Detection and Extraction of Objects in Digital Images
Vladimir Yu. Volkov
Radio Systems Dept.
Saint-Petersburg Electrotechnical University ''LETI'';
Saint-Petersburg State University of Aerospace
Instrumentation
Saint-Petersburg, Russia
vl_volk@mail.ru
Abstract—Detection and extraction of objects of interest out of
monochrome images based on their compactness and isolation are
essential in remote sensing systems data analysis. Algorithms
under consideration are based on the results of multi-threshold
processing, which provides with a set of binary layers. This allows
for further morphological processing of isolated objects in each
binary layer in order to analyze their geometric characteristics
and perform their subsequent selection by geometric criteria. As a
result, one can set an adaptive detection threshold individually for
each of the selected objects. Using selection allows to significantly
reduce the number of false alarms during detection as well as to
use lower-level thresholds this way increasing the probability of
correct detection of the objects of interest. The results of synthetic
test imagery analysis as well as object detection in remote
observational imagery demonstrates explicitly the effectiveness of
the considered algorithms.
Keywords- object detection and extraction; multi-threshold
processing; image segmentation; percolation
I.
INTRODUCTION
The problems of detection, extraction and localization of the
objects of interest are relevant in the analysis of images obtained
by various remote sensing systems and thus are being intensively
studied in the last decades [1–5].
There are various approaches to the image segmentation
problem. Retrospectively, the earlier developed and the simplest
methods were based on comparison of an image with a certain
threshold, this way segmenting the source image into more
intensive (above the threshold) and less intensive (below the
threshold) areas. In threshold based approaches, one of the key
problems in the choice of appropriate criteria for the threshold
selection. Among various approaches, several could be
mentioned as being widely used in applied computer vision,
namely the Otsu method based on maximizing the variance
between the segments while minimizing the variance within
each segment, as well as methods based on the optimization of
corresponding entropy metrics [6]. Other relevant approaches
include clustering based methods with k-means clustering being
the most representative and widespread technique [7], histogram
based methods that focus on finding local peaks and valleys is
the sample histogram computed from all of the pixels in the
Mikhail I. Bogachev
Radio Systems Dept.
Saint-Petersburg Electrotechnical University ''LETI''
Saint-Petersburg, Russia
rogex@yandex.com
image with the balanced histogram algorithm being a
representative example [8], compression based segmentation
that focuses on finding regular patterns in an image this way
aiming at the minimization of the coding length of the data,
which is a common step in the image compression algorithms
[9], as well as edge detection based methods that focus on the
adjustment of neighboring sharp edges to form close region
boundaries [10]. Among more complex alternatives several nonlinear approaches such as the fuzzy logic based non-linear
adaptive thresholds [6] as well as some specialized methods
based on an early adaptive estimation of threshold values from
the raw data even prior to the image formation that are used in
some scanning and tomographic systems are of interest [11].
Segmentation is typically followed by the selection of certain
segments that represent potential objects of interest. In a general
perspective, algorithm performance optimization encourages
possible integration of the image segmentation and object
selection procedures, leading to some of the segment properties
calculated at the segmentation stage being available later for the
object selection process. In contrast, additional parameters of the
segments required for their selection could be calculated at the
object selection stage, this way providing additional information
for choosing a preferential segmentation scenario. Furthermore,
running the entire selection procedure for several segmentation
scenarios may further improve decision making, as it would be
based not only on a priory but also on a posteriori information.
Although this is always done at the cost of the algorithm
performance, as calculation of additional scenarios considerably
enhances the overall computational complexity of the algorithm,
this approach might nevertheless appear attractive when
considering implementation variants for highly parallel
hardware architectures that are common nowadays [12].
In the context of threshold based approaches, the latter
scenario is represented by multi-threshold processing. Various
applications of multi-threshold processing for image
segmentation have been considered in numerous papers, a brief
overview can be found for example in [13, 14]. Multi-threshold
segmentation is often based on the histogram properties of the
original image. In most cases, the last step is to select the optimal
threshold. The properties of the objects of interest and the results
of their selection are not taken into account.
Here we consider the a posteriori decision making concept
discussed above in the context of the multi-threshold image
processing problem, where the statistics required for the image
segmentation and object selection are first being calculated for a
series of test thresholds, and final decisions upon appropriate
segmentation and selection scenarios are based on the analysis
of these statistics for the entire set of the thresholds tested [15].
