IMAGE SEGMENTATION BASED ON PARAMETER ESTIMATION
Younian Wang
Institute of Photogrammetry and Engineering Surveying
University of Hanover, FR Germany
Commission V
Abstract
In this paper a new method for image segmentation is discussed. It is based on the theories of parameter
estimation and hypothesis test of mathematical statistics. The mathematical formulas and criteria of the
method are introduced and derived. The function model and random model of the image are discussed. A
quantitative indez about the separability of the regions are also provided. Some examples are presented to
show the effects of the proposed method.
Key Words: image segmentation, parameter estimation, hypothesis test, machine vision, feature extraction.
1. INTRODUCTION
The problems of image segmentation is key important in
machine vision. It is also essential for many applications
of robot vision in close range photogrammetry. Since the
pioneer work of Roberts, Brice and Fennenma{1] much has
been written about the topic and many methods have been
described in the Literature[2],[1]. The subject continues to
receive a great amount of interest because of its essential role
in machine vision. It is the basis of many tasks in vision area,
e.g. image modelling, image interpretation, scene analysis,
image understanding etc.
Mainly speaking, image segmentation indicates to divide an
image into several regions according to some consistent prin-
ciples. It can also be regarded as the classification of the
image pixels. The mathematical definition of the image seg-
mentation can be addressed as the following:
For an image R, if m sets of pixels Ry, Rs, ..., R4, exist and:
e R; 7: 0;
. Ü R; - R;
il
e R; N R; = 0;
e each R; satisfies some consistent principles;
e any combination of the connected sets does not satisfy
the above consistent principles;
then the (Ry, Rs, ..., Ri) is called a segmentation of the ima-
ge R.
There are mainly two types of the consistent principles.
The first one supposes there is a homogeneity inside a re-
gion, e.g. the same grayvalues. The second one supposes
there is a discontinuity between the regions, e.g. the sud-
den change of the grayvalues. The proposed approaches
of image segmetation can be categorized into three kinds,
namely threshold-based methods, region-based methods and
feature-based methods. The threshold-based methods use
one or several grayvalues as the thresholds to divide the im-
age. But in the most cases it is difficult to find the suitable
thresholds. The feature-based methods include the edge
based methods, which take the edges as the boundaries of
the regions, and the classification based methods, which use
feature based classifier to determine to which region does a
pixel belong. The region based methods involve region grow-
ing methods, region splitting and region merging methods,
and function approximation methods. Each of the above-
mentioned methods has its advantages and disadvantages.
None of them is perfect and suitable for every case.
In this paper a new method is discussed. It is based on
parameter estimation and hypothesis test of mathematical
statistics. So that it is theoretically perfect and mathemat-
ically well represented. With this method the image noise
can be optimally treated. Furthermore the method can also
quantitatively describe the separability of the regions. The
experiments show that it has also great prospects in appli-
cations. Because the images in close range photogrammetry
for the applications of machine vision have usually distinct
objects and backgrounds, the method should be very suit-
able in these occassions to distinguish objects from the back-
grounds. In the following the methodology is discussed and
the mathematical formulas are derived. Its procedures in the
applications are analysed and some examples are presented.
2. THEORY OF PARAMETER ESTIMATION
The tasks of parameter estimation are to determine the un-
known parameters from the observations. There are several
estimation methods for the different models and cases, e.g.
point estimation, unbiased estimation, least square method,
maximum likelihood method. We introduce here only the
least square method for the linear model. If the observations
have a normal distribution, the results of the least square
method are equal to that of the best linear unbiased estima-
tion and the maximum likelhood method[3].
2.1 Least Square Estimation
If the observations are the linear functions of the unknown
parameters, we call it linear model. For the case of the
unlinear model we can use the series expasion according to
Taylor to obtain the linearized model. So we can discuss the
least square method under the linear model without loss of
