Detection and Selection of Compact
Objects in Images
Vladimir Yu. Volkov
Dept. Radioengineering
Saint-Petersburg State Electrotechnical University (LETI);
Saint-Petersburg State University of Aerospace Instrumentation (SUAI)
Saint-Petersburg, Russia
vl_volk@mail.ru
Abstract—The adaptive algorithm of detection and selection of
isolated compact objects on monochrome images in remote
sensing systems is investigated. To characterize compactness, the
ratio of the object perimeter squared to its area is used. Selection
of objects by area and shape is performed on binary slices in the
process of multi-threshold processing, which allows you to set a
detection threshold for each object, ensuring its best
representation. The parameters of the algorithm, the properties
of the decisive statistics are considered and detection
characteristics for an object in the form of a disk under the
action of Gaussian noise are obtained. The effectiveness of the
algorithm is tested on a real image containing compact objects.
The algorithm can also be used to isolate bacteria and spores on
biological slices, to detect inhomogeneity in materials and tissues.
Keywords- multi-threshold image segmentation;
detection; selection and distinction; percolation
I.
object
INTRODUCTION
The problems of detection, extraction and localization of
the objects of interest in noisy images are relevant in the
analysis of images obtained by various remote sensing systems
and thus are being intensively studied in the last decades [1–6].
The main differences between objects and noise structures are
the connectivity of the object's points, the isolation of objects
from each other, and the contrast of intensities. In fact, the
segmentation problem is solved, i.e. the separation of the
original image into regions. Threshold segmentation is most
often used, and thresholds can be global or local.
Theoretical threshold values for a given optimality criterion
can only be used with known statistics of objects and
background. In practical tasks, such information is not
available, so the adaptation of threshold levels is used. The
well-known Otsu algorithm uses an adaptive global threshold.
Among the algorithms that form local thresholds, the BradleyRoth algorithm stands out. These algorithms use the original
image to form thresholds, and do not take into account the
properties of objects of interest and the results of segmentation
in any way. Many objects of interest are characterized by
compactness, which can be quantified and used to improve the
quality of detection and selection. Also an important parameter
is the area of objects. A range of values is usually set for this
parameter.
Various variants of multi-threshold processing are based on
the properties of the histogram of the original image [7,8], and
as a rule do not take into account the properties of objects of
interest and the results of their selection. For heterogeneous
objects, an approach is investigated in [6], which involves the
construction of a three-dimensional hierarchical structure of
objects based on multi-threshold processing using the
percolation effect. This method allows you to link the
properties of sections of an object in neighboring binary layers
and build a hierarchical structure for subsequent segmentation.
Considering the prospects of using the selection results to
solve the problems of distinguishing and recognizing objects of
interest by shape, an important task is to evaluate the
effectiveness of the algorithm under the action of noise. This
article investigates the problem of detecting a compact object
in the form of a disk against a background of noise. The
properties of the decisive statistics, the influence of the
algorithm parameters is considered and the detection
characteristics are calculated. Also, the effectiveness of the
algorithm is tested on a real image containing compact objects
of interest.
II.
MULTI-THRESHOLD OBJECT SELECTION ALGORITHM
A. Multi-threshold Object Selection Approach and
Parameters of the Algorithm
The detection and selection of compact objects taking into
account the restrictions on the area and the compactness
coefficient are considered in [6]. The investigated multithreshold selection algorithm uses as a useful feature the
2
coefficient of perimeter elongation of the object PS = P /4πS,
where P is the perimeter of the object, S is its area [9]. This
characteristic is a geometric invariant and it has a minimum
theoretical value equal to one for a disk-shaped object.
However, measured on noisy images, this coefficient can
significantly increase even for a compact object due to the
appearance of fractal noise structures at its borders, which
dramatically increase the perimeter of the object. This
significantly affects the quality of selection, especially with
small signal-to-noise ratios. Therefore, a detailed analysis of
the characteristics of this method is necessary, which is given
in this article.
