Segmentation of Images Used in Unmanned Aerial Vehicles Navigation Systems

. The paper presents the results of the study of a two-stage procedure for selecting a reference object in the current image formed by a correlation-extreme system used for autonomous navigation of unmanned aerial vehicles. The aim of this paper is to theoretically evaluate the probability of selecting low-dimensional low-contrast objects in the segmented current image according to the proposed two-stage procedure. To achieve this goal, the problem of segmentation of images of the sighting surface and subsequent selection of the reference object in the presence of heterogeneous objects differing in brightness and area characteristics is solved. The most significant result is the justification of application of two-stage procedure of selection of the reference object in the current image by brightness and area parameters using the set thresholds. The significance of the obtained results consists in establishing the dependence of the probability of correct selection of the reference object on the noise level of the current images. It is shown that the probability of correct selection of the object in the image is a function of the threshold value and can be maximised by choosing its value. This approach allows to consider the influence of various factors leading to image noise on the quality of images formed by the navigation system. It is shown that when noise distorts more than 31% of the image pixels, the proposed two-stage procedure allows to ensure the selection of the reference object in the image with a probability not lower than 0.9.


INTRODUCTION
Unmanned aerial vehicles (UAVs) are used for monitoring hard-to-reach surface areas at a considerable distance.They are extensively used in the military search and rescue operations, in assessing the degree of destruction of various objects on land and water.Therefore, it is necessary to further improve navigation systems, the functioning of which is based on the extraction of information about the objects of sighting in various conditions.These tasks are most effectively solved by UAVs equipped with correlation-extreme navigation systems (CENS).The functioning of these systems is based on the comparison of two-dimensional images formed by different sensors depending on the physical nature of the signals with the reference images (RI) prepared in advance and stored in the memory of the onboard computer [1].In these systems, the review-comparative method of forming the solving function is implemented.It characterizes the degree of deviation of the true location of the navigation object from the specified one [1,2].CENS functioning is mainly determined not by the type of signals used, but by the quality of information support based on the processing of informative features of sighting objects [1,3,4].Low quality of information support is the reason of discrepancy between the current images (CI) formed during monitoring and preformed reference images [1,2].The information support depends on the conditions of image acquisition, especially identical conditions of obtaining the initial information during the formation of reference and current images, the presence in some cases of many heterogeneous and similar objects [2,4].The consequence of the mismatch of the compared images is a decrease in the accuracy characteristics of the navigation system, which necessitates the elimination of possible mismatch.A possible direction of eliminating such inconsistency is to reduce the influence factors both at the stage of CI formation and development of the algorithms of primary and secondary processing of CENS [1,5].In addition, the principles of CI formation onboard the UAV should be like the principles of RI formation.Considering the time constraints caused by the UAV flight speed and geometrical conditions of sighting (low altitude), the process of CI formation and its comparison with RI should be operative.This circumstance requires consideration of computational and time costs and imposes restrictions on the use of appropriate stable information features (invariants) about the objects of the sighting surface (SS) [1,2].Considering these factors necessitate further development of image segmentation methods for selection of navigation landmarks on CI as applied to CENS.A considerable number of publications are devoted to the development of methods and algorithms of image formation and processing based on various segmentation methods and algorithms.However, these publications do not consider the mentioned peculiarities of the construction and functioning of CENS used on UAVs, as well as the characteristics and peculiarities of the description of SS objects depending on the type of the geophysical field used to obtain the initial information about the objects [1].Therefore, the task of sighting surface image segmentation and selection of the reference object in the images formed and used in CENS in the presence of many heterogeneous objects that differ in brightness and area characteristics is important and requires the search for new solutions.Mhangara P., Odindi J. ( 2013) proposed to use texture information to identify objects of interest.The essence of the method is to apply spectral features and object-oriented texture features of Haralick for thematic segmentation and classification of urban land use.The disadvantage of the method is certain difficulties in recognising spectra between several types of objects.

