One of the important tasks facing the regional authorities is to monitor the condition of roads and power lines. In the Ulyanovsk region more than 8 thousand km of power lines and more than 9 thousand km of roads (including rural). A significant part of these facilities is located outside the settlements in places with medium and low availability. In many such places there is a problem of uncontrolled forest overgrowth. This work is devoted to solving the problem of automated satellite monitoring of such areas. For this purpose, it is proposed to use a modified convolutional neural network that processes time sequences of multispectral satellite images and allows to allocate territories occupied by forest and undergrowth with high accuracy. This approach allows us to assess the dynamics of overgrowth of the territory and perform the appropriate forecast with sufficient accuracy for practice.
One of the important tasks of the satellite image processing is its thematic mapping, i.e. division of
image into identifiable areas containing the similar visual, correlation or texture characteristics of
pixels. The use of standard segmentation algorithms [
It is possible to overcome the mentioned disadvantages by using neural network procedures of
segmentation and classification of multidimensional data. In work [
points { ,
previous point of time in connection, for example, with cloudiness. The quality analysis of such an algorithm shows the processing comparable accuracy to the qualified operator results.
It should be noted that the results of the satellite images thematic processing provides information related to the peculiarities of the Earth's surface in the previous and current moments of time. However, the necessary element of the RS processing system is the tool that allow to forecast the state of certain objects and form recommendations for responsible persons. For example, let's consider the task related to the forecasting about the dangerous convergence possibility of various natural and technogenic objects. An example of such convergence may be the gradual growth of the forest area along roads or power lines or landslide processes leading to the destruction of various infrastructures. 2. Satellite Image Processing Let us formulate the given problem as follows. Let there be an aggregate of segments describing a certain extended object (a road, an electric power transmission line etc.). The given aggregate is usually described by a vector object having geographical reference in absolute coordinates. Let us separate on this extended object a set of points = ( , ) having the distance between them equal to ∆ . Let us assume that at a certain time instant next to the object there lies a certain extended defined by a set of points each corresponding to a pixel in the original halftone image. For let us construct a perpendicular to the segment [ , + ]. Let us find the point of intersection of this perpendicular and the domain . Obviously the set of , = , . . , } describe a conditional boundary of the domain extended object. It enables to use estimates of the points coordinates { different times
= , . . , as a source of information on the domain forming a prediction about its boundaries at future times > as well. (Figure 1). as viewed from the , = , . . , } obtained at dynamics for the purpose of where and
– white noise samples with zero mean and variance .
Direct measurements based on the results of satellite material image-type related mapping show that MSE is approximately equal to .
, where
Let us suppose that the boundary of the domain
– resolution of the original images.
can move non-uniformly. Thus, for example,
the area of a precipice or a ravine can increase by tens of centimeters per each year and at a certain
moment its rate might increase exponentially. Then we will use doubly stochastic (DS) model [
– scalar parameters – independent normal random variables with zero mean and variance :
– white noise samples with zero mean and variance . and = + , = + , = 1, . . , , = 1, . . , , (1)
−1 Э С
− ; = С = ( = ( − ) Э . ̅ = , ̅ = ) ) .
0 0 0 0
−1 −1 , ,
The assigned notations enable to apply DS nonlinear filtering to observations and for construction of predictions of behaviour of the region in reference to the object Э = ( − ) and = (
− )– extrapolated predictions for the point the time point based on the preceding observations − and − . Denote by − , error covariance matrices at the time point ( − ) , = {
}, = { coordinates at − – filtering
} – diagonal . In doing so let us introduce have the following form: covariance matrices for random increments . Then error covariance matrices for such extrapolation Э = Э = Э − Э Э − Э Э − Э Э − Э
= = ′( −1
) −1 ′( −1) −1 ′(
−1) + , ′( −1) + , If we denote by Э , Э
- the first elements of the vectors Э = Э − ; = Э + ; ), then we can write the following relations (Eq. 27) for DS coordinate filters: = Э + − Э , = Э + − Э .
(3) and Э ;
= = Э + ; The filtering error variance at each step is determined by the matrices = ( − ) Э ,
Special attention must be given to the fact that due to the necessity for the distance from the point observations extended object to the domain to be surveyed, it is possible to simplify the boundaries coordinates filtering process by processing only one coordinate, namely, the distance from the belonging to up to the boundary
at the time point . An aggregate of similar can be processed by a technique identical to the above-described one.
As an illustration of such a technique in figures below series satellite images fragments for the forest tract in Cherdakly district of the Ulyanovsk region for the period 2001-2017 years (figure 2) and Milanovsky opencast colliery on riverbank of the Volga in the northern part of the city of Ulyanovsk for the period 2013-2017 years (figure 3) are presented. Here for convenience of color image perception and its recovery overlapping of visible spectral bands and superposition of the segmented image fragment and normals to the object to be monitored is carried out. In the first case the number of multispectral images to be processed amounted to 42 snapshots, in the second case - 32 snapshots. The minimal time interval for satellite information production amounts to 14 days. operating samples. The training samples were used to specify the filtering parameters, in particular, to estimate the parameters and
. The operating part of the sample was processed by three variable
+ prediction Э are presented. algorithms enabling to carry out the distance prediction The first algorithm (I) involves constructing a simple prediction + basing on the preceding observations.
+ = − wherein only the change speed is taken into account for the time interval ( − , ). The second algorithm (II) assumes linear Kalman filtering of the observations and construction of the extrapolated based on the results of the processing. The third algorithm (III) is in the abovedescribed doubly stochastic filtering of an aggregate of the observations and construction of the vector + . In the table 1 below the values of prediction average errors depending on the object kind Э
On average the DS filter provides prediction accuracy 6% higher than in case of using Kalman filter and 58% higher than in case of simple linear predictions. It enables to estimate coordinates and rate change dynamics for boundaries of the domain to be monitored by using the DS filter. It is estimate (figure 4b). essential that the DS filter enables to quicker respond to abrupt rate change of the processes determining the object behaviour. As an illustration we provide the estimates behaviour for the distance from opencast colliery to one of the points to be monitored (figure 4a) and the parameter The forest tract snapshot. October 2014 The forest tract snapshot. May 2015 The forest tract snapshot. June 2016 Milanovsky opencast colliery snapshot. May Milanovsky opencast colliery snapshot.
May Milanovsky opencast colliery snapshot.
May Milanovsky opencast colliery snapshot.
2016. Beginning of the avalanche processes. Milanovsky opencast colliery snapshot.
2016. Continuation of the avalanche processes. Milanovsky opencast colliery snapshot. May 2016. Cessation of the avalanche processes. 6.7 m
Direct analysis of the given results in comparison with the data of objective monitoring (solid line) indicates superiority of the DS filter over conventional linear Kalman filter in filtering accuracy. As it takes place, this superiority makes itself evident in the most distinct manner in case of abrupt change of the rock collapsing process (and the corresponding reduction of the distance between the opencast colliery and the point to be monitored). This change corresponds to a significant change of the parameter estimate which enables to register considerable changes in the opencast colliery domain state basing only on this estimate dependence nature versus survey time.