Spatial Pattern Discovering by Learning the Isomorphic Subgraph from Multiple Attributed Relational Graphs

Abstract

Inexact graph matching has been widely investigated to relate a set of object/scene primitives extracted from an image to a set of counterparts representing a model or reference. However, little has been done to address how to build such a model or reference. This paper develops the theory for automatic contextual pattern modelling to automatically learn a parametric pattern ARG model from multiple sample ARGs. The learned pattern ARG characterizes the sample ARGs, which represent a pattern observed under different conditions. The maximum-likelihood parameters of the pattern ARG model are estimated via the Expectation-Maximization algorithm. Particularly, for Gaussian attributed and relational density distribution assumptions, analytical expressions are derived to estimate the density parameters of the pattern ARG model. The pattern ARG model with Gaussian distribution assumptions is therefore called the Contextual Gaussian Mixture model. The theory and methodology is applied to the problems of unsupervised spatial pattern extraction from multiple images. The extracted spatial pattern can be used for data summarization, graph matching, and pattern detection. One immediate application of this newly developed theory will be information summarization and retrieval in digital image and video libraries.