Automated Generation of Geometric Theorems from Images of Diagrams
This work addresses the challenge of automated geometric knowledge discovery from images, with potential applications in education and knowledge management, though it appears incremental as it builds on existing techniques like Hough transform and algebraic computation.
The paper tackles the problem of automatically generating geometric theorems from images of diagrams by recognizing objects and mining relations, resulting in a method that effectively produces nontrivial theorems as demonstrated in experiments.
We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.