Segmentation algorithms of biomedical images: development and quantitative evaluation
The article presents the comparative analysis of the biomedical image segmentation methods. The work discusses segmentation methods on the basis of previous labeling and spatial moments. The experimental results show that the developed methods have higher accuracy by signal-noise ratio compared to t...
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irk-123456789-1320752018-04-11T03:03:50Z Segmentation algorithms of biomedical images: development and quantitative evaluation Berezsky, O. Batko, Yu. Melnyk, G. Verbovyy, S. Pitsun, O. Прикладні інтелектуальні технології та системи The article presents the comparative analysis of the biomedical image segmentation methods. The work discusses segmentation methods on the basis of previous labeling and spatial moments. The experimental results show that the developed methods have higher accuracy by signal-noise ratio compared to the nowadays known. Moreover the authors have developed the quantitative evaluation of the segmentation algorithms based on the metrical approach. У статті представлений порівняльний аналіз методів сегментації біомедичних зображень. У роботі досліджуються методи сегментації на основі попередньої розмітки та просторових моментів. Експериментальні результати показують, що розроблені методи мають більш високу точність за співвідношенням сигнал-шум у порівнянні з відомими. Крім того, автори розробили алгоритм кількісної оцінки алгоритмів сегментації на основі метричного підходу. The proposed research has been developed within the state budget project "Hybrid Intelligent Information Technology Diagnosing of Precancerous Breast Cancer Based on Image Analysis" (state registration number 1016U002500). 2016 Article Segmentation algorithms of biomedical images: development and quantitative evaluation / O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun // Штучний інтелект. — 2016. — № 3. — С. 104-115. — Бібліогр.: 19 назв. — англ. 1561-5359 http://dspace.nbuv.gov.ua/handle/123456789/132075 004.9 en Штучний інтелект Інститут проблем штучного інтелекту МОН України та НАН України |
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Прикладні інтелектуальні технології та системи Прикладні інтелектуальні технології та системи |
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Прикладні інтелектуальні технології та системи Прикладні інтелектуальні технології та системи Berezsky, O. Batko, Yu. Melnyk, G. Verbovyy, S. Pitsun, O. Segmentation algorithms of biomedical images: development and quantitative evaluation Штучний інтелект |
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The article presents the comparative analysis of the biomedical image segmentation methods. The work discusses segmentation methods on the basis of previous labeling and spatial moments. The experimental results show that the developed methods have higher accuracy by signal-noise ratio compared to the nowadays known. Moreover the authors have developed the quantitative evaluation of the segmentation algorithms based on the metrical approach. |
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Berezsky, O. Batko, Yu. Melnyk, G. Verbovyy, S. Pitsun, O. |
| author_facet |
Berezsky, O. Batko, Yu. Melnyk, G. Verbovyy, S. Pitsun, O. |
| author_sort |
Berezsky, O. |
| title |
Segmentation algorithms of biomedical images: development and quantitative evaluation |
| title_short |
Segmentation algorithms of biomedical images: development and quantitative evaluation |
| title_full |
Segmentation algorithms of biomedical images: development and quantitative evaluation |
| title_fullStr |
Segmentation algorithms of biomedical images: development and quantitative evaluation |
| title_full_unstemmed |
Segmentation algorithms of biomedical images: development and quantitative evaluation |
| title_sort |
segmentation algorithms of biomedical images: development and quantitative evaluation |
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Інститут проблем штучного інтелекту МОН України та НАН України |
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2016 |
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Прикладні інтелектуальні технології та системи |
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http://dspace.nbuv.gov.ua/handle/123456789/132075 |
| citation_txt |
Segmentation algorithms of biomedical images: development and quantitative evaluation / O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun // Штучний інтелект. — 2016. — № 3. — С. 104-115. — Бібліогр.: 19 назв. — англ. |
| series |
Штучний інтелект |
| work_keys_str_mv |
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| first_indexed |
2025-07-09T16:40:15Z |
| last_indexed |
2025-07-09T16:40:15Z |
| _version_ |
1837189040245309440 |
| fulltext |
ISSN 1561-5359. Штучний інтелект, 2016, № 3
104 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
УДК 004.9
O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
Ternopil National Economic University, Ukraine
Lvivska st., 11, Ternopil, 46006
SEGMENTATION ALGORITHMS OF BIOMEDICAL IMAGES:
DEVELOPMENT AND QUANTITATIVE EVALUATION
О. Березький, Ю. Батько, Г. Мельник, С. Вербовий, О. Піцун
Тернопільський національний економічний університет, Україна
вул. Львівська, 11, Тернопіль, 46006
АЛГОРИТМИ СЕГМЕНТАЦІЇ БІОМЕДИЧНИХ ЗОБРАЖЕНЬ:
РОЗРОБКА ТА КІЛЬКІСНА ОЦІНКА
The article presents the comparative analysis of the biomedical image segmentation methods. The work
discusses segmentation methods on the basis of previous labeling and spatial moments. The experimental results
show that the developed methods have higher accuracy by signal-noise ratio compared to the nowadays known.