The multi-threshold algorithm proposed and investigated in
[6] builds a three-dimensional hierarchical structure of objects
based on a set of binary intensity slices obtained with
increasing threshold values. In this structure, the object of
interest can be located on several binary layers, depending on
its intensity and texture. This state of the object is determined
by the rate of decrease of its area KS = ST+∆T / ST with an
increase in the threshold from value T to T+∆T. This
coefficient depends on the threshold value T and reflects the
properties of the object. If an object quickly loses its area or
breaks into small fragments, then KS is small, and vice versa,
values of KS close to unity indicate a large steepness of the
boundaries and stability of the area.
The limitation of this coefficient affects the number of new
objects that appear in the place of the original one when its
fragmentation increases with an increase in the threshold. An
unambiguous determination of the successor of the original
object on the next layer is possible if this coefficient is greater
than 0.5. Thus, one of the parameters of the algorithm is the
boundary coefficient of object area stability KP. If for a certain
threshold value (percolation threshold) it turns out that
KS < KP, then the original object is considered “dead”, and new
objects are formed from its fragments. When KP is increased to
one, this inequality is always satisfied, and new objects are
created on each layer from fragments of the object on the
previous layer.
Thus, one of the parameters of the algorithm is the
boundary stability coefficient of the area KP. Two more
parameters of the algorithm are related to the selection of
objects by the minimum area Smin and by the compactness
coefficient PSmax, which limits the PS value of selected objects
(see Table 1).
B. Detection of Object with Disk Shape
For certainty and clarification of the influence of the shape
of the object on the detection characteristics, consider an object
in the form of a disk that appears in Gaussian noise. In the
pixels occupied by the object, there is a (positive) shift in the
mathematical expectation of the distribution. The signal-tonoise ratio is defined as a shift related to the RMS value of the
noise. Fig. 1 shows the input and output images for the optimal
shift detection in every pixel according to the Neyman-Pearson
criterion with a false alarm probability F = 0.01 and with a
signal-to-noise ratio d = 2.326. There are two reasons why it is
undesirable to use the accumulation of pixels within the object
boundaries to increase the signal-to-noise ratio. Firstly, the size
of the object is often unknown, and secondly, the accumulation
destroys the boundaries of the object, which are quite
informative.
TABLE I.
№
1
2
3
ALGORITHM PARAMETERS
Name
Boundary coefficient of
object area stability
Minimum area of selected
objects
Maximum value of perimeter
elongation of the object
Symbol
Restrictions
KP
KS ≥ KP
0.5≤ KP ≤1
Smin
S ≥ Smin
PSmax
PS ≤ PSmax
PSmax ≥ 1
Figure 1. Input and output images with Neyman-Pearson threshold
binarization
If you remove small objects in the right image of Fig.1 and
use a fill, then it is possible to restore the shape of the object
quite accurately. However, with an unknown background level,
there is a problem with setting the optimal threshold level.
When the signal-to-noise ratio decreases, the ability to restore
the shape of the object disappears due to fragmentation.
When using detection algorithms with an adaptive
threshold, you will have to face some problems and losses in
the quality of detection. In the case of Otsu threshold, it is
impossible to control the level of false alarms. With small
signal-to-noise ratios, there are problems with highlighting the
shape of the object. In the case of a local adaptive mean
threshold (Bradley-Roth), the problem of suppressing the
background and highlighting the shape of the object remains.
This is illustrated in Fig. 2, which shows the result of
segmentation with a signal-to-noise ratio of d = 2.326.
