Retrieving geometric information from images: the case of hand-drawn diagrams

Abstract

This paper addresses the problem of retrieving meaningful geometric information implied in image data. We outline a general algorithmic scheme to solve the problem in any geometric domain. The scheme, which depends on the domain, may lead to concrete algorithms when the domain is properly and formally specified. Taking plane Euclidean geometry $${\mathbb {E}}$$E as an example of the domain, we show how to formally specify $${\mathbb {E}}$$E and how to concretize the scheme to yield algorithms for the retrieval of meaningful geometric information in $${\mathbb {E}}$$E. For images of hand-drawn diagrams in $${\mathbb {E}}$$E, we present concrete algorithms to retrieve typical geometric objects and geometric relations, as well as their labels, and demonstrate the feasibility of our algorithms with experiments. An example is presented to illustrate how nontrivial geometric theorems can be generated from retrieved geometric objects and relations and thus how implied geometric knowledge may be discovered automatically from images.