Moreover the authors have developed the quantitative evaluation of the segmentation algorithms based on the
metrical approach.
Key words: Biomedical image, segmentation; labeling; spatial moments, evaluation.
У статті представлений порівняльний аналіз методів сегментації біомедичних зображень. У роботі
досліджуються методи сегментації на основі попередньої розмітки та просторових моментів.
Експериментальні результати показують, що розроблені методи мають більш високу точність за
співвідношенням сигнал-шум у порівнянні з відомими. Крім того, автори розробили алгоритм кількісної
оцінки алгоритмів сегментації на основі метричного підходу.
Ключові слова: біомедичні зображення, сегментація, розмітка, просторові моменти, оцінка.
Introduction
Biomedical images are used for diagnostics and treatment. The images of normal and
abnormal cells and tissues are obtained from light microscopes. Those images are modern
histology and cytology research objects. The tasks of microscopic image analysis automation
are solved with the help of automated microscopy systems (AMSs). AMSs consist of
hardware and software systems for digital processing of the microscopic images [1]. One of
the most important stages of optical and geometrical parameter automation measurement is
the selection of microobjects on histological images [2, 3]. The biomedical image analysis
appears to be difficult because of the high variability of parameters and the weak contrast of
most microobjects.
The microobjects of histological images are sections of certain organs’ tissues. The
tissue consists of rounded cells, which are placed in layers. Cells dimensions range from
several micrometers with the smallest of them being from 0.5 to 1.2 microns. Microobjects on
cytological images are the individual cells that are placed randomly.
The histological image analysis, performed with the help of AMSs, consists of the
following stages: imagery, manual and automatic selections of the microobjects (cells, nuclei,
segments of different colour or brightness, etc.), size measurement, shape, position and
optical parameters of the selected microobjects or their parts, their classification and statistical
processing of the measurement results.
Images segmentation leads to the division of images into regions with similar
characteristics. Some of the main image attributes for segmentation are brightness for
monochrome images and colour component for colour images. Edges and textures are also
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© O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun 105
used for segmentation. The segmentation process divides only the image and doesn't identify
individual segments and their relationship [6].
Currently there are no universal methods of the segmentation process. They often use a
set of specialized methods that are the most common for this class of problems. In the work
[2] are proposed the characteristics for the segments after segmentation.
Image segmentation method based on previous labeling
Several approaches to the segmentation algorithm classification are known, namely: Fu
and Mui [8], Pal and Pal [9], Skarbek and Koshana [10], Lucchese and Mitra [11], Jipkate
[12]. The approaches are based on the following criteria: the properties of points, regions,
region edge, a priori knowledge about microobjects, etc. Let’s see the other criteria for the
algorithms segmentation separation. They are: image type (colour, grayscale, binary), nature
of the segmentation process (parallel or sequential processing) [13, 14, 15]. However, these
characteristics are ambiguous. For example, threshold segmentation can occur in parallel or in
sequential modes and handle both binary and grayscale images. It leads to ambiguity in the
classification algorithms for segmentation. In our opinion, the further discussed criteria allow
more complete classification of segmentation algorithms.
Algorithms based on texture properties. The decision to include a point into the segment
is taken on the basis of texture features similarity at that point. This type of algorithms is
recommended to use for images with repetitive regions.
Task definition. The analysis of the segmentation algorithms and biomedical image
features shows that segmentation methods development on the basis of the relations between
points and texture features of regions is a vital task [18].