I. PUBLISHED LITERATURE ANALYSIS
Körting T. S., Fonseca L. M. G., Dutra L. V., Silva F. C. (2010) proposed a re-segmentation method.Its essence is to use a preliminary already over-segmented image as a source image to obtain a new set of objects of interest.The disadvantage of the method is the possible variant of non-fused objects for further analysis.
Dikmen M., Halici U. (2014) developed a two-stage re-segmentation method.The advantage of the method is the post-processing of the image to eliminate some false object segments, and the disadvantage is the presence of some error in assigning shadow segments to the object.
Pandey S. & Khanna P. (2014) They proposed a hierarchical approach to semantic clustering of images.The disadvantage of the approach is the loss of information that a representative image denotes any other image belonging to a cluster.To automatically obtain the total number of clusters, this loss of information is tracked, which is an advantage.
Dhanachandra N., Manglem K., Chanu Y.J. (2015) proposed the image segmentation using subtractive clustering.The advantage of the method is to apply a median filter after k-means algorithm to the resulting image to remove the "unwanted" region in the given image.The disadvantage of the approach is the presence of many "unwanted" regions after subtractive clustering.
To eliminate the drawback regarding the dependence of clustering results on the initial selection of cluster centres, Dao N., Anh D. N. (2015) developed unsupervised segmentation method by incremental clustering.The computational complexity of the approach is compensated by the unnecessary determination of the initial number of clusters and the avoidance of re-clustering the whole image when the number of clusters increases.
Niharika K., Adeeba H., Krishna A. S. R., Yugander P. (2017) proposed an image segmentation method based on k-means and Otsu thresholding clustering methods.The use of the median filter allowed obtain good results of image segmentation with available speckle noise, but only for radar images of the radar.
For segmenting colour images, Zheng X., Lei Q., Yao R., et.al. ( 2018) developed an adaptive k-means clustering method without prior introduction of the number of clusters.This method features reduced light influence on segmentation results, segmentation of colour images of different colour representation models and adaptive selection of the number of clusters.The disadvantages are the impossibility of universal clustering of tone and colour images, as well as the need to represent colour images in the LAB colour model.
Shah N., Patel D., Fränti P. (2021) performed image segmentation by k-means algorithm using Mumford-Shah model.When using k-means algorithm for colour quantization in colour models of image representation, pixels are grouped into clusters only in colour space.The method allows optimising both the shape of segments and their content.
Abeysinghe W., Wong M., Hung C.-C., Bechikh S. (2019) proposed a multi-objective evolutionary clustering algorithm to find optimal cluster centres.The efficiency of the algorithm depends on the choice of the target function, i.e., maximising the inter-cluster distance or minimising the intra-class compactness.The advantage is the generation of a set of "nondominated" solutions no longer under consideration during the algorithm.The disadvantage of the algorithm is the dependence of its efficiency on the choice of the target function.
The results of analysing the segmentation methods of the most closely represented images in CENS in compressed form are shown in Table 1.

Table 1. Analysis of segmentation methods. Name Advantages Disadvantages
The k-means method The segmentation process takes place without prior training.Easy to implement.
Additional processing of the obtained homogeneous areas is required.

Method of emphasising boundaries
The result of segmentation is similar to the results of segmentation by an expert.Easy to implement.High speed performance.
Sensitivity to noise.Difficulty in working with low-contrast images.Additional processing of the results is required.

Break and merge method
Utilises information about the spatial characteristics of points in the image.Excellent results on images with few homogeneous areas.
Sensitivity to the effects of noise.Difficulty in determining unambiguous signs of homogeneous areas.

Segmentation method based on physical properties of objects
Excellent results when the correct object model is selected.Resistant to noise and image defects.

Complexity of segmentation algorithms.
Requires initial information about the shape of objects.

Graph theory method
Fast segmentation algorithms are used.
Local point features are more important than global area features.Difficulty in determining weights of graph nodes and branches.
Thus, the analysis has shown that although there are a significant number of image segmentation techniques, they have limited application depending on the specific task and cannot be directly applied in CENS.

