Helmholtz-Kohlrausch Research Articles

Review Paper: The Helmholtz‐Kohlrausch effect

Abstract— The Helmholtz‐Kohlrausch (H‐K) effect is the influence of color purity on the perceived brightness of a color object (or source). In addition to a review of the effect, a survey of color and brightness‐perception studies from 1825 to the present (including our own studies on disabling glare) is presented. Disabling glare is the blinding experience which results from a bright source in our field of view. There has been a great deal of work on the H‐K effect, and this paper is our personal view of the subject. The H‐K effect has lead to new color‐appearance models which help to describe the brightness/luminance discrepancies, and we will only touch on this subject. It will be shown how the H‐K effect affects many of the displays, mobile devices, and phones. Additionally, how the H‐K effect is involved with our perception at mesopic light levels encountered during night driving will be discussed.

The Brightness of Colour

BackgroundThe perception of brightness depends on spatial context: the same stimulus can appear light or dark depending on what surrounds it. A less well-known but equally important contextual phenomenon is that the colour of a stimulus can also alter its brightness. Specifically, stimuli that are more saturated (i.e. purer in colour) appear brighter than stimuli that are less saturated at the same luminance. Similarly, stimuli that are red or blue appear brighter than equiluminant yellow and green stimuli. This non-linear relationship between stimulus intensity and brightness, called the Helmholtz-Kohlrausch (HK) effect, was first described in the nineteenth century but has never been explained. Here, we take advantage of the relative simplicity of this ‘illusion’ to explain it and contextual effects more generally, by using a simple Bayesian ideal observer model of the human visual ecology. We also use fMRI brain scans to identify the neural correlates of brightness without changing the spatial context of the stimulus, which has complicated the interpretation of related fMRI studies.ResultsRather than modelling human vision directly, we use a Bayesian ideal observer to model human visual ecology. We show that the HK effect is a result of encoding the non-linear statistical relationship between retinal images and natural scenes that would have been experienced by the human visual system in the past. We further show that the complexity of this relationship is due to the response functions of the cone photoreceptors, which themselves are thought to represent an efficient solution to encoding the statistics of images. Finally, we show that the locus of the response to the relationship between images and scenes lies in the primary visual cortex (V1), if not earlier in the visual system, since the brightness of colours (as opposed to their luminance) accords with activity in V1 as measured with fMRI.ConclusionsThe data suggest that perceptions of brightness represent a robust visual response to the likely sources of stimuli, as determined, in this instance, by the known statistical relationship between scenes and their retinal responses. While the responses of the early visual system (receptors in this case) may represent specifically the statistics of images, post receptor responses are more likely represent the statistical relationship between images and scenes. A corollary of this suggestion is that the visual cortex is adapted to relate the retinal image to behaviour given the statistics of its past interactions with the sources of retinal images: the visual cortex is adapted to the signals it receives from the eyes, and not directly to the world beyond.

Confusion between observation and experiment in the Helmholtz–Kohlrausch effect

AbstractThe cause of existing misunderstanding is clarified on the Helmholtz–Kohlrausch (H–K) effect. The misunderstanding is that the effect is the same in magnitude between the variable achromatic color (VAC) and the variable chromatic color (VCC) methods. It comes from the confusion between a single observation and a complete experiment. If both methods are tested in a proper experiment with sufficient observations, then the methods do give different results. The present communication together with a previous article (Color Res Appl 2006; 31: 146–155) will clarify the differences between VAC and VCC methods. For readers' convenience, a simple and accurate experimental method is proposed for grasping the large effect of the VCC method. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 250–253, 2008

Proposal of a new concept for color‐appearance modeling

AbstractA new type of color‐appearance model (CAM) is proposed together with its concept and flow of formulations. The topics described are: (1) The existence of two kinds of color‐appearance models, CAMs previously used and CAMs newly proposed. (2) All the CAMs, previously developed and used, do not predict color‐appearance attribute of perceived lightness of object colors under any illuminations. They may be adequately called “the model for predicting color‐appearance match between object colors under different adapting conditions.” (3) Newly improved CAMs take the Helmholtz–Kohlrausch effect in the VCC method into account. They can determine object colors with the same Tone (equi‐perceived lightness, equi‐whiteness‐blackness, and equi‐perceived chroma) irrespective of hues under reference illuminant. The newly improved models can be named Integrated CAMs. Their applicable fields are described in detail. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 113–120, 2007

