Introduction

In this chapter, a study of shape begins. Throughout the remainder of this book we will continue to look at shape in many different ways. Here, the topic is introduced at the pixel level, providing some simple, local operations that modify shapes, changing connectivity, and providing nonlinear ways to treat noise.

Morphological operations may be considered as either the result of set operations, or the result of composition of functions. Both these approaches are described in this chapter, in order to provide the student with the insight to see similarities and suitability. We will find that set-theoretic ways of thinking about morphology are most appropriate for binary images, and functional notation is more convenient for grayscale images. In section 7.5, an application example of combining dilation, erosion, and distance transform for the purpose of edge linking is provided to illustrate the power of these operations.

Binary Morphology

In this section, we first introduce two basic morphological operators, dilation and erosion. We then define opening and closing, two operators that are developed based on dilation and erosion. We also discuss interesting properties of these operators and their applications in solving computer vision problems.