TY - JOUR N2 - 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. L1 - http://journals.pan.pl/Content/124839/PDF/e23_int.pdf L2 - http://journals.pan.pl/Content/124839 PY - 2022 IS - No 2 EP - e23 DO - 10.24425/gac.2022.141176 KW - transfer function KW - finite element method KW - finite difference methods KW - matrices of the third-order Laplace filters KW - modified differential equations A1 - Winnicki, Ireneusz A1 - Jasinski, Janusz A1 - Pietrek, Slawomir A1 - Kroszczynski, Krzysztof PB - Commitee on Geodesy PAS VL - vol. 71 DA - 2022.10.24 T1 - The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters SP - e23 UR - http://journals.pan.pl/dlibra/publication/edition/124839 T2 - Advances in Geodesy and Geoinformation ER -