METHODS, RESULTS AND DISCUSSION
In accordance with the approaches adopted in [1 -5], the decision function formed by CENS at a point in time t by comparing the current and reference images is of the form: where SP F is an image comparison operator;  The RI is also described by a matrix of brightness values of corresponding pixels: , where , ML are dimensions of RI.
Model (1) does not explicitly consider the influence of various factors on the formation and processing of CI.Such factors as daily, seasonal, and meteorological conditions, the use of masking materials on objects, object saturation, attenuation of signals on the propagation path from the object to the receiving device (for passive systems), additive noise of the sensor of received signals, interpixel, perspective and scale distortions [4].Depending on the type of sensor, its operating frequency, the influence of several factors may have different significance.To a lesser extent it concerns radar, relief and radiometric sensors, as they operate in the long-wave part of the millimeter and short-wave part of the centimeter range.But on sensors operating in the visible range, the influence of factors is much higher.At the same time on the formed image irrespective of sensor type object saturation, electrophysical and area characteristics of objects and backgrounds, and interpixel and geometrical distortions essentially influence.These factors can lead to a reduction and blurring of the contrasts of the object-background pair, and, consequently, to a decrease in the signal-to-noise ratio in the image.As a result, it will lead to erroneous selection of the object of reference in the image.
Problem Statement.The UAV equipped with CENS is supposed to be used in the conditions of developed infrastructure, where there are objects with insignificant differences in brightness and geometric characteristics.Erroneous determination of the object of reference on the СI will inevitably lead to a decrease in the accuracy and probability of UAV location, and when controlling the state of objects, for example, in their destructionto an erroneous assessment of the degree of destruction.
CI model.Let us use the CI model "object on background" [1,2], considering that the object is in the viewing area and has a stable contrast with respect to the surrounding background [1,2], assuming that the object is in the viewing area and has a stable contrast with respect to the surrounding background.
Due to the instability of the brightness of individual elements of the underlying surface and the contrast between the object and the background, we will assume that the CI is defined by the contrast sign of the object and its geometric shape, i.e., as a binary image.The elements of the object correspond to the values 1, and the elements of the background correspond to the values 0. We will solve the problem under the following assumptions and constraints: 1) the background is formed by signals of the surface area, and the object has a negative contrast with respect to the background; 2) the object is homogeneous in brightness; 3) the background around the object has the same property; 4) each ij-th CI element is a normally distributed value with dispersion .(5) For the considered CI models and object and background brightness distributions, it is required to solve the problem of CI segmentation.Its use will provide a high probability of selecting the object of reference.In its turn, it will allow to obtain the minimum error of CENS binding , and in the case of estimation of the object destruction degree -its high accuracy.
Problem solution.The use of brightness and geometric features for segmentation of CI SS with the presence of poorly distinguishable small-sized and low-contrast objects leads to the necessity of combining two stages of object selection: by geometric dimensions and by brightness.Suppose that there are no variations of brightness values within a pixel of homogeneous zones [1].The brightness values of neighboring objects differ insignificantly, but the sensitivity of sighting sensors allows to distinguish them.
According to these conditions, it is necessary to develop an algorithm for image segmentation using brightness and geometric features, which will provide a high probability of selecting the desired object.Let's consider that as geometric features of objects their area is used.The step-bystep process of selection of objects by the selected feature will be carried out in accordance with the selected value of quantization threshold.The threshold values will be chosen in such a way as to select the object in the background considering the presence of similar objects.
At the first stage of object selection by brightness indicator, let's represent CI in the form of image matrix sweep by rows, resulting in a sample of volume 0 J .Let J is the number of cells in the frame with signals from a similar object.Then where 0 J is the total number of frame elements that have fallen into the field of view; v J , w J is the number of frame elements occupied by the anchor object and the background.Mutually incompatible events, consisting in belonging of the sample element to the signal of the background, anchor object and similar object, form a complete group.Consequently, the obtained sample is divided into three nonintersecting classes i ω corresponding to signals from the background w (ω) , similar object and anchoring object (ω) .Taking this into account, the sampling distribution density 0 J is defined by the expression [7]: where i i 0 p = J J , (i = 1,2,3) are apriority class probabilities; ii w (S) = w(S ω ) ) are conditional probability densities of the random variable S , if it belongs to the class i ω , which are defined by expressions (4), (5).
