Remote sensing of the Earth allows to receive information of medium, a high spatial resolution from space vehicles and to conduct hyperspectral measurements. We propose a new approach of construction of 3D-models of the Earth's surface in urban environments using remote sensing technologies. The main idea is the use of the algebra of geometric objects (addition, subtraction, multiplication, a division of objects and grids, multiplication of an object by a factor, raising an object to power, factoring, etc.). These operations automate the process of multidimensional modeling. We have developed programs that automate the process of geometric programming of scenes, in particular, scenes on the surface of the Earth (for example, trees, buildings, roads, and their arrays). In the Matlab software environment, a script library has been developed in the field of processing geometric objects, including such categories as the generation of urban objects; algebraic operations; texturing, marking and painting; work with objects in dynamics; work with random objects; differentiation and integration of objects and others. Examples of programs for automating the construction of 3D models of residential arrays based on the simplest scenarios (using algebraic operations of multiplying an object by a coefficient, a coefficient by a coefficient, an object by an object, an object by a grid of points and a line of points) are given.
In this paper, Haar's generalized wavelet functions are applied to the problem of ecological monitoring by the method of remote sensing of the Earth. We study generalized Haar wavelet series and suggest the use of Tikhonov's regularization method for investigating them for correctness. In the solution of this problem, an important role is played by classes of functions that were introduced and described in detail by I.M. Sobol for studying multidimensional quadrature formulas and it contains functions with rapidly convergent series of wavelet Haar. A theorem on the stability and uniform convergence of the regularized summation function of the generalized wavelet-Haar series of a function from this class with approximate coefficients is proved. The article also examines the problem of using orthogonal transformations in Earth remote sensing technologies for environmental monitoring. Remote sensing of the Earth allows to receive from spacecrafts information of medium, high spatial resolution and to conduct hyperspectral measurements. Spacecrafts have tens or hundreds of spectral channels. To process the images, the device of discrete orthogonal transforms, and namely, wavelet transforms, was used. The aim of the work is to apply the regularization method in one of the problems associated with remote sensing of the Earth and subsequently to process the satellite images through discrete orthogonal transformations, in particular, generalized Haar wavelet transforms. General methods of research. In this paper, Tikhonov's regularization method, the elements of mathematical analysis, the theory of discrete orthogonal transformations, and methods for decoding of satellite images are used. Scientific novelty. The task of processing of archival satellite snapshots (images), in particular, signal filtering, was investigated from the point of view of an incorrectly posed problem. The regularization parameters for discrete orthogonal transformations were determined.
The paper proposes a method for fuzzy interactive enhancement of objects identification in the image which allows identifying hidden or no defined details and objects in the images. The application of the method and its difference from other image enhancement techniques are shown. The paper presents the algorithm and describes the basic processing procedures (sampling, scaling, convolution, contrast). The main processing parameters (increasing and reduction of dimensions, convolutions, brightness, and thresholds contrast) are demonstrated. The results from the applied algorithm are explained on an example related to landfill Kutchino in the Moscow region, on the satellite images with low and high spatial resolution.