- Tytuł:
- 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 - Powiązania:
- https://bibliotekanauki.pl/articles/43852806.pdf
- Data publikacji:
- 2022
- Wydawca:
- Polska Akademia Nauk. Czasopisma i Monografie PAN
- Tematy:
-
metoda elementów skończonych
filtr Laplace'a
równanie różniczkowe
transfer function
finite element method
finite difference method
matrices of the third-order Laplace filters
modified differential equations - Opis:
- 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.
- Źródło:
-
Advances in Geodesy and Geoinformation; 2022, 71, 2; art. no. e23, 2022
2720-7242 - Pojawia się w:
- Advances in Geodesy and Geoinformation
- Dostawca treści:
- Biblioteka Nauki
Artykuł