As can be seen from the above review, there is no universal method of segmentation
and each algorithm has its advantages and disadvantages. The proposed approach uses the
characteristics of individual image points and the relationship between them.
We introduce the notation:
I – input image;
iIs – input image marked by i- type labeling;
ijV – j homogeneous region in the input image marked by і type labeling;
8..1,..1,..1),,,( zmylxzyxMk – the array of coefficients for the relationships k
labeling, l – the width of the input image, m – the height of the input image, z – the
number of the neighboring pixels.
The array of total interconnections coefficients sumM equals (1):
n
k
ksum MM
1
, (1)
where n – the number of previous labeling used in the process of segmentation.
Definition 1. Labeling is the process of splitting the input image I into an array of
homogeneous regions jV based on the criterion of homogeneity KO. Homogeneity criterion
is defined previously by the analysis of the input image I }{ j
KO VI
Definition 2. If two neighboring points ),( 11 yxI and ),( 22 yxI are in homogeneous areas,
the relationship between them equals 1: )),(()),((,1 2211 yxIPyxIPR . Here ),( 11 yxI and
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106 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
),( 22 yxI is two neighboring pixels;
)),(( 11 yxIP – identification of a homogeneous region to which the pixel represents ),( 11 yxI ;
)),(( 22 yxIP – identification of a homogeneous region to which the pixel represents ),( 22 yxI ;
R – the coefficient of the correlation between two pixels.
Definition 3. If two neighboring points ),( 11 yxI and ),( 22 yxI are in different
homogeneous regions then the correlation between them equals 0:
)),(()),((,0 2211 yxIPyxIPR ,
Definition 4. The total coefficient of the relationship between two pixels ),( 11 yxI and
),( 22 yxI is defined as the amount of bonds at n labeling is (2):
niRRsum i ..1, , (2)
where R – coefficient of the relationship between two neighboring pixels ),( 11 yxI and
),( 22 yxI ;
This approach analyzes previous labeling of the image and sets anchor points not only
to a specific area, but also to the neighboring points. Algorithms of the previous labeling can
be selected depending on the input image. The image of stable relationships will be
recognized as homogeneous.
The segmentation algorithm is the following:
1) We provide previous labeling input image I via n labeling;
2) We form the array of factors relationships kM between neighboring points for each
one with n labeling of the input image;
3) We form the total array of factors relationships sumM between neighboring points
for each one with n labeling of the input image;
4) We provide the group input image points I in the homogeneous region based on
the relationships of the total interconnection coefficients sumM .
The previous labeling can be carried out in three ways.
Manual. Labeling of the image on the homogeneous region is carried out manually by n
independent users. This way is time-consuming and subjective because the previous labeling
is influenced by a human factor. The advantage of this approach is that the number of
previous labeling can be minimal.
Automated. The process of the previous labeling uses the known methods of
segmentation, but a user sets the input parameters. The advantages of this approach are high
accuracy and speed with increasing objectivity of the previous labeling.
Automatic. Previous labeling is based on an automatic analysis of the input image, such
as the histogram analysis of brightness distribution and definition of thresholds for labeling.
Since this algorithm was developed for the segmentation of colour images during the
previous auto- labeling images, it offers the transition from a three-dimensional representation
of colour to a one-dimensional. The representation of images in one-dimensional space allows
the automatic analysis of colour distribution histograms of the algorithms to determine thresholds.
Previous labeling can be made in different colour bases.
We use the following rules for the complete segmentation process to classify the input
image points in the homogeneous region based on the relationships between the neighboring points:
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© O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun 107
1) if the relationship between two neighboring points ),( 11 yxI and ),( 22 yxI is max
maxsumM for the input image, then the data points are combined into a homogeneous
region jV (Fig. 1,а).