Thus, the sample consisting of elements of three classes should be divided into two classes to optimally separate the signals of the object from the background signals with respect to the quality indicator to be further specified.
We consider the threshold l of quantization of the sample into two classes to be known.To of them belong the signals of the object, to the otherthe background.Then considering expressions (4), (5) probabilities of errors of the first (second) kind (when the signal belonging to the first (second) class refers to the second (first) class are defined by expressions [5]: Let the probability of occurrence 1 in i H is equal to i r .For comparison of fragments i H with RI consisting of 1, it is more convenient to operate with numbers: each of which represents the number of units in the fragment i H .In (10), J is the number of elements of the object.With this in mind, the decisive rule will be that the fragment j HH , for which: is declared to coincide with RI according to this information feature.
Then the numbers i z are distributed according to the binomial law: The probability of object selection when using the solving rule ( 11) is equal to the probability that the number of ones 0 z , corresponding to a match between the RI and the object, exceeds all other numbers i z ,i 1,K .Let us denote by j 0 A the event consisting in the appearance of 0 z = j 1,J ones in 0 H , and by j i A , i 1,K -the event consisting in the fact that the number of ones i z will not exceed 1 j  .The events According to formula (11), the probabilities of events j i A are defined by the expressions: where k J C are binomial coefficients.Then by the probability multiplication theorem the probability of the event A is equal to: Since the events j L , j 1,J in the aggregate are inconsistent, the probability that the number of ones 0 H in exceeds the number of ones in all other fragments i H , will be determined as follows: where the probabilities j i P(A ) are defined by formulae (12).Given that: (probabilities α, β are given by relations (8), ( 9)), for the probability of object selection by brightness we obtain the final expression: According to expressions (4 -8), we write down: -λl where l = l σ is relative threshold; λ = λσ .At the first stage of object selection on CI, the influence of perspective distortions caused by sighting geometry is not considered.Therefore, at the second stage of object selection by area it is necessary to consider the possibility of occurrence of errors of the first and second kind caused by distortion of geometrical shape of objects depending on the sighting angles [3].
The use of the object area as an information feature is convenient, because when changing the geometry of sighting, it is not the area that changes, but only the shape of the object.Consequently, it is possible to simplify the process of CI formation because there is no need to perform affine transformations.
By analogy with the first stage, at the second stage the errors of the first and second kind will be determined in accordance with analytical expressions: where In this approach to the implementation of object selection in the background, the connectivity of adjacent pixels in the image   Gx is taken into account [6].
Let us consider the principles of threshold processing in this case.At the first stage quantisation is performed using thresholds .As a result, a certain set of slices is formed according to the selected threshold i m L .On them, the objects having the corresponding area will be segmented and the better objects will be selected.In fact, each individual slice is a matrix with the corresponding pixel value.The area that has the larger number of pixels is the object being searched for on the CI.As a criterion for selecting an object on the CI, we choose the total relative area index.The matrices i S are element by element combined with each other.As a result, the final matrix S  will be a set of independent samples in the form of integral area indices.The element ij S  with the largest number of pixels is considered to be the result of the presence of the selection object in the matrix S  .
The probability of object selection on the image c P does not depend on the results of correlation-extreme processing for other segmentation thresholds.Consequently, the resulting probability of selection of the sought object on CI will be determined according to the expression: where i c P is probability of object selection at the i-th step.
Using formula (15) we can calculate the probability of object selection in the image, which increases with each step.This is explained by the increase in the signal-to-noise ratio of the image.
It can be shown that the value of the signal-tonoise ratio of the image q , taking into account errors of the first and second kind, when the required value of the probability of selection of the object in the image takes place, on the basis of the maximum likelihood method using expressions (16 -17) will be determined by the formula [7]: where   Фx is Laplace integral.The probability of exceeding the threshold for each step is defined as: At large values k , the binomial distribution is approximated by a Gaussian distribution.
Thus, based on the above, image segmentation has been proposed to carry out in two stages.The latter include a sequence of the following operations: 1. Estimation of the characteristics of the original image by segmentation features.
