Module 2 : Linearity AGENDA • TVI Vision, Kari Siren • Linearity in general • Theory, what does non-linearity mean when measuring “true” colour • How to measure, compute and characterize linearity error • Demanding case: Linearity in colour grading
TVI Vision TVI Vision cameras • 3 CCD line scan cameras, colour separation by beam splitter • 3 x 1024, 3 x 2048 or 3 x 4096 pixels • speed 5 kiloLines/sec to 35 kiloLines/sec • Up to 12 bit output per channel
Linearity • Relative out put of ideal camera and camera with Peak Linearity Error 3.5% • Output [DN] increases directly proportional to increase of light (photons) without depending the light level. • Non-linearity is in fact small variation of overall system gain K [DN/e-1] • Some times it is necessary to operate with offset to avoid clipping the signal against zero, just take care in calculation….
Theory of measuring colour • Colour is independent of brightness • Colour is proportion of R to G to B • Brightness level should not effect the colour • Why not measure always in same brightness level? • illumination may vary, lamps getting old • target may vary • shadows • dirty factory without people 24/7 you need margin • with the same line you have to measure bright and dark targets • 1% error in linearity is some how visible
X axes is the brightness Y presents out put of 8 bit camera with 3.5% Peak Linearity Error, same linearity error on each channel Color is proportion of R to G to B Right values are R=246 G=143 and B=90 when full brightness Theory of measuring colour
Proportion of R to G vary from 1.8 to 1.3 Proportion of R to B vary from 3.0 to 1.8 Worst effect at level 25% of brightness In this example linearity error start from zero in darkness, many case there is a drastic change near darkness Theory of measuring colour
Theory of measuring colour To visualize the color error • Measured R, G an B values are multiplied with inverse of brightness level • Left you see color in darkness and right in brightness • And with double linearity error it looks like that…..
The standard How to measure, compute and characterize linearity error
The standard • “The linearity error of the illumination setup must be at least a factor of 2 smaller than the linearity error that shall be characterized by this set up.” • To characterize 12 bit camera linearity you must be able to know intensity level with accuracy 13 bit - this is not easy
Demanding case: Grading mink fur color • 3 x 12 bit camera • “white” fur, levels about 3900 DN • “black” fur level can be about 15-25 DN over offset • black/dark brown fur are divided in 16 different groups • difference between groups can be 2-3 DN • difference between groups 0.5 ‰, not %