Petrosyan, Arakel 
  
2 PRELIMINARY NOTES 
The motion of air masses is identified with that of clouds, i.e. with modifications of a shadow pattern of cloudy layer 
observable from space. Generally speaking, this supposition requires the separate proof, however considering of this 
problem goes out for frameworks of a subject in hand. One remark motion of cloudy layer on peculiarity motion of a flow 
pattern, that is population of shadow marks or other peculiarities and heterogeneities. Images that are capable to reveal such 
heterogeneities on required scales are suitable for handling in any spectral band. It can be the shadow patterns of cloudy 
layer in a visible band, shooting in lines of water on large scales, overseeing by transition of impurities in conditional 
colours etc. 
It is evident, that we could place correspondence between sequential images and the distinction between them should be 
reduced to a minimum. As in turbulent flow streamlines can diverge on arbitrary distance, thus strongly changing a flow 
pattern, then critical parameter from the point of view of reliability of operation is the interval between sequential images 
AT, which should be, whenever possible, diminished. As it is a priori mathematically impossible to determine a degree of 
"similarity" or "non-similarity" of a couple of the images, for in fact this problem is a subject of consideration, then it is 
possible to consider that parameter A T should satisfy to a relation 
AT = k Lchar / Vchar or AS - k Lchar. (1) 
Here Lchar and Vchar define a characteristic linear scale of heterogeneities and characteristic velocity on scales of these 
heterogeneities, AS sets expected shift, and value k equals 0.1.. 0.5. Generally speaking, the basic complexity is represented 
by essential strains of the images, at which the topology of lines of identical luminosity varies. In ordinary transition of all 
pattern, the reconstruction is theoretically possible at any value of displacement. During testing algorithm on the synthetic 
images, in a series of cases the reliable outcome was achieved at values k = 2.. 3 and more. 
In reconstructing of a global pattern of atmospheric flow, we shall neglect vertical motions of air masses. In spite of the fact 
that these transitions can lead to essential deformations of a shadow pattern observed from the satellite, the singularities 
with characteristic scales about several hundreds kilometres are maintained long enough. Thus, for reconstruction of a flow 
pattern on a series of the sequential images it is necessary to find in each point of the image a vector of an air flow velocity 
laying in a plane that is perpendicular to ray of sight. In case if for each point of the first image the similar point on second 
will be retrieved, we can construct a field of a deformation of the image and, if knew a temporal interval between two 
images, field of velocities. 
3 STATING A PROBLEM 
Further we shall speak only of the monochromic images implying that a colour pattern we can set with the help of three 
monochromic channels - red, green and dark blue, according to RGB colour model. As a matter of fact, such approach does 
not restrict us to the images, and permits to consider any functions assigning 2D-allocation of any magnitude, for example 
temperatures, luminosity, concentrations etc. For the sake of a determinancy all such function we shall define as "images". 
It is supposed, that the two-dimensional image is determined by restricted continuous together with the first derivative 
function, given on a singly connected domain. The rather feeble requirements to a smoothness were defined proceeding 
from the minimum theoretical requirements. Basically, the requirements to a smoothness can be made more rigorous, and 
the quality of operation of algorithm as a whole seems to be better. As the images, which are subject to handling, are 
discrete representation of the analogue images, i.e. set netting function, the requirements to a smoothness render serious 
influence on used algorithms of approximating. These problems are not bound directly to a primal problem. 
Thus, the starting problem of reconstruction of an instantaneous pattern of flow is reduced to the following: it is required to 
revive a deformation field of a couple of the images translating first image in second one. The deriving of a deformation 
field of is to determine a vector of transition of each point of the first image, i.e. determination of analogue of this point on 
the second image. Therefore for further operation it is required formally to spot concept of "resembling" of points of the 
image. 
  
1150 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000.