The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters

• Autorzy: Winnicki Ireneusz , Jasinski Janusz , Pietrek Sławomir , Kroszczynski Krzysztof

Identyfikatory

DOI

10.24425/gac.2022.141176

• Języki publikacji: EN

Abstrakty

EN

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used third-order 3x3 pixels Laplace contour filters including the difference schemes used to derive them. The authors focused on the mathematical properties of the Laplace filters. The basic reasons of the differences of the properties were studied and indicated using their transfer functions and modified differential equations. The relations between the transfer function for the differential Laplace operator and its difference operators were described and presented graphically. The impact of the corner elements of the masks on the results was discussed. This is a theoretical work. The basic research conducted here refers to a few practical examples which are illustrations of the derived conclusions.We are aware that unambiguous and even categorical final statements as well as indication of areas of the results application always require numerous experiments and frequent dissemination of the results. Therefore, we present only a concise procedure of determination of the mathematical properties of the Laplace contour filters matrices. In the next paper we shall present the spectral characteristic of the fifth order filters of the Laplace type.

Słowa kluczowe

EN

transfer function; finite element method; finite difference method; matrices of the third-order Laplace filters; modified differential equations

PL

metoda elementów skończonych; filtr Laplace'a; równanie różniczkowe

• Wydawca: Komitet Geodezji PAN
• Czasopismo: Advances in Geodesy and Geoinformation
• Rocznik: 2022
• Tom: Vol. 71, no. 2
• Strony: art. no. e23, 2022
• Opis fizyczny: Bibliogr. 66 poz., rys., wykr.

Twórcy

autor

Winnicki Ireneusz

• Military University of Technology, Warsaw, Poland

• https://orcid.org/0000-0001-9170-422X

autor

Jasinski Janusz

• Military University of Technology, Warsaw, Poland

• https://orcid.org/0000-0001-5634-3430

autor

Pietrek Sławomir

• Military University of Technology, Warsaw, Poland

• https://orcid.org/0000-0001-9890-8487

autor

Kroszczynski Krzysztof

• Military University of Technology, Warsaw, Poland

• https://orcid.org/0000-0003-1197-9915

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