Shape Descriptors

Abstract

After having explored ways for describing fabrics as a whole, we will now turn to the quantitative description of individual shapes. Quantifying the geometry of outlines of two dimensional sections is more difficult than one might think at first. This is because there are many aspects of ‘shape’ that may be important, and different aspects may be important in different contexts. In the context of deformation and strain, for example, the lengthening or flattening of grains may be the most important aspect, while in the context of sedimentary maturity, roundness or smoothness versus jaggedness may be the defining quality. When trying to describe shape, one is often faced with the problem of defining a ‘standard shape’ from which the ‘interesting shape’ deviates, and one is asked to define the type of deviation and measure the ‘amount’ or ‘intensity’ of it. Occasionally, there is a theory that provides a definition for the standard state and means for quantifying the deviations—the mechanical theory of deformation is a case in point. However, sometimes shape descriptors are founded on the ‘hunch’ of a researcher who has gathered a lot of experience with a certain class of geometries and who realizes which are the interesting cases, and which are the defining features. Even though it may not appear to be a particularly scientific occupation in itself, quantitative description has great merits, as it is the first step—and often a defining one—in the process of scientific research.