the function of the position. For the simplest 
example, it is a 1-order polynomial. 
T(x,y) =ax + by +c 
The coefficients a,b,c, can be computed by surface fitting 
with least squares method. 
2.3 Clustering algorithm 
Image segmentation is a classification of pixels. There are 
n measures at each pixel instead of one, the grey level, in 
thresholding algorithm. Common measures arc 
(1) Average x =3xi/m 
(2) Mean square deviation sqri(Z(xi-x)%/m) 
(3) Contrast Imax {xi}-min{xi}| 
The clustering algorithms of n-dimensional feature space 
include k-average, ISODATA based on k-average and 
ASP based on ISODATA. 
2.4 Region growing 
Region growing starts at the known pixel or a group of 
pixels and appends all neighboring pixels untill the 
measure of consistency is false. A typical example of 
region growing is separalion-merger algorithm. 
* The investigation has been supported by National Nature Science Funds of P.R.China 
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