Stochastic Model for Image Matching Based on Statistical Analysis of Descriptors

The paper considers the problem of establishing correspondences between images based on the analysis of local structural features. This problem is one of the key tasks in computer vision systems and arises in image registration, object tracking, scene analysis, and three-dimensional reconstruction. The main difficulty in solving this problem is the influence of noise, illumination variations, geometric distortions, and scale changes, which lead to instability of feature descriptors and reduce the accuracy of correspondence estimation. A stochastic model for establishing correspondences between images is proposed in this study. The model is based on the statistical representation of keypoint descriptors and the use of probabilistic criteria for evaluating their similarity. Within the proposed approach, descriptors are considered as random feature vectors characterized by specific statistical parameters. Their properties are described using a multivariate probabilistic model that takes into account the covariance structure of the features and the correlation between descriptor components. Descriptor comparison is performed using a statistical similarity measure that accounts for the variability and distribution of features. To describe the geometric relationship between corresponding points of the images, a spatial transformation model is introduced. The parameters of this transformation are estimated using a likelihood-based approach. Within the stochastic framework, the alignment errors between corresponding points are treated as random variables, which allows the parameter estimation process to be formulated as a statistical optimization problem. The developed mathematical framework provides a formal representation of the image correspondence estimation process and enables parameter estimation using maximum likelihood or maximum a posteriori criteria. The modeling results demonstrate that the use of a stochastic approach improves the robustness of the correspondence estimation procedure under noise and other destabilizing factors. The obtained results confirm the feasibility of applying stochastic models to image analysis tasks and can be used in computer vision systems, automated video analysis, and other applied information systems.