Mathematical Foundations of Image Processing and Analysis, Volume 1

3

Binary Images

Binary images are essentially obtained by preliminary processings of gray-tone (or color or other) images. They are spatially defined on pixels (‘picture elements’ contraction) and take only two values, 0 or 1, hence suggesting their name comes from the computer sciences and engineering field.

3.1. Scene, objects and context

A binary image is generally the result of one (or several) gray-tone (or color or other) image(s) of a scene stage (often partially) observed, with real objects (e.g. powder material, living cells, fibers textiles, cars on a highway and stars in a galaxy), in a particular context (see section 1.2).

Objects with one or more common or similar properties (e.g. physical, chemical or/and geometric) constitute a part or component of the considered binary image(s). A part or a component is called (1) phase (e.g. in the field of Materials Sciences and Engineering) and (2) embedding phase (i.e. a matrix) for the phase that contains the other phases, (3) population (e.g. in Biology), (4) collection (e.g. in Botany), etc., according to the situations covered and the disciplinary areas concerned.

3.1.1. Types of collection of objects

There are basically two major types of collections of objects composing a scene: (1) isolated or dispersed objects and (2) contiguous or aggregated objects. They can be spatially arranged in clusters, or more or less can fill in the available ambient space.

An isolated object [RUS 91; p. 19] [SAX 95; Chapter II] is not in contact ...