One of the main tasks of image preprocessing is to improve the quality of images.
The image quality is characterized by several characteristics. One of the main objective characteristics among them is the image contrast. The image contrast is considered as a dimensionless value that characterizes (quantitatively or qualitatively) a significant or noticeable difference between characteristics of different areas of the image.
The total image contrast is determined generally considering the contrast of particular combinations of elements of the image (objects and background).
Several approaches for determination the contrast value of the image elements (the kernels of contrast) which are used in different applications are known. The great variety of definitions of contrast is very inconvenient. Such situation complicates the solution of many applied tasks as well as it complicates the carrying out comparative analysis of the achieved results for different methods of image contrast enhancement.
A significant disadvantage of the known definitions of the contrast value of image elements (the kernels of contrast) is their dependence on linear transformations of the brightness scale of image.
A comparative analysis of various definitions for quantitative assessment of the image contrast was held. The results of the research of the influence of linear transformations of image brightness scale on the value of quantitative assessment of the contrast for different definitions are given.
Generalized definition and linear definition of the contrast of the image elements on the base of existing requirements for contrast determination under condition of their invariance to linear transformations of the brightness scale are proposed.
Proposed generalized definition and linear definition of contrast of the image elements meet the requirements of asymmetry, equality of entering arguments, uniqueness and certainty of conditions under which equality to zero and extreme values of contrast are achieved. The linear description of contrast satisfies the condition of proportionality of contrast value to the increment of the argument values.
The interconnection of the offered contrast definition with well-known definitions of Nesteruk-Porfyryev contrast and Vorobel contrast are given using transformation coefficients.
The requirements for the metric in the metric space (the axiom of identity, symmetry and triangle inequality) are performed for linear description of contrast. The module of linear contrast in combination with the set (space) of brightness values of image elements forms the Euclidean metric space.