Compact Objects Detection in Noisy 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 aim of the work is to investigate an adaptive
algorithm for detection and selection of isolated compact objects
by their area and shape. For the analysis, monochrome images
inherent in remote sensing systems were considered. Adaptive
multi-threshold approach is based on the formation of a set of
binary slices that are used for morphological processing by
selecting objects, analyzing their geometric characteristics and
subsequent threshold setting for decision making. The use of
selection results to solve problems of distinguishing and
recognizing objects of interest by shape is very promising,
therefore, 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 noise. The properties of the decisive statistics, the
influence of the algorithm parameters on their characteristics are
considered and the detection characteristics are calculated. Also,
the effectiveness of the algorithm is tested on a real image
containing compact objects of interest. In addition to remote
observation systems, the algorithm can be used to isolate bacteria
and spores on biological sections, to detect heterogeneities in
materials and tissues.
Keywords- multi-threshold image segmentation; object detection,
selection and distinction; percolation
I.
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 Bradley-Roth
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.
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
Firstly, the size of the object is often unknown, and secondly,
the accumulation destroys the boundaries of the object, which
are quite informative.
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 (BradleyRoth), 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 signalto-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 an effective 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.
output image for all selected objects (left) and extracted disk by
the use of maximum threshold value (right).
Figure 3. Reducing the probability of a false alarm lgF with threshold T
when removing small objects with S<Smin after selection by area
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.
Figure 5. Distribution of the compactness coefficient PS over objects
in pure noise (LN – lognormal approximation)
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. It is fairly well approximated by a
lognormal distribution with equivalent mathematical
expectation and variance, while the ratio of the mean to the
median is approximately 1.5. When a useful object appears, this
distribution becomes wider. The informative parameter is the
minimum value of PS, which is associated with the threshold.
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.
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 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 contains
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
Figure 7. All extracted objects with d = 10 (left) and extracted disk by the
use of maximum threshold value (right)
preserved, which is important in the tasks of distinguishing
compact objects by shape.
problem of detecting an object in the form of a disk against a
background 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 FOR 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. Statistics of the maximum value
of the optimal threshold were used for selection. These statistics,
as well as the values of the compactness coefficient, make it
possible to distinguish objects by shape. 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). Color scale corresponds to test statistics values
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). Color scale corresponds to test statistics values
IV.
[7]
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. The
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