infocus #48 December 2017 How not to be a Circle: Dimensionless Ratios as Shape Descriptors

DOI: 10.22443/rms.inf.1.155

Ratios of size measurements that are formally dimensionless are provided by most image analysis systems as parameters intended to describe the shape of objects. The two most common are aspect ratio (which is measured in several ways) and formfactor (which also has other names). These are intended to provide complementary descriptions of deviations of the shape from a circle, one representing elongation and the other boundary irregularity. Measurement of the aspect ratio of a variety of shapes based on different definitions for the “length” and “breadth” values used to calculate the ratio, does not indicate that any of the various methods in common use offers a clear advantage in all cases. Formfactor describes only a narrow class of deviations from an ideal circular shape, and when applied to a variety of natural objects provides only weak separation.

This paper compares the values obtained with thesemeasurements, and shows that choosing a particularmodel or models to describe or compare shapes within a narrow range of objects can be useful, but requires careful consideration of what each calculation represents. None of the models consistently corresponds to the visual impression of the shape of objects.