Clarification of differences between variable achromatic color and variable chromatic color methods in the Helmholtz–Kohlrausch effect

AbstractThe Helmholtz–Kohlrausch effect consists of two different approaches: the variable achromatic color (VAC) and variable chromatic color (VCC) methods. In this article the difficult conceptual difference between the methods is clarified using new explanations with their schematic figures. The concept of loci with various parameters on B/L or L/Y ratios is completely different between the two methods. The VCC method can determine perceived lightness values for achromatic and chromatic colors in the whole color space. The VAC method gives perceived lightness deviation between reference achromatic color and each of the various test chromatic colors both kept at the same Munsell Value. The VAC method can never give any information on equiperceived lightness to test chromatic colors. Despite the difference between the two methods, misuse of the VAC method is sometimes found for perceived lightness studies of various chromatic colors, because of its ease in observations. An example is shown for the L scale of OSA‐UCS. © 2006 Wiley Periodicals, Inc. Col Res Appl, 31, 146–155, 2006

Chromatic Strengthと知覚白色度の関係

Using psychological experiments, we investigated the perceived whiteness of a white object under 30 types of illuminants. We used the index we developed in an initial study [J. Illum. Inst. Jpn. Vol.83 No.11 (1999)] and modified in a subsequent study [J. Illum. Inst. Jpn. Vol.85 No.5 (2001)] to evaluate the perceived whiteness. The index is proportional to the total chromatic strength of the spectral stimulus at a constant luminance level; it correlated highly with the experimental results, indicating that it can be used to effectively evaluate the perceived whiteness of a white object under various illuminants.Considering the ability of a spectral stimulus to induce brightness and chromatic perception, we investigated the cause of whiteness perception. We found that whiteness perception, the Helmholtz-Kohlrausch effect, the discrimination threshold level of colorimetric purity, and the G0 function studied by Evans are all caused by a basically common color perception mechanism and that they can be explained uniformly by using chromatic strength.

Color space and its divisions

AbstractA synthesis of the author's recent work on color‐order systems and color‐difference evaluation is provided in context of current knowledge and practices. The development of a colorimetric model is demonstrated using Munsell “Celtic crosses” as a model of perceptual space. Issues surrounding color‐matching functions, unique hues, the Helmholtz–Kohlrausch effect, and lightness and chroma crispening are addressed, as is the difficulty of reconciling a difference‐based hue, chroma, lightness model with an Euclidean model. A new lightness scale and treatment of lightness crispening is proposed. The results indicate that, despite problems, relatively simple modified opponent‐color models provide good accuracy in predicting color‐order system and supra‐threshold small color‐difference data. © 2001 John Wiley & Sons, Inc. Col Res Appl, 26, 209–222, 2001

A structural comparison of the Munsell renotation and the OSA-UCS uniform color systems

A structural comparison has been made of the lightness, chroma, and hue scales of the Munsell system, as expressed in the Munsell Renotations, and of the OSA-UCS system. While the lightness scales are similar (except for the adjustment for the Helmholtz–Kohlrausch effect and the inclusion of a “crispening” effect in OSA–UCS), there are significant differences in the chroma scales along the major chromatic axes. Unlike in CIELAB, the increments in X and Z along these axes for equal chroma steps in both systems do not fall on a continuous function. In the two systems, as well as in CIELAB lines connecting colors of equal chroma differences at different Y values point to nonreal origins. These differ among the three systems. A major difference between Munsell and OSA–UCS is the size of the first chroma step away from gray. An experiment has been performed with the result that the OSA–UCS system is in much better agreement with the average observer in this respect than the Munsell system. OSA–UCS exhibits considerably more internal uniformity in terms of X and Z increments between steps than the Munsell system. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 186–192, 2000

