Linear image filtration based on loss-less structures

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)

The family Chlorobiaceae

Since the discovery of the green sulfur bacteria and the first description by Larsen (1952), this group of bacteria has gained much interest because of a number of highly interesting features. These include the unique structures of the photosynthetic apparatus and the presence of small organelles, the chlorosomes, which act as light-harvesting antenna. Chlorosomes are very powerful light receptors that can capture minute amounts of light and enable the green sulfur bacteria to perform photosynthesis and to grow at very low-light intensities. This has important ecological consequences, because the efficient light harvesting determines the ecological niche of these bacteria at the lowermost part of stratified environments, where the least of light is available. Furthermore, the strict dependency on photosynthesis to provide energy for growth and the obligate phototrophy of the green sulfur bacteria together with their characteristic sulfur metabolism has provoked much interest in their physiology, ecology, and genomics. The oxidation of sulfide as the outmost important photosynthetic electron donor of the green sulfur bacteria involves the deposition of elemental sulfur globules outside the cells and separates the process of sulfide oxidation to sulfate clearly into two steps. In the phylogenetic-based taxonomy, the green sulfur bacteria are treated as family Chlorobiaceae with the genera Chlorobium, Chlorobaculum, Prosthecochloris, and Chloroherpeton

The Family Chromatiaceae

The Chromatiaceae is a family of the Chromatiales within the Gammaproteobacteria and closely related to the Ectothiorhodospiraceae. Representatives of both families are referred to as phototrophic purple sulfur bacteria and typically grow under anoxic conditions in the light using sulfide as photosynthetic electron donor, which is oxidized to sulfate via intermediate accumulation of globules of elemental sulfur. In Chromatiaceae species, the sulfur globules appear inside the cells; in Ectothiorhodospiraceae, they are formed outside the cells and appear in the medium. Characteristic properties of these bacteria are the synthesis of photosynthetic pigments, bacteriochlorophyll a or b, and various types of carotenoids and the formation of a photosynthetic apparatus with reaction center and antenna complexes localized within internal membrane systems. Phototrophic growth, photosynthetic pigment synthesis, and formation of the photosynthetic apparatus and internal membranes are strictly regulated by oxygen and light and become derepressed at low oxygen tensions. Typically, Chromatiaceae are enabled to the photolithoautotrophic mode of growth. A number of species also can grow photoheterotrophically using a limited number of simple organic molecules. Some species also can grow under chemotrophic conditions in the dark, either autotrophically or heterotrophically using oxygen as terminal electron acceptor in respiratory processe