An integer linear program for substitution-tolerant subgraph isomorphism and its use for symbol spotting in technical drawings

Abstract

This paper tackles the problem of substitution-tolerant subgraph isomorphism which is a specific class of error-tolerant isomorphism. This problem aims at finding a subgraph isomorphism of a pattern graph S in a target graph G. This isomorphism only considers label substitutions and forbids vertex and edge insertion in G. This kind of subgraph isomorphism is often needed in pattern recognition problems when graphs are attributed with real values and no exact matching can be found between attributes due to noise.Our proposal to solve the problem of substitution-tolerant subgraph isomorphism relies on its formulation in the Integer Linear Program (ILP) formalism. Using a general ILP solver, the approach is able to find, if one exists, a mapping of a pattern graph into a target graph such that the topology of the searched graph is kept and the editing operations between the labels have a minimal cost.This technique is evaluated on both a set of synthetic graphs and a problem of symbol detection in technical drawings. In the second case, document and symbol images are represented by vector-attributed Region Adjacency Graphs built from a segmentation process. Obtained results demonstrate the relevance of considering subgraph isomorphism as an optimization process.

GEM++: A Tool for Solving Substitution-Tolerant Subgraph Isomorphism

“…This work is an extension of [9], which now allows to handle undirected graphs, numeric and symbolic attributes, feature weighting, and induced sugraph isomorphism. The tool is available online, has been designed to be easily installed on several operating systems and may be customized at several levels.…”

“…The following constraints encode the substitution-tolerant subgraph isomorphism problem (see [9] for a justification of these constraints):…”

“…In [9], we have considered the substitution-tolerant subgraph isomorphism as an optimization problem, modeled with a Binary Linear Program (BLP). A first formulation has been described and some tests have shown the efficiency of the approach for a real world application concerning symbol detection.…”

A Novel Graph Database for Handwritten Word Images

“…In the framework presented in this paper the document images are first preprocessed by means of Difference of Gaussian (DoG)-filtering and binarisation to reduce the influence of noise [14]. On the basis of these preprocessed document images, single word images are automatically segmented from the document and labelled with a ground truth 5 . Next, word images are skeletonised by a 3 × 3 thinning operator [15].…”

“…In the last four decades quite an arsenal of algorithms has been proposed for the task of graph matching [1,2]. Moreover, also different benchmarking datasets for graph-based pattern recognition have been made available such as ARG [3], IAM [4], or ILPIso [5]. These dataset repositories consist of synthetically generated graphs as well as graphs that represent real world objects.…”