Context. The Gibbs phenomenon introduces significant distortions for most popular 2D graphics standards because they use a finite sum of harmonics when image processing by expansion of the signal into a two-dimensional Fourier series is used in order to reduce the size of the graphical file. Thus, the reduction of this phenomenon is a very important problem.
Objective. The aim of the current work is the application of two-dimensional Padé-type approximations with the aim of elimination of the Gibbs phenomenon in image processing and reduction of the size of the resulting image file.
Method. We use the two-dimensional Padé-type approximants method which we have developed earlier to reduce the Gibbs phenomenon for the harmonic two-dimensional Fourier series. A definition of a Padé-type functional is proposed. For this purpose, we use the generalized two-dimensional Padé approximation proposed by Chisholm when the range of the frequency values on the integer grid is selected according to the Vavilov method. The proposed scheme makes it possible to determine a set of series coefficients necessary and sufficient for construction of a Padé-type approximation with a given structure of the numerator and denominator. We consider some examples of Padé approximants application to simple discontinuous template functions for both formulaic and discrete representation.
Results. The study gives us an opportunity to make some conclusions about practical usage of the Padé-type approximation and about its advantages. They demonstrate effective elimination of distortions inherent to Gibbs phenomena for the Padé-type approximant. It is well seen that Padé-type approximant is significantly more visually appropriate than Fourier one. Application of the Padétype approximation also leads to sufficient decrease of approximants’ parameter number without the loss of precision.
Conclusions. The applicability of the technique and the possibility of its application to improve the accuracy of calculations are demonstrated. The study gives us an opportunity to make conclusions about the advantages of the Padé-type approximation practical usage.
ABSTRACT:Vegetation and water bodies are a fundamental element of urban ecosystems, and water mapping is critical for urban and landscape planning and management. A methodology of automated recognition of vegetation and water bodies on the territory of megacities in satellite images of sub-meter spatial resolution of the visible and IR bands is proposed. By processing multispectral images from the satellite SuperView-1A, vector layers of recognized plant and water objects were obtained. Analysis of the results of image processing showed a sufficiently high accuracy of the delineation of the boundaries of recognized objects and a good separation of classes. The developed methodology provides a significant increase of the efficiency and reliability of updating maps of large cities while reducing financial costs. Due to the high degree of automation, the proposed methodology can be implemented in the form of a geo-information web service functioning in the interests of a wide range of public services and commercial institutions.
In this paper we propose a new technique for the solution of the image segmentation problem which is based on the concept of a piecewise smooth approximation of some target functional. We discuss in details the consistency of the new statement of segmentation problem and its solvability. We focus our main intension on the rigor mathematical substantiation of the proposed approach, deriving the corresponding optimality conditions, and show that the new optimization problem is rather flexible and powerful model to the study of variational image segmentation problems. We illustrate the accuracy and efficiency of the proposed algorithm by numerical experiences.
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