Development of a cone space for obtaining a simple representation of receptor and post receptor mechanisms.


We wanted to investigate spatio-temporal interactions between chromatic and achromatic surfaces, such as chromatic induction or chromatic motion. Most attempts to investigate these issues are limited to just a few colors. We developed a set of stimuli that include the gamut of color available on a color video monitor. These colors are equiluminant and equally detectable.


How did we construct the Teufel colors

We first constrained the parameter luminance by determining a plane of equal luminance in SML space. We chose a luminance of 42 cd/m2. By definition this plane also contains the color white with that luminance. Next we constrained detection by determining detection thresholds for a range of colors situated in the plane of equal luminance. We found that the locus of colors having the five-fold detection threshold can be described well as a circle around white in a modified SML space. By going around the circle all colors available within these constraints are included. The radius of the circle is given by five times the value of detection thresholds. We then defined 16 colors that are situated on this circle and separated by segments of equal width on the circle.


What are they good for?

We now have 16 colors on a circle around white of luminance 42 cd/m2 in SML space. The position of these colors can be described by 3 sinusoidal functions. These functions quantify the cone excitations of our colors. From these functions we can compute the excitations of the postreceptoral mechanisms. If we now measure psychophysical thresholds in an induction task using these colors as inducers, we can predict how they depend on cone contrasts according to these mechanisms.


Detailed description of Teufel colors

These are 16 isoluminant, equally detectable and perceptually equidistant colors. They cover the hues available on a standard color monitor and provide a convenient representation for illustrating a difference between receptoral and postreceptoral mechanisms with respect to chromatic induction and adaptation.

The position of these colors in the space spanned by the excitations of S-, M- and L-cones (cone space) has been determined using psychophysical methods such as flicker fusion photometry and detection experiments. In conventional cone space (MacLeod & Boynton 1979) these colors form an ellipse situated on a plane of equal luminance.

Using flicker fusion photometry we first determined the plane of equal brightness for 5 color normal observers. Due to a small contribution of S-cones to the perceived brightness the plane of equal brightness is tilted with respect to the sum of L- and M-cone signals (see Figure a). Generally, scaling of the three base vectors s, m, l of cone space (the cone fundamentals) is set arbitrarily to s=m=l=1 (Kaiser & Boynton 1996). Rescaling cone fundamentals as


s = .06

m = .37

l = .63


yields a simple representation of colors using the polar coordinates r (radius) and f (azimuth angle) in cone space or cone difference space. Equally detectable colors lie on a circle with radius r being equal to the detection threshold in a plane of equal luminance in cone difference space (see figure a). Increase of azimuth angle f corresponds to going counterclockwise around the circle. The 16 colors shown at the end of this page are generated by advancing in steps of equal increments of f around a circle with a radius of five times the detection threshold (as measured in five observers). These results are described in detail in Teufel & Wehrhahn (2000).




The best-fitting sinusoidal functions in cone contrast space that approximate the detection circle are


cS = 0.1006 sin (f - 289.1)

cM = 0.0098 sin (f)

cL = - 0.0040 sin (f - 48.8).





Following the thin arrows in the figure - going from a to b - illustrates how the cone excitations of two of the colors situated at azimuth angles 180 and 270 are transformed into S-cone contrasts (cS), M-cone contrasts (cM) and L-cone contrasts (cL) at corresponding azimuth angles f. To test the validity of this representation the results of many detection experiments of five subjects are plotted (see figure at the right hand side above). Observers had to indicate the occurrence of small rectangular chromatic and isoluminant stimuli to the left or right of the fixation point. Thresholds were computed at 75% of psychometric functions. Each point (cS, cM, cL) is the result of 300 stimulus presentations. These data are well approximated by the cone contrast functions as shown below.



These functions are shown in the figure (panels a – c) below. They describe the contributions of the three receptoral mechanisms to the detection of the respective colors indicated by stars. Using (cS, cM, cL) the contributions to the detection of the 16 colors can be expressed in terms of the postreceptoral chromatic mechanisms blue- yellow { cS - (cM + cL)} and red-green { cM - cL }. These are are shown in panels d and e in the figure below. Since the colors are isoluminant, the receptoral mechanisms S-cone contrast plotted in a. and the post receptoral mechanism blue-yellow plotted in d. are indentical for the 16 colors considered here.

We used these colors to investigate the shift in color of a gray test field surrounded by either of the 16 colors. The three monitor guns (R,G,B) are calibrated using a spectrophotometer. Psychophysical thresholds can then be transformed into values of cone contrasts (cS, cM, cL) and plotted as a function of the azimuthal angle f. The Figure above shows that from the cone contrasts (the receptoral mechanisms) the contributions of the postreceptoral mechanism, red-green and blue-yellow can be computed.

As mentioned above use of these colors in psychophysical experiments requires a calibrated monitor and an otherwise well defined setting.  Monitors used for browsing the internet generally do not satisfy these conditions.





With these caveats the picture below qualitatively mirrors the detectability and hue range of the Teufel colors.  





Cone contrasts as well as CIE coordinates (x, y, Y) of these colors are in the table below (Teufel & Wehrhahn 2000).

This paper also descibes the derivation from flicker fusion photometry and detection experiments and the geometrical considerations leading to the color space described above.





Kaiser PK Boynton RM (1996) Human Color Vision. Optical Society of America, Washington D.C.


MacAdam DL (1942) Visual sensitivities to color differences in daylight. J Opt Soc America 32: 247-274


MacLeod DIA Boynton RM (1979) Chromaticity diagram showing cone excitation by stimuli of equal luminance. J Opt Soc America 69: 1183-1186


Teufel HJ Wehrhahn C (2000) Evidence for the contribution of S-cones to the detection of flicker brightness and red-green. J Opt Soc America A 17: 994-1006


Teufel HJ Wehrhahn C (2004) Chromatic induction in humans: How are the cone signals combined to provide opponent processing? Vision Research 44: 2425-2435.