Discovering geometric theorems from scanned and photographed images of diagrams

Abstract

This paper extends our work on automated discovery of geometric theorems from diagrams by taking scanned and photographed images instead of images produced with dynamic geometry software. We first adopt techniques of Hough transform and randomized detection algorithms to detect geometric objects from scanned and photographed images, then use methods of image matching to recognize labels for the detected geometric objects, and finally employ numerical-computationbased methods to mine geometric relations among the objects. Experiments with a preliminary implementation of the techniques and methods demonstrate the effectiveness and efficiency of geometric information retrieval from scanned and photographed images for the purpose of discovering geometric theorems automatically.