Figure 2. Results of Otsu binarization (left) and Bradley-Roth
thresholding (right)
C. Object Selection by Area and Compactness
Object selection is a powerful means of improving the
efficiency of algorithms. Fig. 3 shows the dependences of the
probability of a false alarm F on the threshold level T in the
case of removing objects with an area smaller than Smin from
the output binary image. In this case, it is possible to gain in the
probability of correct detection of the object by reducing the
threshold level. A similar effect of reducing the probability of a
false alarm F is observed in the case of selection of objects by
compactness. Fig. 4 shows the effect of joint selection of
objects by area and compactness at PSmax = 10. Thus, the
selection allows you to significantly clear the output image
from the remnants of the background.
contains output image for all selected objects (left) and
extracted disk by the use of maximum threshold value (right).
Figure 5. Distribution of the compactness coefficient PS over objects
in pure noise (LN – lognormal approximation)
Figure 3. Reducing the probability of a false alarm lgF with threshold T
when removing small objects with S<Smin after selection by area
Figure 6. Distributions of optimal threshold values Topt over objects Nobj in
pure noise (left) and for disk in noise with d = 10 (right)
Figure 4. Reducing the probability of a false alarm lgF with threshold T
when removing objects with PS>PSmax after selection by compactness
D. Crucial statistics and detection efficiency
Multi-threshold algorithm determines the best binarization
threshold for each object which corresponds to the minimum
value of the compactness coefficient PS. In the case of pure
noise, the selected objects have different compactness
coefficients, the distribution of which over the objects is shown
in Fig. 5 for KP = 0.5. For compact objects, the algorithm finds
this minimum at high threshold values, and for background
objects – at lower values. The calculated threshold values are
used to detect and distinguish compact objects among the
background ones.
The algorithm generates a collection of objects that are
indexed by their thresholds, as shown in Fig. 6 (left). The
object of interest can be selected separately by selecting the
maximum threshold value (in the right image of Fig. 6). Fig. 7
Figure 7. All extracted objects with d = 10 (left) and extracted disk by the
use of maximum threshold value (right)
Detection characteristics were obtained by modelling with
number of iterations M = 50 and are presented in Fig.8.
Selection parameters KP, Smin and PS were chosen so as to
obtain false alarm probability less than F = 0.01 (see Fig. 4).
Dashed line corresponds to Neyman-Pearson detector for the
same false alarm probability which is calculated by the
formulas DT = Φ(d − t NP ) , where tNP = 2.326 is the threshold
for F = 0.01, using the probability integral Φ in the Laplace
form. As follows from the analysis, the multi-threshold
selection algorithm provides some gain in the quality of
detection of compact objects in relation to known procedures.
The algorithm has three parameters for controlling the
process, which are easily understood physically. It is
insensitive to changes in the image scale, if you do not take
into account the selection by area. The shape of the object of
interest is also preserved, which is important in the tasks of
distinguishing compact objects by shape.
The problem of detecting an object in the form of a disk against
a background of noise is considered.
1
DT
Ddisk
0.9
0.8
0.7
D
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
d
Figure 8. Detection probability D depending on signal-to-noise ratio d for
disk in noise with Smin = 50; PSmax = 10; and false alarm probability F < 0.01
III.
MULTI-THRESHOLD PROCESSING FOE REAL IMAGES
Two examples (Fig. 9 and Fig. 10) illustrate the
effectiveness of using the compactness coefficient PS to
distinguish objects by shape in remote sensing images. Each
isolated object is selected separately, and can be localized and
measured.
Figure 10. Real image with objects (top) and result of object selection
(bottom)
It is established that higher detection thresholds are
obtained for compact objects than for background objects,
which makes it possible to use these statistics for detection.
Comparative characteristics of detecting an object in the form
of a disk against a background of noise are obtained. The
effectiveness of the algorithm has been tested on real images
containing compact objects of interest.
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Figure 9. Real image with compact objects (top) and result of object
selection (bottom)
IV.
CONCLUSIONS
The problem of detection and selection of compact objects
on monochrome images generated by remote surveillance
systems is considered. An adaptive multi-threshold algorithm
with selection of objects by area and by the coefficient of
perimeter elongation was chosen for the study. The influence
of the algorithm parameters on the properties of the decisive
statistics and on the detection characteristics is investigated.
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