In the case of selecting a group of homogeneous objects, a
simple approach can be used, where the best global threshold
value is obtained from the maximum area occupied by objects
of a certain size or shape parameters, which is optimized among
the entire range of test thresholds [16]. For dissimilar objects, an
alternative approach is developed that involves the
reconstruction of a three-dimensional hierarchical structure of
objects based on multi-threshold processing using the
percolation effect [17]. This approach allows linking the
properties of an object cuts in neighboring binary layers and
build a hierarchical structure for subsequent segmentation [18].
The methodology under consideration contains easily
implementable computational operations, a small number of
adjustable parameters, while being efficient especially for highly
parallel hardware architectures. The goal is to estimate its
effectiveness in the detection and selection of compact objects
in noisy synthetic and observational images.
II.
SELECTION OF OBJECTS IN MULTI-THRESHOLD IMAGE
PROCESSING
To implement the above idea in a working algorithm, it is
essential to find appropriate quantities that could characterize
segmentation results in the context of the selection of the objects
of interest. Although such adjustments should be generally
based on the expected properties of the object of interest that
may vary considerably between different areas of application
thus being largely problem oriented, there are some universal
strategies that are expected to be applicable in a general context
with only minor problem-specific adjustments.
The very first requirement is that reasonable metrics should
be scalable, i.e., they should not depend on the image scale, at
least in the first approximation, not to mention inevitable
discreteness effects at the moment. Invariant geometric metrics
include the ratio of an object's perimeter squared to the area of
the object PS = P2/4πS. This feature characterizes the
compactness of the object [19]. The normalizing coefficient 4π
is introduced in order to provide a unity value of the coefficient
for the most compact planar object with given area, which is a
circle. Noise and background objects are usually characterized
by fractured edges, so their PS values significantly exceed one.
Objects of interest that have a compact shape have lower
coefficient values than noise induced segments, which makes it
possible to detect and select them from a noisy background.
Another geometric invariant is the coefficient of extension
of the main axis of the describing ellipse PL = πL2/4S also
normalized such that it is equal to one for a simple circle [20].
When using the PS and PL coefficients, the threshold level can
be set for each of the selected objects by the minimum value of
this coefficient in a certain binary layer. In this case, adaptive
local thresholds can be obtained. These methods can
significantly reduce the number of false alarms during detection
and use lower-level thresholds this way increasing the
probability of correct detection of the objects of interest.
III. THE HIERARCHICAL STRUCTURE ON THE BASIS OF
MULTITHRESHOLD PROCESSING TAKING INTO ACCOUNT THE
EFFECT OF PERCOLATION
To select a local threshold, one should first determine the
relationship between the individual layers, and establish whether
each pixel belongs to the same or to a new object observed in the
next binary layer above the previous one. Accordingly, one
needs to establish links between pixels with the same
coordinates in different binary layers. After the introduction of a
certain parameter that determines the specified relationship
between pixels in different layers, a three-dimensional
hierarchical structure can be formed on the basis of a single
binary object, obtained at a zero threshold value and occupying
the entire image area. To resolve the above problem, an
algorithm based on the percolation principle is further used [18].
The original grayscale image I(x, y) is being subjected to a
set of thresholds T resulting in a series of binary layers BT:
{BT = 1 if I(x, y) ≥ T; BT = 0 if I(x, y) < T}, in which a subset of
units represents objects of interest, while a subset of zeros refers
to the background. For the starting threshold T = 0, the
corresponding binary layer contains a single global isolated
object with an area of S0, occupying the full size of the image.
Now let the threshold T be increased by ∆T and a new binary
layer be created above the previous one satisfying I(x, y) > ∆T.
For small ∆T only a few pixels are being excluded from the
object, although its area ST < S0 is being consecutively reduced
at each step. Further enhancement of the threshold increases the
proportion of pixels outside of the single global object. At a
certain point these pixels merge together forming gaps in the
image. Finally, these gaps merge together resulting in the
decomposition of the single object and its separation into several
isolated fragments. This kind of phase transition event is known
as percolation [17]. After the destruction of the original object,
a set of fragments is formed in its place, each representing its
potential successor. In this case, one should decide whether there
is a successor to the original object at all, or whether the original
object is eliminated, and all appeared fragments should be
accounted as new objects. To do this, one requires a parameter
that characterizes the stability of each isolated object when the
threshold changes. This parameter is associated with the rate at
which the area of an isolated object decreases as the threshold
increases.
