Liniowa filtracja obrazów cyfrowych za pomocą struktur bezstratnych

• Autorzy: Wirski R. T. , Strzeszewski B.

Warianty tytułu

EN

Linear image filtration based on loss-less structures

• Języki publikacji: PL

Abstrakty

PL

W artykule przedstawiono nową technikę implementacji filtrów dwuwymiarowych. Polega ona na rozkładzie macierzy modelu Roessera na kaskadowe połączenie rotatorów Givens'a. Dzięki nowatorskiemu zastosowaniu permutacji otrzymuje się strukturę potokową o dużej odporności na błędy obliczeń o skończonej precyzji.

EN

In this paper, a novel two-dimensional FIR filter implementation technique is presented. It is based on a concept of orthogonal filters known from 1-D domain. The key of the algorithm is to represent a 2-D system as a cascade connection of two 1-D systems, which are described by 1-D transfer function vectors, given by (7). Each 1-D system is transformed into an orthogonal system via the synthesis of a paraunitary transfer matrix [5]. As a result, one obtains a cascade connection of two 1-D systems described by orthogonal state-space equations. Then, the equations can be combined to form orthogonal Roesser model matrices (14), and can be implemented using Givens Rotations and delay elements. The technique is illustrated by an example of an edge detection kernel filter whose convolution matrix is given by (15). Following the algorithm presented in the paper, there was obtained the Roesser model (22) and its decomposition into the cascade connection of Givens rotations whose parameters are collected in Tab 1. It was implemented using Audio Video Development Kit Stratix II GX. Givens rotation blocks were built by means of DSP blocks available in FPGA chip. Additionally, a system that realizes the same convolution matrix (15), but based on a direct structure (nine multipliers), was built for comparable purposes. Two tests were performed: an impulse response and sensitivity of frequency response to coefficient changes. The impulse response of both systems is the same up to finite precision errors. The sensitivity is much lower for the rotation structure (Fig. 2) when compared to the direct structure (Fig. 3).

Słowa kluczowe

PL

filtr cyfrowy; przetwarzanie 2-D; filtr ortogonalny; skończona odpowiedź impulsowa

EN

digital filter; 2-D processing; orthogonal filter; finite impulse response

• Wydawca: Wydawnictwo PAK
• Czasopismo: Pomiary Automatyka Kontrola
• Rocznik: 2014
• Tom: R. 60, nr 10
• Strony: 812--815
• Opis fizyczny: Bibliogr. 9 poz., tab., wykr.

Twórcy

autor

Wirski R. T.

• Wydział Elektroniki i Informatyki Politechniki Koszalińskiej, ul. Śniadeckich 2, 75-453 Koszalin

autor

Strzeszewski B.

• Wydział Elektroniki i Informatyki Politechniki Koszalińskiej, ul. Śniadeckich 2, 75-453 Koszalin

Bibliografia

• [1] Zadeh L. A., Desoer C. A.: Linear System Theory: The State Space Approach, McGraw-Hill Series in System Science, New York, NY: McGraw-Hill, 1963.
• [2] Bose N. K.: Multidimensional digital signal processing: Problems, progress and future scopes, Proc. IEEE, vol. 78, no. 4, pp. 590-597, Apr. 1990.
• [3] Roesser R. P.: A discrete state-space model for linear image processing, IEEE Trans. Autom. Control, vol. 20, no. 1, pp. 1–10, Feb. 1975.
• [4] Vaidyanathan P. P.: A unified approach to orthogonal digital filters and wave digital filters, based on LBR two-pair extraction, IEEE Trans. on Circuits and Systems, vol. CAS-32, pp. 673-686, July 1985.
• [5] Wirski R. T.: Synthesis of orthogonal Roesser model for twodimensional FIR filters, in International Symposium on Information Theory and its Applications (ISITA2010), Taichung - Taiwan, Oct. 2010.
• [6] Piekarski M.: Stanowa metoda syntezy macierzy transmitancji cyfrowych filtrów ortogonalnych. Materiały X KK TOiUE, Gdańsk, 1987, ss. 145–150
• [7] Wirski R. T.: On the realization of 2-D orthogonal state-space systems, Signal Processing, vol. 88, pp. 2747–2753, 2008.
• [8] Wawryn K., Wirski R. and Strzeszewski B.: Implementation of finite im-pulse response systems using rotation structures, in Information Theory and its Applications (ISITA), 2010 International Symposium on, Oct. 2010, pp. 606-610.
• [9] Golub G. H. and Van Loan C. F.: Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.