In practice the relationship between a pixel value

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Unformatted text preview: r any other relevant physical magnitude. In practice, the relationship between a pixel value and the corresponding physical quantity is usually complex and almost always non-linear. The exposure function specifying the relationship between the logarithmic light intensity B and the resulting film density D is almost linear within a certain range. The slope of the linear part is traditionally referred to as the “gamma” value of the photographic material. The term was adopted later to characterize other devices such as the cathode ray tube (CRT), that has a nonlinear relation between the amplitude (voltage) of the video signal and the emitted light. To compensate for this non-linearity a gamma correction can be applied to the video signal before visualizing it with a CRT. 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 26 Gamma correction (2) The gamma correction is based on the gamma function. Where ° is called the gamma value. If a is limited to the interval [0 1], then – independent of ° – the value of the gamma function also stays within [0 1] and the function always runs through the points (0,0) and (1,1). Depending on the value of °, the function can imitated both logarithmic and exponential types of function. Because of its monotony properties the function can easily be inverted that again leads to a gamma function with the new gamma value 1/°: Device ° 2.5 camera light 1.8 to 2.8 Receiver (TV, …) The transfer characteristic of a device with gamma value ° is compensated for by a gamma correction with 1/°. The resulting signal b is proportional to the original light intensity B. CRT, LCD 1/1.956=0.5 1 camera gamma correction corrected signal where s denotes the output signal of a certain device (e.g. a camera). 19.05.2009 Dr. Pierre Elbischger - MIP1/ISAP'SS09 27 Gamma correction (3) Gamma correction denotes a simple point operation to compensate for the transfer characteristics of different input and output devices and to map them to a unified intensity space (“cali...
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