Pseudogradient Estimation of Digital Images Interframe Geometrical Deformations
A. G. · 2007
The considered PGAs can be directly used in various applied problems of image processing. The algorithms of this class can be applied to image processing in the conditions of a priori uncertainty, they assume small computational expenses and do not require the preliminary estimation of the parameters of the image to be studied. The estimates formed through them are immune to impulse interference and converge to optimal values under rather weak conditions. At an unknown set of the parameters of geometrical deformations model PGAs enable to estimate shifts of each node of image sample grid. At a given IIGD model the processing of the image samples can be performed in an arbitrary order, for example, in order of scanning with decimation that is determined by the hardware speed, which facilitates obtaining a tradeoff between image entering rate and the speed of the available hardware. The mentioned properties make them attractive for usage in real time systems. Unfortunately a limited size of this manuscript does not make it possible to consider some important aspects of this lead of investigations, in particular, the analysis of probabilistic properties and computational expenses at PGAs structural optimization for the situation when the goal function has several extremums. Let us note two more such aspects for further study in the form of the problem definition. A disadvantage of the PGAs when performing the processing of real images is in the presence of local extremums of the goal function estimate characterizing the estimation quality which significantly reduces convergence speed or even may lead to its failure at some realizations in the process of estimate convergence. Besides, algorithms of this class have a comparably small range of operating. At that the estimate convergence character and computational expenses in many respects depend on the image samples local sample size used on various iterations of estimation. Thus the development and study of the methods of a priori and a posteriori optimization of size and plan of the sample used to obtain the goal function pseudogradient is considered to be a vital problem. One of the trends of a posteriori optimization is planned in the part 3.3 in this work. Of works concerned with a priori optimization we can highlight (Samojlov, 2006; Minkina et al., 2005). Modern information systems are characterized by increasing rate of the entering data. It gives rise to the vitality of pseudogradient procedures optimization on criteria of computational expense minimum and iterations number minimum at limitations on computational expenses. We should note that many scientists addressed to the study of precision potentiality of the pseudogradient procedures, in particular, (Albert & Gardner, 1967; Benveniste et al., 1990). Asymptotic rate of convergence of the estimates to be formed has been profoundly studied in works (Chung, 1954; Sacks, 1958), in works (Goodwin & Payne, 1977; Soderstrom, 1981) and others the conditions of asymptotic normality of various pseudogradient procedures have been found, the works (Kushner & Clark, 1978; Tsypkin & Polyak, 1974) are devoted to estimation of asymptotic rate of convergence. However, for practical application of these procedures the investigation of their precision potentiality at a finite number of iterations is of significant importance. Unfortunately, at present this issue has been studied insufficiently. It is due to the fact that at a finite number of iterations an analysis of interframe deformations parameter estimates probabilistic properties is complicated by a large number of factors whose effect cannot be ignored. These are the nature of probability densities and autocorrelation functions of images and interfering noise, the kind of goal function determining the quality of estimation, the parameters of the