For each couple of consecutive layers, the object areas ratio
ST+∆T / ST characterizes the proportion of connected pixels that
remain inside the isolated object. Once an increasing number of
pixels fall out of the object each time the threshold is being
incremented by ∆T, leading to the new value T+k∆T, for the kth layer, the fraction of pixels remaining within the object
Kp = ST+∆T / ST can be considered as a characteristic of the
expected persistency (stability of the area) for the object as the
threshold increases. As long as the ratio Kp is equal to or more
than 1/2, the object in the upper layer can be considered as the
unambiguous successor of the object in the lower layer, which
turns out to be its only predecessor or base object. If the base
object is precisely divided in two halves, both fragments, minus
the pixels that form the gap, are smaller in area than ST/2, and
thus two new objects appear.
25
5
30
25
20
10
20
15
15
15
10
20
10
5
0
40
25
5
30
40
30
30
20
10
15
20
25
20
10
0
5
10
30
0
b
Npix
a
0
As a result of this approach, a three-dimensional hierarchical
structure is formed, containing all the selected objects, in which
each pixel no longer belongs to one binary layer, but can
correspond to several binary layers k = 0, ... , K in the structure.
Based on this construction, it is possible to generalize image
segmentation and selection of objects. To do this, restrictions are
introduced on the area of the selected objects and other
geometric features that characterize its compactness and shape.
For each selected object that passes through multiple binary
layers in a three-dimensional representation, the optimal Topt
threshold corresponding to the layer with its best cut can be
selected by various geometric or textural criteria. Particular
examples of selection quantities are the areas or the ranges of
areas of selected objects as well as the invariant geometric
coefficients PS and PL discussed above.
An example in Fig. 1 explains the above. The image is being
binarized by a discrete threshold. The original object at
T = 0 slowly loses its area with increasing threshold (Fig. 1c). Its
persistence coefficient Kp is more than one half and the object is
fragmented into two parts at the threshold T1 = 17 (Fig. 1d).
Then the first of the two objects disappears after its percolation
threshold Tc1 = 21. Its percolation coefficient is very small; it is
less than 0.01. The second object has a slightly higher
percolation coefficient, equal to 0.12.
IV.
1
2
T
c
1
1
0.9
5
OBJECT SELECTION USING ADAPTIVE GLOBAL
THRESHOLD
The simplest selection is based on the area of objects. In
some cases, there is a priori information about the typical size or
area of objects. Too small objects should be removed from
consideration, which significantly reduces the computational
complexity of the algorithms. Thus, the minimum area Smin of
the object of interest is one of the algorithm parameters.
0.9
5
0.8
10
0.7
0.8
10
0.7
0.6
15
0.6
15
0.5
0.4
20
0.5
0.4
20
0.3
25
0.3
25
0.2
0.1
30
0.2
0.1
30
0
5
10
15
20
d
25
30
0
5
10
15
20
25
30
e
Figure 1. Example of two Gaussian objects (a,b) and the percolation effect:
c – reducing areas in pixels for two objects with increasing threshold: total area
– dashed line; (d,e) – binary slices at the moment of percolation at threshold
T = 17
Let the object first appear as a result of percolation of a larger
object at threshold T and occupy the area ST that we later denote
as its base area. With increasing T, the area of the object
monotonously decays until either the object disappears entirely
indicated by ST+(K+1)∆T = 0 or the object disintegrates indicated
by ST+(K+1)∆T / ST+K∆T < Kp. The change in area over the
lifetime of an object ST+K·∆T / ST can be considered as its
percolation coefficient PC. The value of the threshold level TK
is considered the percolation threshold Tc for this object.
The simulation results are shown in Fig. 2 which contains 49
squared objects of 16×16 pixels with standard Gaussian noise
background (Fig. 2a). The signal-to-noise ratio (relative
expectation shift or deflection) in each pixel is d = 1.163. The
dependence of the total number of connected objects on the
threshold value is shown in Fig. 2b. When selecting objects by
area with Kp = 0.75, acceptable distortion of object boundaries
is achieved at the threshold value T = 133 (Fig. 2c).
At lower threshold values, the shape of objects is distorted
by fractal noise, which significantly fragments the boundaries.
