...1
Except in rare instances where the illumination is so intense as to damage the imaging apparatus, as, for example, when the sun burns through photographic negative film and appears black in the final print or scan.
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... sense2
In a typical imaging situation with 480 by 640 images and 256 grey values, this amounts to solving 307200 equations in 257 unknowns: 256 for F and one for K.
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... zero3
This choice is arbitrary, as could have been fixed at any point. However, it is common practice, when working with logarithmic units, to define the maximum quantity as zero (e.g. audio and video recorders typically have signal measurement meters calibrated so maximum signal input corresponds to 0dB), and since is assumed to be monotonic, the constraint makes entirely negative when images are of increasing exposure ().
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... images4
This summation over level sets is reminiscent of Lebesgue integration (e.g. the form of summation in (15) is to the earlier form of the summation given in (9) as Lebesgue integration is to Riemann integration, so we will call it ``Lebesgue summation''.
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... multiplication5
Also known as element-by-element multiplication and denoted by ``.*'' in Octave, or nonstandard proprietary work-alikes such as Matlab.
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