Scientific Imaging

An image is a two-dimensional distribution of brightness or grey levels which can be described as

function

where, x and y are coordinates on the Cartesian plane of the camera sensor whilst the function f is amplitude at the pair of coordinates (x,y). This function is the grey level at that point. A colour image is three functions merged together at that point and can be described as a “vector-valued” function.

rgb function

f is always a positive scalar value

function limits

Meaning, that the value of the function f is some finite value in a range, greater than 0 and less than some designated value.

For a correctly exposed image, the value f will always be a number somewhere on the dynamic range.

Astronomically speaking, the quality of an image depends on a number of factors which include, the seeing conditions, the quality of the telescope optics and the point spread function. In terms of biological imaging, the image quality will depend on the quality of sample preparation, and once again the optical properties of the microscope.

The function f can be characterized by two components, illumination and reflectance, donated by i(x,y) and r(x,y), respectively, which combine as a product to form

function components

where,

illumination component

and

reflectivity component

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