Methods of constructing vector fields of natural objects' movements based on a series of consecutive satellite images are considered: cloud formations in the atmosphere based on a series of consecutive images obtained from geostationary satellites; water masses and ice fields based on a series of images from low-orbit satellites; using the example of the evolution of bipolar spots, the trajectories of trial corks in the Solar photosphere are constructed based on the data of sounders installed on heliophysical satellite observatories.
( − 1)
(1) Here — the average value of pixels in the standard , — the average value of the image elements in the area covered by the reference. The denominator in (1) uses the product of the standard deviation of the pixels of the standard by the standard deviation of the pixels of the image in the area covered by the reference.
In general, the size and orientation of the standard object found in the next image of a series
of images may have diferent values in the subsequent image. The expression (1) normalized
with respect to changes in amplitudes is not the same with respect to rotation or changes
in the size (scaling) of the standard. In [
According to [
In the presented work, the standard displacements are determined on the basis of determining the maximum of the cross-correlation coeficient in the spatial domain in accordance with the formula (1). In this case, the standard can be transformed, consisting of scaling, rotation and transfer. An eficient algorithm based on the scanning rows method has been developed. The obtained results of computational experiments on images from the METEOSAT-8 spacecraft indicate both the need to take into account the scaling and rotation of the standard, and the acceptable time of the corresponding calculations. Level 1B data (10-bit pixels) is used.
The solution of the problem consists of the following basic steps: search square standard objects in the current image , based on achieving the maximum contrast or maximum entropy; the center of the standard coincides with the center of the square; search for the positions of the found standard in the subsequent image , based on the achievement of the maximum value of the cross-correlation coeficient; plotting vector fields of spatial movements of objects in accordance with the found positions.
Search for standards. The search for standards is based on the methodology proposed by
EUMETSAT [
The search for secondary standard of the Targ_Size size is performed in the grid nodes with the Grid_Size size. The size of the square area centered at the grid nodes for searching for standards is set by the Targ_Search parameter. The allowed minimum distance between the standards is controlled by the Targ_Dist parameter. The optimal position for the standard within the search area is the one where the maximum value of the control parameter Par — contrast or entropy is reached. When searching for standards within a region of the Targ_Search size, local averages and standard deviations calculated from the 3 × 3 neighborhood are used. Contrast is defined as the diference between the maximum and minimum values of the local averages. In addition to the listed parameters that determine the “physical” characteristics, when searching for standards, the parameters that characterize the “variability” of the image inside the area covered by the standard are used: Min_St_Dev — the minimum value of the local standard deviation, Num_Gr_SD — the minimum number of pixels with a standard deviation greater than Min_St_Dev.
Determination of standard ofsets. The ofset is determined for each of the K_Targs found benchmarks. The search for a new standard position is performed inside a square area of the Search_Size size. The center of the search area coincides with the original position of the standard. The new position of the standard is the position where the maximum value of the cross-correlation coeficient Corr is reached. During the scan of the search area, the standard is subjected to scaling and rotation transformations. The scale and angle of rotation of the standard are determined by the following parameters: Scale_Min — the minimum value of the scale of the standard; Scale_Max — the maximum value of the scale of the standard; Scale_Delta — the increment of the scale of the standard; Angle_Beg — the initial angle of rotation of the standard in degrees; Angle_End — the final angle of rotation of the standard in degrees; Angle_Delta — the increment of the angle of rotation of the standard in degrees. Since, in general, the transformed discrete grid of the reference does not coincide with the discrete grid of the output image, it becomes necessary to interpolate the pixel values. We ofer three ways to get the pixel values of the transformed standard: rounding to the nearest integer; bilinear interpolation; bicubic interpolation.
One of the important uses of satellite data is the monitoring the movement of water pollution and ice fields in marine areas.
The problem of constructing the fields of propagation of marine pollution from
diferenttime satellite data is closely related to the problem of determining the speed and direction of
vectors of spatial movements of water masses [
A similar approach is used in monitoring the spatial movements of ice fields. Here, mosaics, made up of radar satellite images transformed into the same cartographic basis, are mainly used (images of the Arctic Ocean are most often used, because of their importance for the purposes of meteorology and ships navigation).
The process of entering the coordinates of tracer objects consists in specifying their position on the current and next images and saving the entered coordinates in a file that will be used in the final stage of processing and saved for further use.
At the same time, satellite images are pre-made to “fix” the contours of the coastline using reference points, and, thus, on the maps of the distribution of the fields of spatial movements of natural objects, the stationary land is separated from the moving objects.
The Delaunay triangulation is constructed based on the entered coordinates of the objects in the current image. Each triangle of the triangulation corresponds to a triangle in the following image. Such a set of pairs of triangles determined the set of piecewise afine transformations of the plane. These transformations are applied to the nodes of the regular grid in the current image, thereby forming the required displacement vectors.
Simultaneously with the construction of the vector fields of spatial displacements of water masses and ice fields, histograms of the velocities and directions of these vectors can be constructed.
Theoretically, the technologies for constructing displacement fields of natural objects presented in paragraphs 1 and 2 can be applied to image sequences of any length. However, in the practice of constructing operational hydrometeorological forecasts, for which these technologies were developed, no more than 3–4 images are mainly used. Interactive versions of the corresponding programs are used for this purpose.
But in the processing of data obtained from heliophysical satellite platforms, there is a need
to process a series of consecutive images with a length of 100 or more frames. An example is the
image of a bipolar group of spots shown in Figure 5. We use here data from the Helioseismic and
Magnetic Imager of the Solar Dynamics Observatory (NASA, USA). The goal of processing from
the point of view of visualization is to build a field of horizontal velocities of the so-called “trial
corks”, which at the initial moment are located in the nodes of a regular rectangular grid. As
the process progresses, it is necessary to track the trajectory of each trial cork. We considered
a series of images of diferent duration from 2 to 4 hours with an interval of 135 s. between
frames [
For this purpose, we used a console program [
The research was partially carried out within the framework of the state task of the ICM&MG SB RAS 0251-2021-0003.