A simple detector with a Neumann-Pearson threshold gives a
false alarm probability F = 0.01 in each pixel, as shown in
Fig. 2d, but the probability of detection is only D = 0.12, so the
objects are highly fragmented and none of them retain its
squared shape. The corresponding detection characteristic is
shown by the right curve in Fig. 4, where x-axis contains the
signal-to-noise ratio (deflection). Widely used Otsu detector
gives too many false alarms as it is shown in Fig. 2e.
selection, such a threshold will give a significantly greater
probability of false alarm (0.32) (that is shown in Fig. 4, 2).
Detection curve for every pixel in the case of object selection
goes between these two as it is shown in Fig. 4, 3. Results are
obtained by simulation so y-axis presents estimate of detection
probability. The threshold deflection now is equal to 0.5
providing a gain in signal-to-noise ratio about 6 dB. If there is
information about the shape of signal area, the characteristic can
be improved using accumulation.
50
Nobj
100
150
200
250
50
100
150
200
T
250
a
b
T = 133 Object number i= 2870 LENGTH = 180
200
50
150
150
100
200
50
1
lg10 F
100
2
3
5
250
100
150
200
250
c
Smin
Otsu Threshold
50
50
100
100
150
150
200
200
Figure 3. Dependence of the threshold exceeding degree for noise
(logarithm of false alarms probability) upon the area Smin. Curves 1 to 5
correspond to rising threshold levels T = 150, 155, 160, 165, 170, respectively.
2
100
d
150
200
250
50
100
150
200
250
e
Figure 2. Detection of square objects in noise: a – test image; b – dependence
of number of selected objects on threshold value; c – percolation-based adaptive
multi-threshold selection; d – Neymann-Pearson detector; e – Otsu detector.
The brightness scale in Fig. 2c shows the value of the object area.
The probability of false alarm depends on the minimal area
Smin of the detected objects (x-axis), as shown in Fig. 3 in
logarithmic scale. The curves are obtained by simulation. For a
given threshold and for each area Smin (which is laid in pixels
along the horizontal axis), the amount of noise exceedances has
been calculated and normalized to the field size. The y-axis is
the decimal logarithm of this normalized value which
corresponds to the estimated degree of false alarm probability.
Curves 1 to 5 correspond to the rising threshold levels T = 150,
155, 160, 165, 170, respectively.
The consequence of selection and removal of small objects
is the ability to reduce the threshold level while maintaining low
false alarm probability when useful objects are detected. The
larger the area of noise objects to be removed, the lower the
detection threshold can be set at the same probability of false
alarm. For Smin = 150 in this task it gives normalized threshold
tNP = 0.47 instead of 2.326 (see Fig. 4, 1). It is clear that without
D
250
250
50
4
0
50
3
1
S/N
Figure 4. Detection characteristics for object selection by area for Smin=150.
The x-axis contains signal-to-noise ratio (deflection). 1 - Curve on the right –
Neymann-Pearson (NP) detector with high threshold; curve on the left – NP
detector with low threshold; curve in the middle – detector for low threshold
with object selection
It is worth noting that the adaptation of the threshold level to
the maximum of the selected objects makes sense in those
situations when the scene contains a sufficient number of them.
In addition, this method gives a slightly lower value of the
threshold level. These shortcomings can be eliminated by the use
of geometric invariants [19].
V. OBJECT SELECTION USING ADAPTIVE LOCAL
THRESHOLD BASED ON GEOMETRIC CRITERIA
Consider first binarization of a white noise field with
restriction Smin=10 which can substantially reduce the number
of isolated objects after binarization. The dependence of object
number Nobj upon threshold value T is shown in Fig. 5, a, curve
1, where the maximum number of objects is 500. The bottom
curve 2 presents the dependence of maximum (over all objects
in the given slice) perimeter elongation coefficient PSmax upon
the threshold value. Obviously this coefficient reaches big
values (here about 90) for noisy objects with fractal structures.
Area preselection reduces the probability of noise emissions as
shown in Fig. 5b (left bottom curve) compared to simple
binarization (right bottom curve), while it has virtually no effect
on the values of the perimeter elongation coefficient PS for the
remaining objects.
F
Nobj ; Psmax
1
2
2
VI.