2. Selection of the feature type.3. Selection of objects according to the selected features.
4. Formation of a set of segmented images.As an indicator of the segmentation method efficiency, we will use the probability of correct image segmentation and selection of the binding object.Therefore, it is sufficient to use relations (15) and (20) to estimate the efficiency of segmentation.This approach allows us to consider the influence of various factors that lead to image noise on the quality of image formation and the evaluation of the effectiveness of CENS functioning.
According to the above approach to image segmentation used in UAV CENS, the structure of the image segmentation algorithm using luminance and geometry will have the form shown in Fig. 1.
Modelling results.
Let us choose a radio-metric receiver as the CENS sensor.Using the zone model of the image, by processing the aerial image of the reference area, a matrix of numbers is constructed, the elements of which characterise the distribution of radio brightness temperatures of the given area.
In this matrix, a rectangular and some area around it.The matrix should not contain 12 MM -submatrices "similar" to the RI.This means that the coefficient of mutual correlation of these submatrices with RI exceeds a certain threshold, so that a priori not to reduce the probability of correct selection of the object.In the initial matrix, the 12 NN -submatrix of the unnoised CI containing RI is selected.The coordinates of the upper left corner of the RI matrix in the CI matrix op op i , j represent the estimated parameter.The principle of CI and RI modelling implicitly assumes that: 1) the grids of RI and CI coincide, i.e. there is no need to shift RI within half-width of the resolution element; 2) there is no rotation of RI relative to CI.
To simulate the noise component the image caused by the noise of the radiometric channels, a normally distributed value with zero mean and variance 2 is added to each element of the modelled image (for simplicity, the noise variance of all channels is chosen to be the same).This completes the modelling part of the algorithm.
The total number of realisations processed in the series of realisations used to calculate one value of the probability of correct selection of an object in a segmented image с P was z N = 400.Figures 2 -7 show the results of the estimation of the object selection performance on the segmented image for two values of the signalto-noise ratio 0 q  and 4 q  .The results of estimation of the probability of correct selection of an object in the segmented image are invariant with respect to the size and nature of the initial data, because c P in accordance with (15 -19) is determined by the values of the signal-to-noise ratio.It is shown that it is necessary to additionally use area characteristics of objects for selection of the object of reference on CI of sighting surfaces with heterogeneous and similar objects.As a result, the influence of perspective distortions of CI on the selection of the object of reference will decrease.Analytical relations for estimation of probability of correct selection of objects are obtained.These relations are a function of the selected quantisation threshold at each step of object selection considering errors of the first and second kind.
By means of modelling the efficiency of object selection on segmented CI depending on the quality of initial images is estimated.It is shown that application of the proposed approach to image segmentation allows to carry out object selection with probability not lower than 0.9 for typical values of signal-to-noise ratios of images formed by CENS in real conditions.
image obtained for the sighting angle of view  at the moment of time t ; formed in advance for one of the sighting angles i  .The current image is represented by brightness values of objects and backgrounds of the viewed surface in resolution elements: is the brightness of the image element v -th of the object v is brightness of the image element w -th of background w S ; V and W are the numbers of objects and backgrounds of different brightness and shape in the original image.

.
noise dispersion in the receiving channels of CENS is the same, i.e. 22 ij σ = σ .Let us denote the contrast of the sought object with respect to the surrounding background by Then the brightness distribution densities of the background and the object are defined by the expressions[4]:

H 12 T
p .For a given threshold l , we convert the original SCI image into a binary image H by the rule: Let us estimate the probability of selecting an object in the image as follows.Let the size of the object be ×T cells.Let us partition the CI matrix into rectangular submatrices 12 T ×T .If at such a partitioning of the CI it does not contain an integer number of cells with the object, then increase the frame size to contain an integer number of submatrices 12 T ×T , which we denote by K +1 .In this case, the estimates of the probability of selection of the object on the CI are underestimated due to the frame enlargement.Let us assume that the true position of the object falls into one of the submatrices and denote by 0 HH the fragment of the CI corresponding to the RI, and i

Fig. 1 .
Fig. 1.Structure of the algorithm for image segmentation using bright and geometric features.

Fig. 7 .
Fig. 7.The results of estimating the probability of object segmentation at: S = 90%, q ≈ 0.The results of dependence