2. Multidimensional Image Models and Processing

The problems of developing mathematical models and statistical algorithms for processing of multidimensional images and their sequences are presented in this chapter. Different types of random fields are taken for the basic mathematical image model. This implies two main problems associated with image modeling, namely, model analysis and synthesis. The main attention is paid to the correlation aspect, i.e. evaluation of the correlation function of a random field generated by a given model and, vice versa, development of a model generating a random field with a predetermined correlation function. For this purpose, new models (tensor and wave) and new versions of autoregressive models (with multiple roots) are suggested. The problems of image simulation on the curved surfaces are considered. The suggested models are used to synthesize the algorithms of multidimensional image processing and their sequences. The tensor filtration of imaging sequences and recursive filtration of multidimensional images, as well as the asymptotic characteristics of efficiency of random field filtration on grids of arbitrary dimension are suggested. The problem of object and anomaly detection on the background of interfering images is considered for the images of any dimension, e.g. for multi-zone data. It is shown that four equivalent forms of the optimal decision rule, which reflect various aspects of detection procedure, exist. Potential efficiency of anomaly detection is analyzed. The problems of alignment and estimation of parameters for interframe geometric image transformations are considered for multidimensional image sequences. A tensor procedure of simultaneous filtration of multidimensional image sequence and their interframe displacements are suggested. A method based on a fixed point of a complex geometric image transformation was investigated in order to evaluate large interframe displacements. Options for adaptive image processing algorithms are also discussed in this chapter. In this context, pseudo-gradient procedures are taken as a basis, as they do not require preliminary evaluation of any characteristics of the processed data. This allows to develop the high-performance algorithms that can be implemented in real-time systems.