Recognition of the type of figures by methods of statistical identification (Q2704115)

The author considers a number of random 2D shape classes. Each class arises as a random multiplicative deformation of an ideal star shaped form described by its centroid radii. He establishes a statistical model of the scenario and determines the maximum likelihood classifier for classifying a realization of an unknown class. He applies his theory to discriminating between sand grains with good success. The paper is well written and easy to read.NEWLINENEWLINENEWLINEIntroduction: In experimental sciences one frequently observes objects placedin a Euclidean space \(R^k\), for instance in a plane \(R^2\). Often it is reasonable to suppose that such an object has been obtained from one of \(m\) different types of ideal forms by an individual random deformation of its contour. It is then of interest to try to reconstruct the original form of the object by a method of statistical identification. The aim of this contribution is to show that the procedures of discriminant analysis can be used to resolve such problems.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00040].