This chapter provides a brief introduction to the theory of morphological signal processing and its applications to image analysis and nonlinear filtering. By ‘‘morphological signal processing’’ we mean a broad and coherent collection of theoretical concepts, mathematical tools for signal analysis, nonlinear signal operators, design methodologies, and applications systems that are based on or related to mathematical morphology (MM), a set-and lattice-theoretic methodology for image analysis. MM aims at quantitatively describing the geometrical structure of image objects. Its mathematical origins stem from set theory, lattice algebra, convex analysis, and integral and stochastic geometry. It was initiated mainly by Matheron [42] and Serra [58] in the 1960s. Some of its early signal operations are also found in the work of other researchers who used cellular automata and Boolean=threshold logic to analyze binary image data in the 1950s and 1960s, as surveyed in [49,54]. MM has formalized these earlier operations and has also added numerous new concepts and image operations. In the 1970s it was extended to gray-level images [22,45,58,62]. Originally MM was applied to analyzing images from geological or biological specimens. However, its rich theoretical framework, algorithmic efficiency, easy implementability on special hardware, and suitability for many shape-oriented problems have propelled

its widespread diffusion and adoption by many academic and industry groups in many countries as one among the dominant image analysis methodologies. Many of these research groups have also extended the theory and applications of MM. As a result, MM nowadays offers many theoretical and algorithmic tools to and inspires new directions in many research areas from the fields of signal processing, image processing and machine vision, and pattern recognition.