Prediction of experimental results on additivity‐law failure

Experimental results on additivity-law failure observed by direct brightness matching are estimated for various combinations of two spectrum colors. The estimations are made by using the prediction equation of the Brightness/Luminance (B/L) ratio effect on chromatic colors, which is based upon the Variable Chromatic Color (VCC) method for the effect. The predicted results confirm the existence of the two types of additivity-law failures called enhancement or cancellation, already reported by several researchers. The prediction equation also clarifies that the effect of additivity-law failure does not change for a wide change of adapting luminance used in observation. Both B/L effect and additivity-law failure can be estimated quite nicely by the same prediction equation without making any modification to it. The Helmholtz–Kohlrausch effect can imply both effects in its wide definition. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 32–42, 2000

Prediction of experimental results on additivity-law failure

Experimental results on additivity-law failure observed by direct brightness matching are estimated for various combinations of two spectrum colors. The estimations are made by using the prediction equation of the Brightness/Luminance (B/L) ratio effect on chromatic colors, which is based upon the Variable Chromatic Color (VCC) method for the effect. The predicted results confirm the existence of the two types of additivity-law failures called enhancement or cancellation, already reported by several researchers. The prediction equation also clarifies that the effect of additivity-law failure does not change for a wide change of adapting luminance used in observation. Both B/L effect and additivity-law failure can be estimated quite nicely by the same prediction equation without making any modification to it. The Helmholtz–Kohlrausch effect can imply both effects in its wide definition. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 32–42, 2000

A colorimetric explanation of the Helmholtz–Kohlrausch effect

The Helmholtz–Kohlrausch effect is related with the chromatic strengths of spectral colors suggested by R. M. Evans. An estimate of the chromatic strengths of spectral colors is given by using the color-matching functions and their combinations. The estimate of the chromatic strength corresponds to “chromaticness per unit luminance” at each spectral color. The derived chromatic-strength function is very similar to the Helmholtz–Kohlrausch effect and the zero-grayness function by Evans for spectral colors. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23: 374–378, 1998

A colorimetric explanation of the Helmholtz-Kohlrausch effect

The Helmholtz–Kohlrausch effect is related with the chromatic strengths of spectral colors suggested by R. M. Evans. An estimate of the chromatic strengths of spectral colors is given by using the color-matching functions and their combinations. The estimate of the chromatic strength corresponds to “chromaticness per unit luminance” at each spectral color. The derived chromatic-strength function is very similar to the Helmholtz–Kohlrausch effect and the zero-grayness function by Evans for spectral colors. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23: 374–378, 1998

Relations between the two kinds of representation methods in the Helmholtz-Kohlrausch effect

There are two kinds of representation methods of the Helmholtz-Kohlrausch effect; one is the Variable-Achromatic-Color method, and the other the Variable-Chromatic-Color method. The following three items are described in detail. (1) How to use and adapt the prediction equations of the two methods to their practical applications. (2) Theoretical derivations of the prediction equations in both methods, and clarification of the simple relation existing between the numerical coefficients used in the prediction equations on the two methods. (3) Logical consistency between the long series of studies on the H-K effect by the author and his colleagues. © 1998 John Wiley & Sons, Inc. Col Res Appl, 23, 288–301, 1998

Helmholtz-Kohlruasch効果におけるVAC法とVCC法の関係

There are two methods of representing the Helmholtz-Kohlrausch (H-K) effect, the VAC method (Variable-Achromatic-Color method) and the VCC method (Variable-Chromatic-Color method). This paper (1) describes how to use and adapt the prediction equations of the two methods to their practical applications, (2) theoretically derives the prediction equations in both methods, and (3) clarifies the relationships between the numerical coefficients used in the prediction equations for the two methods.

