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

Winnicki Ireneusz, Jasinski Janusz, Pietrek Sławomir, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 2

art. no. e23, 2022

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.

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

Winnicki Ireneusz, Pietrek Sławomir, Jasinski Janusz, Kroszczynski Krzysztof

Advances in Geodesy and Geoinformation

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2022

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Vol. 71, no. 2

art. no. e26, 2022

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 fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method – FDM and finite element method – FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method.

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Ortogonalna realizacja potokowego filtru Laplace'a do przetwarzania obrazów medycznych 2D

Poczekajło Paweł, Suszyński Robert

Przegląd Elektrotechniczny

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2020

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R. 96, nr 9

80--84

PL

W artykule przedstawiono dwie realizację filtru Gaussa 1D. Pierwsza oparta jest na bezpośredniej implementacji splotu, druga oparta została na filtrze ortogonalnym realizowanym za pomocą rotatorów Givensa. Obie realizacje został przeanalizowane pod kątem wrażliwości na kwantowanie współczynników dla 8-, 16- i 24-bitowych rejestrów. Wyznaczono i porównano błędy średniokwadratowe charakterystyki amplitudowej oraz błędy dla odpowiedzi systemu na pobudzenie losowym szumem i deltą Kroneckera.

EN

In the paper, two realizations of 1D Gauss filter are presented. The first realization is based on direct structure with convolution, in the second orthogonal filter with use Givens rotations is realized. Both systems are analyzed of sensitivity on coefficient quantization for 8-, 16- and 24- bits length of register. Also determined mean squared errors for amplitude characteristices, impulse responses and responses on noise excitation.

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Testing Texture of VHR Panchromatic Data as a Feature of Land Cover Classification

Lewiński S., Aleksandrowicz S., Banaszkiewicz M.

Acta Geophysica

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2015

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Vol. 63, no. 2

547--567

EN

While it is well-known that texture can be used to classify very high resolution (VHR) data, the limits of its applicability have not been unequivocally specified. This study examines whether it is possible to divide satellite images into two classes associated with “low” and “high” texture values in the initial stage of processing VHR images. This approach can be effectively used in object-oriented classification. Based on the panchromatic channel of KOMPSAT-2 images from five areas of Europe, datasets with down-sampled pixel resolutions of 1, 2, 4, 8, and 16 m were prepared. These images were processed using different texture analysis techniques in order to discriminate between basic land cover classes. Results were assessed using the normalized feature space distance expressed by the Jeffries–Matusita distance. The best results were observed for images with the highest resolution processed by the Laplacian filter. Our research shows that a classification approach based on the idea of “low” and “high” textures can be effectively applied to panchromatic data with a resolution of 8 m or higher.

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Application of the Image Analysis Technique for Estimating the Dimensions of Spliced Connections of Yarn - Ends

Drobina R., Machnio M.S.

Fibres & Textiles in Eastern Europe

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2006

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Vol. 14, no. 3 (57)

63--69

EN

In order to determine the geometrical dimensions of the spliced connections of yarn-ends, an algorithm was elaborated using the image analysis technique to determine their dimensions. By applying a Laplace filter, an optimum quality of images with distinguished regions of homogeneity was achieved. The ‘Arithmetic Operations’ procedure was used to determine the geometrical dimensions of the spliced yarn-ends, and the small random error values (below 0.6%) of the average value of measurement results give evidence of the high repeatability of the results. The algorithm of image digitalisation we proposed, together with measurements of the geometry of spliced connections of yarn ends, enabled their identification. The connection of yarn-ends by splicing was realised with the use of the Jointair 4941 splicing-device from Mesdan.

PL

Przeprowadzono cyfrową analizę obrazu zaplatanych połączeń końców przędz wykonanych na urządzeniu zaplatającym Jointair 4941 firmy Mesdan. Opracowano algorytm wyznaczania wymiarów geometrycznych zaplatanych połączeń końców przędz oraz przeprowadzono cyfrową analizę przetwarzania obrazu. Następnie dokonano wyboru techniki obróbki obrazów i rodzaju filtra przetwarzania maski obiektu, dzięki której uzyskano redukcję zakłóceń zdigitalizowanego obrazu. Dzięki zastosowaniu techniki filtra Laplace’a uzyskano obrazy z wydzielonymi obszarami jednorodności maski obiektu. Do wyznaczenia wymiarów geometrycznych zaplatanych połączeń końców przędz wykorzystano procedury „Arithmetic Operations”, a uzyskane wyniki, w tym stosunkowo małe wartości błędów pomiarów świadczą o wysokiej powtarzalności wyników. Zaproponowany algorytm digitalizacji obrazu zaplatanych połączeń końców przędz umożliwił stosunkowo pełną i dokładną identyfikację tych połączeń.

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Application of the image analysis technique for textile identification

Drobina R., Machnio M. S.

Autex Research Journal

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2006

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Vol. 6, no. 1

40--48

EN

Computer image analysis techniques used for identifying textile products, especially linear textile products, are presented in this paper, together with a brief review of the historical development of these methods. Automatic and semi-automatic image correction methods are described, which are often applied for identification of linear textile products, and can also be used to identify spliced yarn-end connections.