Introduction

Abstract

In the late 1960s Blum (1967) first suggested that medial loci, later generalized and called symmetry sets and central sets by mathematicians (Yomdin, 1981; Mather, 1983; Millman, 1980), would provide an effective means of representing objects appearing in 2D images. Soon thereafter Blum suggested the extension of medial loci to objects in 3D images. These object representations have since come to have an important role in the description of shape. In this introductory chapter we explore the forms the medial representation of objects can take, and we give some history of its development and use. To start, Section 1.1 places the medial representation of objects into the context of alternative representations.

This chapter sets the context for the subsequent material covered in this book, which is organized in three parts. Part I of the book describes in detail the the mathematical properties of the medial representation and the relation between it and the corresponding object boundary. Section 1.2 of this chapter introduces this material by giving the basic mathematical definition and properties of the medial representation. Section 1.3 cites evidence for medial representations as models of human vision. Part II of the book presents algorithms that have been proposed for going from a boundary to a medial representation or from a medial representation to a boundary representation, and it discusses their performance. Section 1.4 of this chapter overviews such methods, including some that are not detailed later in the book. Finally, Part III of the book covers selected applications of the medial representation in image analysis. These include segmentation, shape characterization, recognition, object labeling, and registration. Section 1.5 of this chapter introduces these applications.