Simple estimation methods for the Helmholtz?Kohlrausch effect

Four kinds of simple estimation equations are proposed for the Helmholtz—Kohlrausch effect. Two of them can be used for luminous colors, and the other two for object colors. In each of luminous and object colors, the two estimation equations are given to each of the Variable-Achromatic-Color (VAC) and the Variable-Chromatic-Color (VCC) methods. All the equations are similar in type to the Ware—Cowan equation. They give the ratio between luminance (or metric lightness) of test color stimulus and its equivalent luminance (or equivalent lightness) directly. Though their computations are simple, they can apply to various H—K effects including their adapting luminance dependency. The applicable fields of the proposed equations are wider than those of the Ware—Cowan equation. The proposed equations can be applied to predict the H—K effect within the whole chromaticity gamut including spectral colors, spectral luminosity functions based on direct color matching from 0.01 Td to 100 000 Td using the photopic and the scotopic spectral luminosity functions specified by CIE, equivalent lightness values of NCS colors, and others. © 1997 John Wiley & Sons, Inc. Col Res Appl. 22, 385–401, 1997

Prediction of the Helmholtz-Kohlrausch effect using the CIELUV formula

The Helmholtz-Kohlrausch effect was predicted by using the CIELUV formula. The predictions were done to the chromatic colors in the whole chromaticity gamut including spectral colors by the Variable Achromatic Color (VAC) and the Variable Chromatic Color (VCC) methods. The effect of adapting-illuminance change in the perceived lightness of chromatic object colors was also taken into account in the prediction. The prediction equations by the CIELUV formula gave results quite similar to those by the equation for predicting the Helmholtz-Kohlrausch effect using the nonlinear color-appearance model. Their computational procedures for estimating various effects are very simple and easy to use. © 1996 John Wiley & Sons, Inc.

Prediction of the Helmholtz-Kohlrausch effect (VCC method) using the Swedish NCS system

The existence of the two methods of representation of the Helmholtz-Kohlrausch (H-K) effect was clarified in the previous studies by one of the authors. They are the Variable Chromatic Color (VCC) and the Variable Achromatic Color (VAC) methods. The effect by the VCC method is significantly larger than that by the VAC method, and the former is more effective in visual photometry than the latter. The authors already derived a prediction equation of the H-K effect by the VCC method using the CIELUV formula. In this work, a VCC prediction equation was directly derived from the colorimetric values of the Swedish Natural Color System (NCS). The new VCC equation is almost the same as the VCC equation previously reported. This again clearly suggests the existence of the two representation methods, and the theoretical method used for deriving the previous VCC equation is proved to be correct. © 1996 John Wiley & Sons, Inc.

表面色の明るさマッチング・データとその解析

In order to evaluate the Helmholtz-Kohlrausch effect, heterochromatic lightness matches on 64 Munsell colors of 4/were made by 26 obsevers, and 88 Munsell colors of 6/by 24 observers. A bipartite field subtending a visual angle of 3°×3° with a surround was used. A surround of N4 was used for the test colors of 4/and of N6 for those of 6/. All heterochromatic lightness matches were made under fluorescent light (x =0.3126, y=0.3168; 4551x), and the viewing geometry was normal (0°) illumination with approximately 45°viewing. The individual data obtained by all observers and also their means are given in tabular form and the latter are also given in graphical form. The mean data were examined on the basis of the CIELAR color space, then an experimental formula was derived which gives the correlate for lightness of a surface color in terms of L*, C*, and h°. These results are compared with similar ones reported previously by other researchers. The results obtained in the present study indicate that the lightness of surface colors may be substantially predicted by a rather nonlinear equation of C* than linear one and there is a weak trend whereby the Helmholtz-Kohlrausch effect on surface colors having constant value of C* shows another shallow minimum at h°=300 which has never been reported.

Helmholtz-Kohlrausch効果, 測色純度弁別, およびG0関数について

Helmholtz-Kohlrausch効果, 測色純度弁別, およびG<SUB>0</SUB>関数について

Existence of two kinds of representations of the helmholtz‐kohlrausch effect. II. the models

AbstractA formulation for predicting the Helmholtz‐Kohlrausch (H‐K) effect is given to the new VCC (variable chromatic color) method, which can derive the luminance factors of various chromatic object colors that match in perceived lightness with a fixed achromatic color. By using the formulation, the H‐K effect by the VCC method is predicted within the whole chromaticity gamut including spectral colors. the magnitude of the effect in logarithmic scale by the VCC method is estimated to be twice as large as that by the VAC (variable achromatic color) method previously used. It is also stated that the VCC method is practically more important than the VAC method. the effectiveness of the new formulation is confirmed by comparing its predictions with the observations in two kinds of experiments. © 1994 John Wiley &amp; Sons. Inc.