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Liniowa filtracja obrazów cyfrowych za pomocą struktur bezstratnych

Wirski R. T., Strzeszewski B.

Pomiary Automatyka Kontrola

2014

R. 60, nr 10

812--815

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.

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).