This chapter provides a brief introduction to the theory of morphological signal processing and its applications toimage analysis andnonlinear 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-theoreticmethodology 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 | Petros Maragos. Morphological Signal and Image Processing. 2000 CRC Press LLC. http . Morphological Signal and Image Processing Petros Maragos Georgia Institute of Technology Introduction Morphological Operators for Sets and Signals Boolean Operators and Threshold Logic Morphological Set Operators Morphological Signal Operators and Nonlinear Convolutions Median Rank and Stack Operators Universality of Morphological Operators Morphological Operators and Lattice Theory Slope Transforms Multiscale Morphological Image Analysis Binary Multiscale Morphology via Distance Transforms Multiresolution Morphology Differential Equations for Continuous-Scale Morphology Applications to Image Processing and Vision Noise Suppression Feature Extraction Shape Representation via Skeleton Transforms Shape Thinning Size Distributions Fractals Image Segmentation Conclusions Acknowledgment References Introduction 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 .
