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

100%

Winnicki I. , Pietrek S. , Jasinski J. , Kroszczynski K.

tom Vol. 71, no. 2

art. no. e26, 2022

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.

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

80%

Poczekajło P. , Suszyński R.

tom R. 96, nr 9

80--84

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.

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.

Application of the image analysis technique for textile identification

60%

Drobina R. , Machnio M. S.

tom Vol. 6, no. 1

40--48

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.