ABSTRACT
Image analysis aims at extracting information from an image. Image transformations are of three types: unary (one image in and one image out), dyadic (two images in and one image out), and information extraction (image in and information out). The language of mathematical morphology is set theory, topology, lattice algebra, and function. In binary images, each picture element (pixel) is a tuple or a 2-dimensional vector of the (x, y)-plane. The binary image is a matrix containing object (or foreground) pixels of value 1 and nonobject (or background) pixels of value 0. We treat the binary image as a set whose elements are composed of all the pixels of value 1. In grayscale images, each element is a triple (or a 3-dimensional vector); that is, (x, y) plus the third dimension corresponding to the pixel’s intensity value. Sets in higher dimensional spaces can contain other image attributes.
