Object Identification on Low-Count Images by Means of Maximum-Likelihood Descriptors of Precedents

Abstract

The objects recognition/identification problem is considered. More specifically, the identification of the objects according to their intensity form (shape) on images of a special class is in the focus of the paper. The considered special class of images (low-count images) is related to the registration of low-intensity radiation and, therefore, relatively small numbers of photo-counts. Typical properties of low-count images are low signal-noise ratio, low contrast, and fuzzy shape of imaged objects. Therefore, classical methods intended to recognize images with acceptable quality characteristics are, in general, not sufficiently efficient for images of the considered class; new recognition approaches must be developed for them. Such an approach is proposed in the present paper. The proposed approach is oriented to methods of statistical (machine) learning and is intended to identify objects given by a set of random points (counts). In the framework of the discussed approach, the recognition problem is formalized as the statistical classification (identification) problem for the intensity of point processes with respect to classes formed according to the data observed earlier (precedents). To implement the proposed approach, we reduce the recognition problem to the problem of statistical learning with the maximum-likelihood descriptions of observed precedents. In the framework of the discussed approach, the identification process for intensities to be recognized is treated as follows: for each such intensity, we select a precedent from the already formed database such that it is maximum-likelihood for its description. We extend the notion of precedents up to the class of affine-like form transformations; i.e., the recognized image is determined up to its size and location. In the present paper, the proposed approach is developed up to the algorithmic implementation level. The structure of the obtained algorithms is close to the structure of the well-known EM-algorithm in its variational-Bayesian treatment.