FCA-Based Two Dimensional Pattern Matching

Abstract

We propose a concept lattice-based approach to multiple two dimensional pattern matching problems. It is assumed that a pattern can be described as a set of vertices (or pixels) and that a small set of vertices around each vertex corresponds to an attribute in a concept lattice. Typically, an attribute should be a succinct characterisation of domain-dependent relevant information about the neighbourhood of the vertex. The set of objects in the lattice is the set of 2D patterns to be matched. Searching in the 2D image is carried out in reference to the intents of lattice concepts. Thus, by searching a small region of the text, one can efficiently identify which sets of pattern objects may potentially be found in a larger environment of that region. As experimental data, we use 2D images derived from microchip design layouts and 2D matching patterns derived from microchip design rules.