Multi-Dimensional Interval Algebra with Symmetry for Describing Block Layouts

Abstract

Describing the relative positions of Rectangular boxes on a page is a fundamental task in document layout processing. Typically, this is achieved by comparing quantitative values of the endpoints of the rectangle. Such a representation expresses a property that is basic for the “interval” asa conjunction of relations for the “point”. In this work, we adopt a qualitative interval projection model to describe the relative positions of such blocks using interval algebra, which defines the spatial relation of two points only in terms of precedence, coincidence and post-occurrence. Such relations have not been found very meaningful in document or other media layout con texts since they cannot capture symmetry.

In this work, we propose an extension of interval algebra by defining secondary operators (e.g. “centered”) which are expressed in terms of basic interval algebra operators. By extending the ordering of intervals to higher dimensions, Multidimensional Interval Algebra can capture the notion of tangency and alignment between blocks while retaining the relative size information. We present several examples from the document domain to show that this information is sufficient to identify the layout of block structured formats. While this representation does not provide any immediate benefit to document analysis per se - the fact that it provides a compact yet complete vocabulary enables its use in abstraction tasks such as learning the grammar of a document sets by studying a series of examples.