2) If the point of interconnection ),( 11 yxI with the neighboring point ),( 22 yxI is
bigger than the relationship with the other neighboring points, these points are combined into
a homogeneous region jV ;
3) If the point ),( 11 yxI has the same relationship with two (or more) neighboring points
),,(),,(),,( 332211 zyxMzyxMzyxM sumsumsum , which are combined in a homogeneous
region jj VyxIVyxI ),(,),( 3322 , then this point is connected to the corresponding
homogeneous region jVyxI ),( 11 (Fig. 1,b);
4) If the point ),( 11 yxI has the same relationship with two (or more) neighboring points
),,(),,(),,( 332211 zyxMzyxMzyxM sumsumsum , which do not belong to one homogeneous
region jiVyxIVyxI ji ,),(,),( 3322 , the point is connected to the area with more
neighbors (fig. 1,c).
a) b) c)
Fig. 1 Example of points integration
The result of the algorithm is a set of homogeneous regions. Because microobjects in
the image usually consist of groups of homogeneous regions, we use the procedure for an
additional association of homogeneous regions.
Texture segmentation algorithm
Texture segmentation algorithm consists of the following steps [15]
a) calculation of the texture features for each image point within the sliding window
size WW,
b) the constructed texture field segmentation.
We use textural features based on spatial moments of the field and the distribution of
gray levels matrix.
The texture image can be quantitatively described by simple statistical characteristics,
such as mathematical expectation, dispersion and moments of higher order [10]. The term
spatial moments (SMs) comes from mechanics. When SMs are being applied to the images, it
reflects the distribution of gray levels in the image along its axis. On their basis we can
calculate the features of the region that are invariant to rotation, translation and scale [11].
Spatial moments of the region in the point with the coordinates ),( yx and function value of
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108 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
the gray level ),( yxf are calculated as (3):
dxdyyxfyxm qp
qp ),(, (3)
We consider the image as a function of two variables f(x,y) and calculating the number
of lower-order moments for each pixel in the image for 2)( qp . The moments are
calculated within the local window size WW around each pixel.
In the discrete version of the SMs, within the window bounders, with the center pixel
being (i, j), moments are calculated as the sum with normalized coordinates (xm, yn):
2/
2/
2/
2/
, ),(
W
W
W
W
q
n
p
mqp yxnmfm (4)
where m,n – the coordinates of the point related to the window.
In our algorithm we use moment of inertia m1,1.
In gray levels of the distribution matrix (GLDM) [18] Pd for translating vector d=(dx,
dy), value pi,j is the number of gray level of pair value occurrences, where i and j are placed at
a distance d. Thus, for each image point f(x, у) the matrix Pd can be associated, which
characterizes the distribution of brightness in the window size WW centered at coordinates
(x, i). The elements of the matrix Pd are defined as the following:
Dnm
dndmnmjid xxfjiP
),(
,,, );(),( (5)
where D – window with WW dimensions (W - odd),
i, j = 0,255 – the brightness value of the point,
nmx , – the brightness value of the point with coordinates (m,n).
The function );( ,,, dndmnmji xxf is defined as:
else
ixandjxor
jxandix
xxf dndmnm
dndmnm
dndmnmji
,0
)(
)(,1
);( ,,
,,
,,, (6)
The function is an indicator of the fact, that points that are located at a given distance,
have certain levels of brightness. The parameter d determines the distance at which
neighboring points are analyzed. On the basis of GLDM the textural features are determined:
energy, entropy, contrast, homogeneity and correlation.
Texture features are calculated on the matrix Pd(i, j), that describes the distribution of
brightness within the region with its center in the point (x, у). After processing the entire
image for each feature of the matrix, the field of texture features is formed. The matrix
contains the values of features in all processed points. To describe the features, we use the
auxiliary values:
j
j jijPm ),( ,
j
j jiPp ),( , (7)
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© O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun 109
mathematical expectation
i
iipMx ;
The following formulas, that enable to calculate the characteristics, are presented below.
1. Total mean value:
i
ii pmF1 (8)
2. Inertia:
i j
jiPjiF ),()( 2
2 (9)
The proposed algorithm of image texture segmentation consists of the following steps:
1. Construction of the texture field G, every point of which is Gg according to (1)
g(i,j) = m1,1 =
2/
2/
2/
2/
),(
W
W
W
W
nm yxnmf (10)
2. Normalization G, g [0, 255].
3. Search for the thresholds t1, t2,..., tn using the following steps:
a) Setting the interval R=[a, b]; a=0 and b=255.
b) Calculation the mathematical expectation µ and the standard deviation of all pixels
from the interval R.
c) Calculation of the thresholds t1 і t2 as t1 = k and t2 = k ;
d) Calculation of the intervals 11 ta , 12 tb ;
e) Repeat steps da , n/2 times (n – number of thresholds) setting new limits of the
interval 11 ta , b and 1a , 12 tb .