PRACTICAL EXAMPLES OF PROCESSING WITH REMOTE
OBSERVATION
Let us consider an observational remote sensing image
shown in Fig. 7a. The task is to select and localize compact
objects (e.g., buildings) in this scene. The proposed method is
next applied with Smin = 150 and PSmax = 50. The selection
results are presented in Fig. 7b where brightness corresponds to
the threshold values. Image contains 82 objects which are
selected by the use of local adaptive threshold for every object.
Corresponding dependence of threshold values is shown in Fig.
8a where x-axis contains numbers of isolated objects. Adaptive
local threshold is set for every object by the use of optimization
process. Typical U-shaped optimization curve is presented in
Fig.8b.
1
T
50
T
100
a
b
150
Figure 5. Results of Gaussian noise processing: a – number of selected objects
Nobj (1) and maximum perimeter elongation coefficient PSmax (2) after area
selection with Smin = 10; b – probabilities of noise emissions for simple
binarization (1) and after preselection by area with Smin = 10 (2).
200
250
50
100
It is interesting to investigate the influence of limitations on
the coefficient PS. Obviously restriction on maximum value for
PS results in additional removing of noise objects which have
too large elongation coefficients. It seems these objects have
fractal structures and do not represent the objects of interest. The
value PSmax is the second important parameter for adaptive
object selection. Algorithm removes objects with PS > PSmax.
150
200
250
300
350
400
450
500
lg10 F
a
b
Figure 7. Object selection in a television image with with Smin = 150 and
PSmax = 50. Brightness corresponds to the adaptive threshold values.
As it can be shown from analysis limitations on perimeter
elongation coefficient PS can decrease the false alarm
probability in the detection task. It may result in more efficient
detection of objects corresponding to the PS and the gain is
dependent on this value which in turn depends on the threshold.
So the gain substantially depends on the object shape. As a
result, the curves get a dip at low threshold values (see Fig. 6).
Topt
Figure 6. The dependence of logarithm for rate of exceedances
(false alarm rate) upon normalizing threshold for Smin = 10 and PSmax = 1000,
300, 100, 10, 3 (from top to the bottom)
Ps
tNP
nobj
a
T
b
Figure 8. The dependence of adaptive threshold values on the object number
(a) and typical U-shaped optimization curve (b).
VII. CONCLUSIONS
To summarize, a recently proposed algorithm for the
adaptive selection of compact and prolonged objects based on
images of remote observations has been investigated. Based on
the results of the initial multi-threshold processing of the raw
image, the algorithm effectively selects isolated objects in each
of the binary layers. Next by considering a series of binary layers
one containing the object's best representation in terms of the
applied geometric criterion is being selected. The key idea of the
algorithm is that the decision bases on a posteriori information
about the properties of objects that can be selected from each
binary layer, and finding the best layer in terms of the properties
of these objects. The quantitative analysis performed here
indicated that by using this information, one can successfully
implement the adaptive selection, while preserving the shape of
each object of interest, despite the presence of non-stationary
background. In a considered test detection problem, the use of
selection results provides with benefit that is equivalent to
approx. 6 dB gain in the signal-to-noise ratio.
The effectiveness of the algorithm is supported by both
computer simulations and analysis of empirical observational
imagery obtained from the remote observation applications. We
believe that other relevant examples from remote observation
problems could be resolved using similar strategy. Moreover, in
addition to direct benefits from using a posteriori information
from the initial multi-threshold processing, the proposed
approach also leads to a generalized hierarchical object
reconstruction that in turn generalizes segmentation and
selection problems in comparison with the conventional image
analysis.
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
VIII. ACKNOWLEDMENT
We would like to thank the Russian Science Foundation
(project No. 16-19-00172) for the financial support of this work.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
G. Cheng, J Han, “A survey on object detection in optical remote sensing
images,” ISPRS Journal of Photogrammetry and Remote Sensing, vol.
