Image Processing Fundamentals

Linearity

It is generally desirable that the relationship between the input physical signal (e.g. photons) and the output signal (e.g. voltage) be linear. Formally this means (as in eq. ) that if we have two images, a and b, and two arbitrary complex constants, w₁ and w₂ and a linear camera response, then:

where R{*} is the camera response and c is the camera output. In practice the relationship between input a and output c is frequently given by:

where is the gamma of the recording medium. For a truly linear recording system we must have = 1 and offset = 0. Unfortunately, the offset is almost never zero and thus we must compensate for this if the intention is to extract intensity measurements. Compensation techniques are discussed in Section 10.1.

Typical values of that may be encountered are listed in Table 8. Modern cameras often have the ability to switch electronically between various values of .

Sensor	Surface		Possible advantages
CCD chip	Silicon	1.0	Linear
Vidicon Tube	Sb₂S₃	0.6	Compresses dynamic range `->` high contrast scenes
Film	Silver halide	< 1.0	Compresses dynamic range `->` high contrast scenes
Film	Silver halide	> 1.0	Expands dynamic range `->` low contrast scenes

Table 8: Comparison of of various sensors