4. Segmentation of the texture field G and as a result we obtain n+1 binary masks si,
i={1, ...,n+1}:
else
tyxgtif
yxs
ii
i
0
),(1
),(
1
(11)
where t0 =0, tn+1 = 255.
5. Segmentation of the input image aiming to obtain n+1 images is
, i={1, ...,n+1}
else
yxsifyxf
yxs
i
i
0
1),(),(
),(
(12)
To test the GLDM (5) as a texture feature we must perform this algorithm constructing
g(i,j) = F5 in step 1. The parameter k serves to control the spacing between the lowest and
highest thresholds.
The optimal number of thresholds n (the number of algorithm iterations respectively)
may be set a priori based on the application. The number of thresholds can also be chosen on
the basis of signal/noise ratio changes . The value of can be calculated between the
original and segmented image of the average values of pixels inside the segments.
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110 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
The quantitative evaluation algorithms
The quantitative evaluation of the segmentation algorithms quality is based on the
following algorithms [23].
The algorithm for determining the discrete Frechet distance.
Сonsider the algorithm for determining the discrete Frechet distance, in case of two
contours (Fig. 2).
1. Let the contour of each segment C and R be presented in the form of the
polygonal curves (11).
),...,()( 1 rvvC , ),...,()( 1 swwR , (11)
where r , s – the number of linearly approximated segments.
2. Let’s form a sequence L between the curves C and R
)(),...,(),( ,,, 2211 mm bababa wvwvwvL , 11 a , 11 b , ram , sbm .
3. We obtain the Euclidean norm of the sequence ),(max||||
,...1, ji ba
mji
wvdL
,
using the following steps.
3.1. If i=1 and j=1, then the distance is given as the Euclidean distance between the
points (Formula 12).
2)(
ij ab vwd ; (12)
3.2. If i>1 and j=1, then the distance is given by the formula (13).
)}(),(max{
111 ,, baba wvdwvd
ii
(13)
3.3. If i=1 and j>1, then the distance is:
)}(),(max{ ,, 111 jj baba wvdwvd
(14)
3.4. If i>1 and j>1, then the distance is given by the formula 15.
),,(),,(min(max
111 iiii baba wvdwvd )),(),,(
1 iiii baba wvdwvd
(15)
Fig. 2 Determining the discrete Frechet distance
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© O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun 111
The algorithm for determining the Hausdorff distance
Let’s use the results of the regions contours representation. Let’s present the regions 1O
and 2O in the form of the convex polygons ),...,,( 211 mvvvO and ),...,,( 212 nwwwO ,
where iv ( mi ,1 ), iw ( ni ,1 ) – the sequences of vertices linearly approximated sections of
the external borders of the regions. Then the Hausdorff distance between the convex regions
1O and 2O is calculated according to formula 16:
)},(max),,(maxmax{),( 22
,...,1
11
,...,1
21 12 iiO
ni
iiO
mi
H badbadOOd
, (16)
where ),( 11
2 iiO bad – the projections of the vertex region 1O to the region 2O ,
),( 22
1 iiO bad – the projections of the vertex region 2O to the region 1O [24].
The projections
lOd ( 2,1l ) are calculated according to the expression:
casesother in 0
),(),(,),(),(
),(
lO
O
OInteriowvwvProjwv
wvd l
l
where ),( wvProj
lO – the point at
which a minimum Euclidean distance is implemented from a point ),( wvP to the region lO
[23].
Let’s present the Hausdorff determining distance algorithm by the following steps:
1. Let’s set up the polygonal regions with the sequences vertices ),...,,( 211 mvvvO and
),...,,( 212 nwwwO that are obtained from the previous algorithm. We find the distances
lOd
( 2,1l ) for all vertices of regions 1O and 2O according to the expression (3).
2. According to the expression (2) we obtain Hd .
Experimental results
In order to carry out computer experiments the software module has been developed in
Java programming language using the OpenCV computer vision library. This module is
designed for pre-processing & image segmentation and the evaluation segmentation results. It
implements segmentation algorithms developed by the authors. The segmentation algorithms
are evaluated, based on the metric approach [16]. The preprocessing algorithm is presented in
details [19].
