Good morning Tim,

The Helmholtz - Kohlrausch effect and Visual Colour Difference Space

I have been working in the field of colorimetric modelling for many years (see my 2010 PhD thesis posted on RG). I have thereby learned a deep respect for the CIE Standard Observer colorimetry system and also its ambiguity with respect to “visual colour difference space”.  It’s almost uncanny ability to predict colour matches in both surface colour and coloured light experiments is commercially very valuable and worth in-depth academic study.As related in items  2 and 3 of my published papers listed below, the Helmholtz Kohlrausch effect must be regarded as a distinct  post receptor phenomenon  and must be modelled as such.

It is not widely recognised that the scalar basis and unit difference metric of CIE Tristimulus XYZ  and L*a*b* colour space is fundamentally physical rather than psycho-physical and is specified in terms of watts of stimulus power. The resulting complexity of the cause and effect visual difference metric in such spaces is simply evidence of a whole set of unquantified (visual response) parameters.

Clearly the OSA – UCS model and indeed many alternative colour difference models partially address this complex, nonlinear and potentially multi-dimensional phenomenon with varying levels of success. However, note carefully if you will two important features of such models. They all without exception use a data fit approach based on visual match data sets and in each case the resulting visual difference metric is generated by reference to the metric of the CIE L*a*b* colour space.

It follows that colour difference and colour space modelling using colour match data is fundamentally ambiguous and therefore flawed as a basis for modelling the visual response to light stimuli. In consequence I therefore reject this approach and offer a completely different approach.

In my alternative approach an ideal  uniform colour space known as a  Grassmann Structure or sequence of such structures  replace CIE L*a*b* space  as the reference metric. In such spaces Grassmann’s Laws of additive mixture hold exactly true, unit difference value is a strictly constant and the (again ideal) visual colour difference co-ordinates are quantified by well-defined scalar basis vectors. Think if you will of a three dimension space quantified by Lightness Chroma and Hue vectors. In both theory and practice all that remains is to map the quantifying experimental data sets onto this model. The  following three of my published papers give full detail of this process.

"Control of Colour, by Using Measurement and Feedback", D.P. Oulton and I. Porat, J.Text.Inst., 83, No.3, p 453.   1992.

“Notes Toward a Verifiable Vector Algebraic Basis for Colorimetric Modelling” D.P.Oulton, Color Research and Application  2009,Volume 34 No. 2 pp 163 – 169 Publ. John Wiley Interscience New York

“Vector‐based modelling of colour difference: a pilot study of the DE2000 colour difference model” DP Oulton, S Westland - Coloration Technology, 2017 - Wiley Online Library

Regards and best wishes

David.

Good Morning David,

Thank you for your answer. I am looking for a space to use while investigating color naming here, so am looking for a space which is psycho-physical in nature, and accept that it will inevitably be ambiguous and only able to provide approximate results, and will be based on a physical model with specific adjustments for post receptor phenomena.

I read your article “Notes Toward a Verifiable Vector Algebraic Basis for Colorimetric Modelling”, and share your opinion that a color difference metric based directly on tristimulus values would be preferable to the current systems based on CIE L*a*b* and an additional complex calculation.

It seems like there should be some mechanism behind the human perception of color difference, and that this mechanism should be explainable in a more fundamental way than finding a function to fit visual match data sets.

This would seem to be particularly desirable given that even the complex calculations currently used still seem to have room for improvement.

Regards,

Timothy

'morning Tim

Thank you for your reply, You could perhaps try Gaurav Sharma's DE2000 model without further debate; 

I comment further as follows, starting with my 2017 paper

Vector‐based modelling of colour difference: a pilot study of the DE2000 colour difference model

The real problem is that infinitely many three-dimensional colorimetric models  may be constructed that are observer- metameric to what Cohen calls the spectrally defined  'fundamental metamer'.(or FM) of the visual response.

 "Metameric color stimuli, fundamental metamers, and Wyszecki's metameric blacks" JB Cohen, WE Kappauf - The American journal of psychology, 1982 - JSTOR

His papers are a bit difficult but they do offer a way forward. I show in my 2017 paper that Cohen's FM is in effect a full replacement for the metamerically ambiguous  CIELAB  model as a basis for modelling post receptor phenomena such as the Helholtz Kohlrauch effect. My approach would necessarily require the experimental determination of a full set of well specified spectral vectors and  visual experiments  are suggested which seek to quantify observed visual difference changes by visual equivalence and magnitude estimation procedures.. In principle  the members of this set would in aggregate quantify the FM.

Regards

David.

I asked this question originally because I had read several articles which stated that the Helmholtz-Kohlrausch effect increased the perceived brightness of a high chroma color by up to a factor of 2.5, which made me think it was important to model it in when converting from a physical to perceptual color model. There are various formulas to estimate the magnitude of the Helmholtz-Kohlrausch effect, and they generally predict at most a 50% increase in perceived brightness compared to CIE L*a*b* lightness, and predict little difference in the red to yellow region. (“Apparent Greyscale: A Simple and Fast Conversion to Perceptually Accurate Images and Video” Kaleigh Smith, Pierre-Edouard Landes, Joëlle Thollot, Karol Myszkowski 2008 Fig.2 compares various formulas). At least for object surface colors the Helmholtz-Kohlrausch effect is small compared to the effect of the non-linear relationship between physical luminance and perceived lightness, which does make a color with 20% of the physical luminance of white to appear to have 50% of the perceived lightness of white, but applies regardless of chroma.