Introduction

Shape plays an important part in the processing of visual information, from art through to science. Within computer vision there have been many applications of shape to aid in the analysis of images, and standard shape descriptors include compactness, eccentricity, circularity, ellipticity, and rectangularity.

This paper describes a shape measure that has received little attention: rectilinearity. One of our motivations in developing a rectilinearity shape measure is to provide a useful tool for the analysis of buildings in aerial photographs. Since many buildings appear rectilinear from an overhead view then such a shape measure could be used in a hypothesis and test paradigm to filter out unlikely candidates which have inappropriate shapes.

As well as filtering out non-rectilinear shapes it is sometimes also useful to retain only non-rectilinear shapes. For example, in order to detect landslide induced changes between a time-lapsed pair of images, rectangular regions of change can be eliminated since they arise from new buildings or fields with altered cultivation patterns.

Note that a variety of rectilinearity measures for polygons which are based only on a measure of their angles can be derived very easily. But such a measure would imply that the polygons with the same angles have the same estimated rectilinearity which is not always acceptable (see Fig. 1).

Figure: Two given $5$-gons have identical angles, but it is natural to expect that $P$ should have a higher estimated rectilinearity than $Q$.