Encyclopedia of Color Science and Technology

2016 Edition
| Editors: Ming Ronnier Luo

Minimally Distinct Border

  • Michael H. Brill
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-8071-7_261


In an exactly abutting pair of spatially uniform colored regions, if one of the regions is varied in radiance until the border between the regions is least conspicuous to a human observer, that border becomes a minimally distinct border (MDB) and is seen as having maximal blur and minimal contrast. The term MDB is used both for the border itself and for the psychophysical method used to derive it.

Historical Beginnings

The minimally distinct border was first reported by Boynton and Kaiser [1] in connection with psychophysical experiments. From the beginning, it was realized that the condition of MDB occurs when the two abutting regions have the same luminance. Hence, the condition of MDB is best understood in terms of the properties of luminance. (See next section.)

However, the history of the MDB is not just about luminance [2, 3]. The MDB was first used in an attempt to quantify complete color differences regardless of their size. Previously, whereas small color differences could be quantified by discrimination thresholds, large color differences were assessed by magnitude estimation. Compared to magnitude estimation, the assessment of strength of a visual border seemed to offer greater precision. In such experiments, subjects were asked to define the achromatic contrast that they deemed as equivalent to the chromatic contrast of a given border. When the radiances were titrated so as to produce a condition of MDB – hence equality of luminance –one could then look at the strength of the border as a function of the other color coordinates. Historically, MDB experiments tended to compare a monochromatic light with a reference white, so it was thought that the MDB in such cases quantified saturation or departure from the white. As technology developed to present more light at shorter wavelengths (470 nm and lower), it was observed that the MDB could quantify only a “tritanopic saturation,” because no short-wave-sensitive (blue-sensitive) photoreceptors contributed to MDB. In fact, the MDB was observed to vanish completely for lights that were the same in all but their short-wavelength content – hence the name “tritanopic,” which derives from the nomenclature of color blindness. To quote Boynton [2]: “The blue-sensitive cones […] seem to be free of any serious spatial or temporal responsibilities in vision.”

Luminance and MDB

Luminance of a light was initially thought to be linear in the light’s radiance and to transform perceptually to its brightness. Following this definition, two spectrally different lights were declared to have the same luminance if the radiance of one light was adjusted so its brightness matched the brightness of the other light. Early in the twentieth century, a more precise definition for luminance was devised: Two lights are equally luminous if, when the lights are presented alternately, the perceived flicker vanishes at the lowest frequency of alternation. The practice of finding equally luminous lights using this definition is called flicker photometry.

To be in harmony with both these definitions, in 1924, the Commission Internationale de l’Eclairage (CIE) developed a hybrid definition based on experiments of both sorts: flicker fusion of two alternating lights and direct brightness comparison of two lights at neighboring wavelengths [4]. As defined by the CIE, the luminance of any light is proportional to the integral of its spectral power distribution weighted by a function V(λ) (called the luminosity function) derived from these experiments.

In the next 30 years, it was discovered that V(λ) could not capture all the facts about iso-luminous lights. For one thing, Deane Judd found in 1951 that V(λ) should be modified to have a larger contribution at short wavelengths. Also, the physical size of the light stimulus (field size) was found to have an influence on luminosity, as testified by the 1964 CIE colorimetric standard that was tailored to a 10° field size rather than to the 2° field size previously used. Finally, the luminosity of lights at low (scotopic) radiance follows the spectral sensitivity of the rods rather than the cones of the visual system. The low-light limit of luminance also entailed a transition to the high-light limit through a radiance domain known as the mesopic, in which both rods and cones operate.

Clearly the 1924 CIE definition of luminosity, although ubiquitous in industrial and other practical usage, diverges from what is found in actual visual systems. Therefore, vision researchers prefer to define luminance according to an empirical criterion, such as implied by flicker photometry. Once this definition is adopted, it is found that various other visual phenomena depend only on luminance of the stimulating light. In particular, visual acuity is a function only of luminance. In fact, the evidence supports the characterization of luminance as a channel in human vision, fed by long- and medium-wavelength-sensitive cones, occasionally by rods, and never by the short-wavelength-sensitive cones. The luminance channel is tuned to stimuli of the highest spatial and temporal frequencies perceivable by the visual system.

Using the vision-science definition of luminance described above, the condition of MDB between two abutting light patches occurs when the patches have the same luminance.

Measuring MDB

An MDB experiment finds the relative luminance of a light field as follows. For a fixed reference field, the MDB radiance of a monochromatic test field at wavelength λ is measured. The ratio of the reference to test radiance at MDB is proportional to the test field’s luminance as a function of wavelength.

The MDB used in this way can be an empirical definition of luminance. In fact, because MDB presents the test and reference stimulus simultaneously, it has been touted as superior to flicker photometry as a method of measuring luminance.

MDB studies have been done over a variety of geometric conditions. Typically, the experiments involve a bipartite field of two semicircles (test field and reference field). The semicircles meet at a diameter on which the subject is directed to fixate. Alternatively, if one wants to compare the strength of an MDB with the strength of an achromatic border, one can divide the field into quarters of a circle, the top two comprising the achromatic border and the bottom two comprising the chromatic MDB.

It should be noted that creating the geometric conditions for MDB is not trivial. For example, an achromatizing lens is recommended to remove chromatic aberration, which would otherwise disturb the edge between the abutting fields.

Physiological Basis

The measurement of MDB was possible in macaque retina under several experimental conditions, most notably when the border was moved back and forth in the macaque’s visual field. Two kinds of retinal mechanisms, fast (phasic) and slow (tonic), were examined as possible vehicles for MDB, and evidence favored the phasic mechanism [5].

As with any psychophysical measure of luminance, additivity (i.e., Abney’s law) has been found to be imperfect, but this is hardly surprising since the luminance channel in vision receives inputs from more than one cone channel, and cone response is nonlinear in light intensity. Furthermore, the low-luminance limit must engage the rods as well as the cones, so additivity cannot be a strict property of MDB.

Extension to Mesopic Photometry

Raphael and MacLeod [6] discovered that equating luminance at various mesopic radiance levels (in which both rods and cones enter the function) is correlated strongly with achieving MDB at these levels.



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  2. 2.
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    Kaiser, P.K., Lee, B.B., Martin, P.R., Valberg, A.: The physiological basis of the minimally distinct border demonstrated in the retinal ganglion cells in the macaque retina. J. Physiol. 422, 153–183 (1990)CrossRefGoogle Scholar
  6. 6.
    Raphael, S., MacLeod, D.I.A.: Minimally distinct borders in mesopic vision. J. Vis. 8(17), article 75 (2008)Google Scholar

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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.DatacolorLawrencevilleUSA