Linear is an adjective, not a noun!

Linear and nonlinear

Modern image sensor devices such as CCD and CMOS sensors effectively convert photons to electrons: They produce signals whose amplitude is proportional to physical intensity; they are said to be linear.

Video signals were historically processed through analog circuits that had linear response to voltage. Today’s digital video systems are often linear with respect to the arithmetic performed on the pixel values. Video systems are said to be linear.

However, linearity in one domain cannot be carried across to another domain if a nonlinear function separates the two. In video, scene luminance is in a linear optical domain, and the video signal is subject to linear operations in the electrical signal domain. However, OECF and EOCF functions are imposed between the domains. Luminance and pixel value are therefore not linearly related. When you ask an optical engineer if her system is linear, she will say, “Of course!” – referring to intensity, radiance, or luminance. When you ask a video engineer if his system is linear, he will say, “Of course!” – referring to arithmetic on pixel values. However, a nonlinear transform lies between the two systems: A linear operation performed in one domain is not linear in the other.

If your computation involves perception, nonlinear representation may be required. If you perform a discrete cosine transform (DCT) on image data as part of image compression, as in JPEG, you should use coding that exhibits perceptual uniformity, in order to minimize the perceptibility of the errors that will be introduced by the coding process.