117, pp. 11–28, 2016
E. Arias-Castro, G. R. Grimmett, “Cluster detection in networks using
percolation,” Bernoulli, vol. 19(2), pp. 676–719, 2013
G. P. Patil, C. Taillie, “Upper level set scan statistic for detecting
arbitrarily shaped hotspots. Environmental and Ecological
Statistics,” vol. 11, pp. 183–197, 2004
W. Zhou, A. Troy, “An Object-Oriented Approach for Analyzing and
Characterizing Urban Landscape at the Parcel Level,” International
Journal of Remote Sensing, vol. 29(11), pp. 3119–3135, 2008
H. Gu, Y. Han, Y. Yang, H. Li, Z. Liu, U. Soergel, T. Blaschke, S. Cui,
“An efficient parallel multi-scale segmentation method for remote sensing
imagery,” Remote Sensing, vol. 10(4), pp.590–608, 2018
A. Kashanipour, N. Milani, H. Eghrary, "Robust Classification Using
Fuzzy Rule-Based Particle Swarm Optimization," IEEE Congress on
Image and Signal Processing, vol. 2, pp. 110–114, 2008
L. Barghout, J. Sheynin, "Real-world scene perception and perceptual
organization: Lessons from Computer Vision," Journal of Vision, vol. 13
(9), pp. 709, 2013
A. Anjos, H. Shahbazkia, "Bi-Level Image Thresholding – A Fast
Method, " Biosignals, vol. 2, pp. 70-76, 2008
[19]
[20]
M. Hossein, R. Shankar, Y. Allen S. Sastry, Y. Ma, "Segmentation of
Natural Images by Texture and Boundary Compression," International
Journal of Computer Vision, vol. 95, pp. 86–98, 2011
R. Kimmel, A.M. Bruckstein, "Fast Edge Integration," International
Journal of Computer Vision, vol. 53(3), pp. 225–243, 2003
K. J. Batenburg, J. Sijbers, "Optimal Threshold Selection for Tomogram
Segmentation by Projection Distance Minimization," IEEE Transactions
on Medical Imaging, vol. 28 (5), pp. 676–686, 2009
D. Bogayevskiy, S. Ezhov, D. Kaplun, D. Minenko, S. Aryashev, K.
Petrov, “Study of Vector Processor Architectures for Image Processing
Using Model Profiling, ”, Proceedings of the 8th Mediterranean
Conference on Embedded Computing, pp. 8760039, 2019
B. D. Shivahare, S. K. Gupta, “Multilevel Thresholding based Image
Segmentation using Whale Optimization Algorithm,” International
Journal of Innovative Technology and Exploring Engineering (IJITEE),
vol. 8, Issue-12, October 2019
E. Cuevas, A. González, F. Fausto, D. Zaldívar, M. Pérez-Cisneros,
“Multithreshold Segmentation by Using an Algorithm Based on the
Behavior of Locust Swarms,” Mathematical Problems in Engineering,
Article ID 805357, 2015
V. Volkov, “Extraction of extended small-scale objects in digital images.
Int. Arch. Photogramm. Remote Sens. Spatial Inf. Sci., vol. XL-5/ W6,
pp. 87–93, 2015. https://doi.org/10.5194/isprsarchives-XL-5-W6-872015
M. Bogachev, V. Volkov, O. Markelov, E. Trizna, D. Baydamshina, V.
Melnikov, R. Murtazina, P. Zelenikhin, I. Sharafutdinov, A. Kayumov,
“Fast and simple tool for the quantification of biofilm-embedded cells
sub-populations from fluorescent microscopic images,” PLoS One, vol.
13, Iss. 3, p. e0192022, 2018
M. Langovoy, O. Wittich, “Randomized algorithms for statistical image
analysis and site percolation on square lattices,” Statistica Neerlandica,
vol. 67, pp. 337–353, 2013. doi:10.1111/stan.12010
V. Yu. Volkov, M. I. Bogachev, A. R. Kayumov, “Object Selection in
Computer Vision:from Multi-Thresholding to Percolation Based Scene
Representation,” in: Computer Vision in Advanced Control Systems-5,
Intelligent Systems Reference Library, Springer, pp. 161-194, 2019.
https://www.springer.com/gp/book/9783030337940
MI Bogachev, VY Volkov, G Kolaev, L Chernova, I Vishnyakov, Airat
Kayumov, “Selection and quantification of objects in microscopic
images: from multi-criteria to multi-threshold analysis,” Bionanoscience,
vol. 9(1), pp. 59-65
V. Melnikov, M. I. Bogachev, V. Y. Volkov, O.A. Markelov, “Selection
and Analysis of Objects in Multi-Threshold Image Processing,”
Proceedings of the IEEE Conference of Russian Young Researchers in
Electrical and Electronic Engineering, pp. 1202-1205, 2019