Fig. 7 shows the fragment of a histological image of a breast tissue slice. Histological
images contain such complex micro-objects as parietes of glands and ducts. The texture
analysis is calculating of textural features space based on PM (Fig. 8b) and its threshold
processing.
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112 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
a)original image b) expert
segmentation
c) k – means d) Watershed e) Algorithm on
the basis of
previous
labelings
Fig. 7 Previous labeling images by different algorithms
a) initial image b) space of texture features
Fig. 8 A fragment of the initial image and the image space of texture features
As a result of threshold processing we have obtained labeling (Fig. 9,a) as well as have
identified the breast duct paries (Fig. 9,b).
a) labeling b) ducts paries image
Fig. 9 Labeling image and the ducts parietes identification
Table 1 shows the comparison of image segmentation algorithms. The Hausdorff,
Frechet, Gromov – Hausdorff, Gromov – Frechet metrics are used for the comparison.
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© O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun 113
Table 1. Comparison of segmentation algorithms
metric algorithm Hausdorff
metric
Gromov-
Hausdorff
metric
Frechet
metric
Gromov-
Frechet
metric
k-means 67.89 64.63 67.89 64.63
watershed 130.9 125.7 132,76 126.1
The algorithm is based on the
previous labeling
64,38 63,27 64,38 63,27
Table 2 shows the results of the evaluation of the texture segmentation algorithm.
Table 2. Evaluation of texture segmentation algorithms
Standard image Texture
segmentation
1 Hausdorff metric
2 Gromov-Hausdorff metric
3 Frechet metric
4 Gromov-Frechet metric
1 124.14
2 121.64
3 260.93
4 165.92
1 342.06
2 333.95
3 342.06
4 333.95
1 113
2 108.17
3 412.95
4 393.07
1 431.18
2 430.72
3 432.65
4 430.75
1 190.06
2 190.06
3 224.61
4 224.61
Conclusion
1. Using of connection points for the segmentation of biomedical images has a number
of advantages compared to the characteristics of the individual points:
- the ability to process images of any type;
- the increased resistance to image segmentation when the micro-objects are close to
each other.
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114 © O. Berezsky, Yu. Batko, G. Melnyk, S. Verbovyy, O. Pitsun
- reducing of the input image noise and distortion effect on the overall result by
analyzing of images with different segmentation algorithms.
2. The texture segmentation application, based on spatial moments, allows identifying
complex micro-objects such as cell layers, the parietes of blood vessels and ducts.
3. Using of the Hausdorff, Fréchet, Gromov – Hausdorff, Gromov - Fréchet metrics
provides quantifying of the segmentation algorithms quality in automatic mode.
Acknowledgment
The proposed research has been developed within the state budget project "Hybrid
Intelligent Information Technology Diagnosing of Precancerous Breast Cancer Based on
Image Analysis" (state registration number 1016U002500).
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RESUME
O.M. Berezsky, Yu.M. Batko, G.M. Melnyk, S.O. Verbovyy, O.Y. Pitsun
Segmentation algorithms of biomedical images: development and quantitative evaluation
The article presents the comparative analysis of the biomedical image segmentation
methods. The work discusses segmentation methods on the basis of previous labeling and
spatial moments. The experimental results show that the developed methods have higher
accuracy by signal-noise ratio compared to the nowadays known.
This paper showing that the using of connection points for the segmentation of
biomedical images has a number of advantages compared to the characteristics of the
individual points such as: the ability to process images of any type; the increased resistance to
image segmentation when the micro-objects are close to each other, reducing distortion effect
on the overall result by analyzing of images with different segmentation algorithms.
The texture segmentation application, based on spatial moments, allows identifying
complex micro-objects such as cell layers, the parietes of blood vessels and ducts.
Moreover the authors have developed the quantitative evaluation of the segmentation
algorithms based on the metrical approach. Using of the Hausdorff, Fréchet, Gromov –
Hausdorff, Gromov - Fréchet metrics provides quantifying of the segmentation algorithms
quality in automatic mode.
Надійшла до редакції 04.09.2016
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