Mathematical Morphology

This chapter describes the basic operations and applications of mathematical morphology, which is based on lattice theory and random geometry to study geometric structures. It defines the basic operators such as dilation and erosion and structuring elements of binary images and grayscale images. The commonly used image preprocessing strategies are image filtering and image reconstruction. The chapter describes the basic knowledge of morphological reconstruction as well as the basic operations of morphological reconstruction by introducing geodesic erosion, geodesic dilation, and their applications. It also describes the simplest yet effective segmentation algorithm, namely the watershed transform. The chapter introduces the commonly used watershed transforms based on distance, gradient, and control markers. It shows how to extend the mathematical morphology to the color space and then completed the basic operations such as the dilation and erosion in color space.