Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical problems in geotechnologies

The report is partially supported by RFBR (projects 03-07-90239, 03-07-96837).

The specific task accompanying remote SENSING THE EARTH FROM SPACE for the purpose of the regional monitoring is geographical binding of the received images to a cartographical material. Qualitative complexity of a problem of recognition, overlapping and the control in real time geometrical and physical properties of observably dynamically varied objects demands the significant resources of accessible hardware-software means of the supercomputer centre used by the Laboratory of Images processing of Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Science within the framework of projects RFBR 03-07-90239, 03-07-96837.

In the paper presented adaptibility is considered here in different aspects: 1)adaptive nature of videoinformation component of GIS-data, 2)adaptive nature of mechanisms for remote sensing data processing, 3) adaptive nature of interdisciplinary staff of developers providing directed progress to achieve the planned goals.

1. Let us consider reasons for specification or alternation of the GIS-data in detail. Transformation forms or their mutual location on the Earth surface in observation time is typical for plain digital display images of some Earth terrestrial objects mapped. Such changes observed during specific time intervals are caused by natural processes of their development dynamics and by dynamic errors of cartographic geocoding of the object display. Coordinate and videographic information like color, bar texture, text designation and conventional signs are assigned to geometric objects under GIS data acquisition. In case of objects' modification (form, dislocation, rotation, scale, etc.) it is desirable to keep integrity of cartographic image of the displayed object. Here, each component of the image should find "its own place", i.e. to adapt itself to transformation occurred. Thus, in this situation we consider adaptive nature of GIS-data as ability to change orientation, scale and location automatically with keeping topological integrity of the perceived cartographic image.

A great obstacle to provide accuracy of linear and area measurements is in information roughness on altitude coordinates of objects' location. For example, only geometrical treatment of pure geographical interpretation with rather accurate GIS-scheme of motor highways may differ significantly (by 25% and more) from actual distances. In this case the more accurate geobinding is required (special signs, namely kilometer posts placed by surface services using geodetic measuring devices).

2. Multizonality that provides combining heterogeneous information obtained via different channels and diapasons of scanning rays that reduces information incompleteness as well as remoteness from the object under study hampering placement of fixed positions of geocoding for assignment of coordinate system of cartographic image are specific for remote sensing. In particular, outlines of water reservoirs are one of the most appreciable identification parameters aero-space images of the Earth. Their seasonal fluctuations of water level can be referred to such tasks - in case of drying that creates serious obstacles for automatic binding the image to a cartographical basis. As this takes place, the levels are presented as sequence of embedded plain geometrical forms describing water table at a certain time. We face similar problems under analysis of digital images of the same district but obtained from different heights and under different inclinations of film-making chambers. Besides angular and perspective distortions here begin to play a role the problems caused by rectangle form of a grid for raster image creation that leads to deformed image (in case of rotation) as by its form as by shift come into play as well concerning its true position. Thus, geocoding used for interrelated objects should provide acceptable area combining of the most displayed objects.

3. The method of Virtual Addressing of the GIS-DATA is aimed on maintenance of adaptibility of them and is supported by parallelism of the Vertical Data Processing. VDP is offered as the tool for construction dynamic objects. For example, the accuracy of tools for manual measuring coordinates may be much higher, rather than accuracy of definition of a reference point of binding. While transferring results at a cartographical basis it is necessary to solve a problem of specification of objects coordinates, that linearly depends on coordinates of a reference point. In this case, it is desirable to have an opportunity to allocate group and shift them (direct or indirect groups displacement), i.e. effectively recalculate the true coordinates of displayed objects. So, Virtual Addressing is understood as such mechanisms of the description of an arrangement of the interconnected groups of spatial objects which allow not only static, but also the dynamic control of the data coordination. To achieve the goal the mechanism of assignment of functional dependencies replacing standard set of assigned scalar values is used.

A). Application of not absolute but relative coordinates is a special case of functional dependencies' assignment. If the point "a" is assigned by its absolute coordinates, then the point "b" will be assigned relative to "a" coordinates under condition that in coordinate position absolute shifts of point "b" relative to "a" is specified. In other words, absolute values of the coordinates of a point "b" can be found by adding the absolute value of coordinates "a" and appropriate shifts from "b".

Developing the idea on relative addressing, it is possible to construct a tree of topological coordinate dependencies; as this takes place, two interpretations of relative addressing can be used:

a) displacement of a point "c" be relative to "b" and "a", calculated as the sum of shifts displacement "c" be relative to "b" and "a",

b) and displacement of a point "c", considered only as single-level displacement of absolute coordinate using dynamically calculated "b"

If input parameters changes according to function binding F("а", "b", "c"), the adjusting process (updating) is given with minimal units' transformation, i.e. it starts from leaves, then comes to branches and finally touches stem coordinates. Modification upside-down is represented rather effective, to make changes in inverse order keeping topological and geometrical correlation on the leaves of the topological tree of the object coordinate dependencies.

B). Each point may have only one root and the only defined sub-tree group of dependent points under such definition of relative addressing. Operating in discrete-measuring set of coordinate presentation, we face the problem of point identification. Understanding of impossibility of absolute point assignment of coordinates allows to speak about accuracy of each concrete point assignment. Complication of topological dependence tree presentation by means identification solution brings to topological graph of dependencies where a number of function values (topologically consistent) are defined. Automatic check of consistency of options of topological graph presentation makes possible discussing accuracy of presentation and mechanisms for automatic computing of the "nearest" correct presentation. Note, here we deal with a qualitatively big volume of calculations of excess combinatory type.

4. Support of virtual addressing technique (VA) by vertical data processing (VDP). One of the arguments in favor of VA is its effective realization using vertical processing, i.e. application of VDP suggested by V.Shuman in 1960. Unlike typical ("horizontal") processing when all data are loaded into processor consistently one after another in the course of VDP appropriate binary code bits (i.e. one seniority) for some data are put concurrently into processor. Direct dependence of processing time on the data code size is a peculiarity of program realization of arithmetical operations with vertically arranged "short" data. It makes processing of "short" data more efficient. Moreover, use of hardware circuits of bit-by-bit operations (and, or, not, EXCLUDING OR , or, etc.) allows to use parallelism directly that provides realization of mass operations with vertical data. Of particular interest this feature is for multiprocessor SIMD-systems where processing the data put into different processors is performed by means of the unified program. If we consider SIMD-system registers as components of a "very long" register, we can process up to tens of thousands data units simultaneously.

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