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6.1 Introduction

Mathematical morphology provides an approach to the processing of digital images that is based on the spatial structure of objects in a scene [Gon92, Har92, Pra91, Soi02]. Unlike linear and nonlinear operators discussed so far, morphological operators modify the shape of pixel groupings instead of their amplitude. However, in analogy with these operators, binary morphological operators may be implemented using convolution-like algorithms, with the fundamental operations of addition and multiplication replaced by logical OR and AND.
Section 6.2 contains a short description of the theoretical foundations of mathematical morphology. Dilation and erosion, the two fundamental morphological operators, are presented in Section 6.3. A number of important operators that are defined in terms of dilation and erosion can also be found in the section. In Section 6.4, the grayscale morphological operators are presented. Following the introduction of the basic operators, Section 6.5 continues with a presentation of several morphological formulations of useful image processing tasks such as edge detection and thinning and several advanced segmentation operators. These include the watershed and distance transforms and a function for connected components analysis of binary images.