Discovering Geometric Theorems from Scanned and Photographed Images of Diagrams

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9201)


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-computation-based 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.


Shape recognition Pattern matching Theorem discovery Geometric knowledge management 



The authors wish to thank the referees for their constructive comments which have helped improve the paper significantly. This work has been supported by the project SKLSDE-2015ZX-18.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.LMIB - School of Mathematics and Systems ScienceBeihang UniversityBeijingChina
  2. 2.SKLSDE - School of Computer Science and EngineeringBeihang UniversityBeijingChina

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