Searching for Geometric Theorems Using Features Retrieved from Diagrams

Searching for knowledge objects from knowledge bases is a basic problem that need be investigated in the context of knowledge management. For geometric knowledge objects such as theorems, natural language representations may not exactly reveal the features and structures of geometric entities, and that is why keyword-based searching is often unsatisfactory. To obtain high-quality results of searching for theorems in plane Euclidean geometry with images of diagrams as input, we propose a method using geometric features retrieved from the images. The method consists of four main steps: 1 retrieve geometric features, with formal representations, from an input image of a diagram D using pattern recognition and numerical verification; 2 construct a graph G corresponding to D from the retrieved features and weaken G to match graphs produced from formal representations of theorems in OpenGeo, an open geometric knowledge base; 3 calculate the degree of relevance between G and the graph for each theorem found from OpenGeo; 4i¾?rank the resulting theorems according to their degrees of relevance. This method, based on graph matching, takes into account the structures of diagrams and works effectively. It is capable of finding out theorems of higher degree of relevance and may have potential applications in geometric knowledge management and education.