This book provides a comprehensive overview of morphological image operators, focusing on their mathematical foundations and applications. It is authored by Henk J.A.M. Heijmans and published by the Centre for Mathematics and Computer Science in Amsterdam. The book is structured into 13 chapters, each covering different aspects of morphological image processing. Chapter 1 introduces the basic principles of morphology, including a typical example and the concept of morphological convolution. Chapter 2 discusses complete lattices, Boolean lattices, and regular closed sets, while Chapter 3 explores operators on complete lattices, including adjunctions, openings, and closings. Chapter 4 focuses on translation-invariant operators, such as dilation, erosion, and grey-scale morphology. Chapter 5 delves into adjunctions, dilations, and erosions, including polar morphology and grey-scale functions. Chapter 6 examines openings and closings, covering their algebraic theory and various types, such as annular openings. Chapter 7 discusses hit-or-miss topology and semi-continuity, while Chapter 8 addresses discretization techniques. Chapter 9 explores convexity, distance, and connectivity in image processing. Chapter 10 presents lattice representations of functions, including admissible lattices and function representations. Chapter 11 focuses on morphology for grey-scale images, including semi-flat and flat function operators. Chapter 12 discusses morphological filters, including filters, overfilters, and invariance domains. Chapter 13 covers filtering and iteration, including order convergence, iteration, and the centre operator. The book also includes a bibliography, notation index, and subject index. The content is suitable for researchers and practitioners in the field of image processing and mathematical morphology.This book provides a comprehensive overview of morphological image operators, focusing on their mathematical foundations and applications. It is authored by Henk J.A.M. Heijmans and published by the Centre for Mathematics and Computer Science in Amsterdam. The book is structured into 13 chapters, each covering different aspects of morphological image processing. Chapter 1 introduces the basic principles of morphology, including a typical example and the concept of morphological convolution. Chapter 2 discusses complete lattices, Boolean lattices, and regular closed sets, while Chapter 3 explores operators on complete lattices, including adjunctions, openings, and closings. Chapter 4 focuses on translation-invariant operators, such as dilation, erosion, and grey-scale morphology. Chapter 5 delves into adjunctions, dilations, and erosions, including polar morphology and grey-scale functions. Chapter 6 examines openings and closings, covering their algebraic theory and various types, such as annular openings. Chapter 7 discusses hit-or-miss topology and semi-continuity, while Chapter 8 addresses discretization techniques. Chapter 9 explores convexity, distance, and connectivity in image processing. Chapter 10 presents lattice representations of functions, including admissible lattices and function representations. Chapter 11 focuses on morphology for grey-scale images, including semi-flat and flat function operators. Chapter 12 discusses morphological filters, including filters, overfilters, and invariance domains. Chapter 13 covers filtering and iteration, including order convergence, iteration, and the centre operator. The book also includes a bibliography, notation index, and subject index. The content is suitable for researchers and practitioners in the field of image processing and mathematical morphology.