Mathematical Foundations of Image Processing and Analysis, Volume 1

1

Gray-Tone Images

In this textbook, the term image will have a physical meaning and will refer to a one-, two- or threedimensional (3D), continuous or discrete (including the digital form) radiometric spatial distribution of light (or another radiation) intensities.

1.1. Intensity images, pixels and gray tones

Radiometric images are spatially defined on pixels (contraction of “picture elements”) with intensity values called gray tones. Such images are often abusively called “black and white” images in the common language (panchromatic images is better suited and sometimes used in relation to the visible light and the human eye) [ALL 10; Original 1st ed., 1890]. In this book, they will be naturally designated as gray-tone images. Color images (e.g. three colors according to the human visual perception), multispectral images (e.g. four or five colors as in satellite imagery) [LEE 05] [PET 10; p. 665] and hyperspectral images (i.e. numerous almost monochromatic channels) [CHA 03b] will not be discussed because they require specific frameworks and approaches, still subject to particular mathematical research works.

The term illumination designates the incident light (or another radiation, such as an electromagnetic or nuclear radiation, e.g. gamma rays and X-rays) [DAI 74, HEN 02, BAR 04, HOR 06].

There exist a lot of imaging modalities, in particular for materials investigation, and in biological and medical imaging, but also in many other scientific, engineering or technical fields, ...