Inertia tensor as a way of feature vector definition for one-dimensional signatures

Signature is a simple representation of an object or a process in the form of a mathematical function, a feature vector, a geometric shape, or others, intended to uniquely capture the significant characteristics of an object or a process at a certain state. Often, signature is used alone as a feature vector. But in many applications signature to feature space transformation can be done to reveal specific important features of signature itself, e.g. shape or statistical properties, and therefore significantly reduce the number of features. Such transformation can be done in number of ways, e.g. using wavelet or statistical analysis. In this paper we propose a novel technique of revealing different shape and statistical properties of a signature by treating it as a discrete rigid body and computing its inertia tensor and mass center coordinates. We study two basic cases of different mass distribution. We demonstrate the use of this method of surface analysis of ceramic parts manufactured by layered manufacturing technique.