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imaginary numbers for the outputs of the Gain-Offset_Gamma f

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AE lover Guest	Posted: Sun Jun 22, 2008 11:58 pm    Post subject: imaginary numbers for the outputs of the Gain-Offset_Gamma f Hi all, I am using the GOG model Y=(gain*X+offset) ^gamma to fit the tone curve of each channel of a monitor. ( X is normalized to be between 0 and 1). My results are a negative offset and non-integer gamma. I get a problem with the low digital values. At a low digital value, the (gain*X+offset) is negative , and thus the (gain*X+offset) ^gamma will be an imaginary number (gamma is around 2.3). Can you please suggest what should I do? Just take the real part, or anything else? Thanks
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Gernot Hoffmann Guest	Posted: Mon Jun 23, 2008 1:03 pm    Post subject: Re: imaginary numbers for the outputs of the Gain-Offset_Gam AE lover schrieb: Quote: Hi all, I am using the GOG model Y=(gain*X+offset) ^gamma to fit the tone curve of each channel of a monitor. ( X is normalized to be between 0 and 1). My results are a negative offset and non-integer gamma. I get a problem with the low digital values. At a low digital value, the (gain*X+offset) is negative , and thus the (gain*X+offset) ^gamma will be an imaginary number (gamma is around 2.3). Can you please suggest what should I do? Just take the real part, or anything else? Thanks Model 1 The curve fitting for pairs xi,yi can be done by minimizing F(yo,G) (your model with two instead of three parameters): ui = yo+(1-yo)*xi Si = ui^G - yi F(yo,G)=Sum(i=1 to M) [Si]^2 As you said, this fails for ui<0 (of course G is noninteger). The standard approach is to set Si=0 if ui<0. I found this advice in one of Henry R.Kang's books, ch.14: Color Technology for Electronic Imaging Devices. For an uncalibrated CRT monitor this is physically somewhat reasonable (a weak explanation) if we interpret ui as a control voltage: For ui<0 the luminance doesn't become negative. For a numerical function minimization which is based on an assumed continuous function F(yo,G), such a definition is obviously a desaster: searching a (relative) minimum for an occasionally jumping function is at least not reliable. Model 2 For a calibrated monitor the model 1 is wrong, because the calibration software tries to establish a behaviour like this model 2: y=yo+(1-yo)*x^G This can be seen from the visually flat slope at the origin for a couple of measured data sets: http://www.fho-emden.de/~hoffmann/measgamma10022004.pdf For LCD/TFT monitors, model 1 is IMHO not the least valid. The tone reproduction curve doesn't follow a nonlinear physical law but a mathematically defined correction for an essentially linear output device, in order to achieve the same behaviour as for a calibrated CRT. Best regards --Gernot Hoffmann
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grADE Guest	Posted: Tue Jun 24, 2008 8:57 am    Post subject: Re: imaginary numbers for the outputs of the Gain-Offset_Gam Hi AE lover, You should look at the ACS CDL specs if you are working on gain offset gamma which i assume means you are working with video or film images. Their specifications relate to a Cross platform specification which means different applications can interpret the Color Correction Data and 'emulate' the same values or correction using their own internal mathematical formulae. The ASC CDL spec is for representing CC Changes where Monitors and calibration are presumed correct. I could not understand otherwise why you are attempting to change a monitors characteristics with simple 2 dimensional math. This may work for CRT monitors but given LCD and Plasmas characteristics 2D math will simply not work. Adrian Hauser Digital Intermediate Color Correction Cutting Edge Sydney On Jun 23, 11:03 pm, Gernot Hoffmann <hoffm...@fho-emden.de> wrote: Quote: AE lover schrieb: Hi all, I am using the GOG model Y=(gain*X+offset) ^gamma to fit the tone curve of each channel of a monitor. ( X is normalized to be between 0 and 1). My results are a negative offset and non-integer gamma. I get a problem with the low digital values. At a low digital value, the (gain*X+offset) is negative , and thus the (gain*X+offset) ^gamma will be an imaginary number (gamma is around 2.3). Can you please suggest what should I do?  Just take the real part, or anything else? Thanks Model 1 The curve fitting for pairs xi,yi can be done by minimizing F(yo,G) (your model with two instead of three parameters): ui = yo+(1-yo)*xi Si = ui^G - yi F(yo,G)=Sum(i=1 to M) [Si]^2 As you said, this fails for ui<0 (of course G is noninteger). The standard approach is to set Si=0 if ui<0. I found this advice in one of Henry R.Kang's books, ch.14: Color Technology for Electronic Imaging Devices. For an uncalibrated CRT monitor this is physically somewhat reasonable (a weak explanation) if we interpret ui as a control voltage: For ui<0 the luminance doesn't become negative. For a numerical function minimization which is based on an assumed continuous function F(yo,G), such a definition is obviously a desaster: searching a (relative) minimum for an occasionally jumping function is at least not reliable. Model 2 For a calibrated monitor the model 1 is wrong, because the calibration software tries to establish a behaviour like this model 2: y=yo+(1-yo)*x^G This can be seen from the visually flat slope at the origin for a couple of measured data sets:http://www.fho-emden.de/~hoffmann/measgamma10022004.pdf For LCD/TFT monitors, model 1 is IMHO not the least valid. The tone reproduction curve doesn't follow a nonlinear physical law but a mathematically defined correction for an essentially linear output device, in order to achieve the same behaviour as for a calibrated CRT. Best regards --Gernot Hoffmann
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Roger Breton Guest	Posted: Tue Jul 01, 2008 4:23 am    Post subject: Re: imaginary numbers for the outputs of the Gain-Offset_Gam I am not as versed in math as Gernot Hoffman -- please see his excellent primers in PDF on his site. And I'm not as versed in programming as Graeme and Gerard, but I have a hunch you'll never be able to fit enough of the measured gamma with a simple power function. Maybe it would help model the relationship with a lookup table? Seems the way the more advanced modeling is going. Roger Quote: Hi all, I am using the GOG model Y=(gain*X+offset) ^gamma to fit the tone curve of each channel of a monitor. ( X is normalized to be between 0 and 1). My results are a negative offset and non-integer gamma. I get a problem with the low digital values. At a low digital value, the (gain*X+offset) is negative , and thus the (gain*X+offset) ^gamma will be an imaginary number (gamma is around 2.3). Can you please suggest what should I do? Just take the real part, or anything else? Thanks
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AE lover Guest	Posted: Thu Jul 03, 2008 11:05 pm    Post subject: Re: imaginary numbers for the outputs of the Gain-Offset_Gam Thank you guys for interesting suggestions. Yes, I will switch to use look-up table, instead. On Jun 30, 7:23 pm, Roger Breton <gr...@videotron.ca> wrote: Quote: I am not as versed in math as Gernot Hoffman -- please see his excellent primers in PDF on his site. And I'm not as versed in programming as Graeme and Gerard, but I have a hunch you'll never be able to fit enough of the measured gamma with a simple power function. Maybe it would help model the relationship with a lookup table? Seems the way the more advanced modeling is going. Roger Hi all, I am using the GOG model Y=(gain*X+offset) ^gamma to fit the tone curve of each channel of a monitor. ( X is normalized to be between 0 and 1). My results are a negative offset and non-integer gamma. I get a problem with the low digital values. At a low digital value, the (gain*X+offset) is negative , and thus the (gain*X+offset) ^gamma will be an imaginary number (gamma is around 2.3). Can you please suggest what should I do?  Just take the real part, or anything else? Thanks- Hide quoted text - - Show quoted text -
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