Demystifying the CIE ΔE 2000 Formula

By Carlos Stanza & Jinkai Qian

Understanding the perceptual differences between colors is essential in various fields, such as printing, graphic design, branding, packaging, paint and coatings, textiles, and more! In this context, the Delta E value serves as a crucial metric. Delta E quantifies the disparity between two colors and plays a pivotal role in determining their visual discernibility. Generally, a 1 DE00  is deemed the threshold, indicating that any value below it signifies an imperceptible difference, while a DE00  greater than 1 indicates a perceivable distinction between the colors.

MacAdam ellipse
MacAdam ellipse – Plotted on a chromaticity diagram, each ellipses serve to delineate areas wherein all colors seamlessly blend with the central hue, imperceptible to the average human eye. These ellipses are ten times their actual size, as depicted in MacAdam’s paper.

While Delta E (ΔE) is a valuable metric for quantifying color differences, human color perception is far from uniform. On average, there are more Long (L) wavelength cone photoreceptors in the retinas of human vision system (eyes) than Short and Medium wavelength ones. Due to the this difference, our eyes have a larger tolerance for colors in the 560 nm range than other colors near 400 nm or 700 nm (more light allows higher signal-to-noise ratio). The unequal sensitivity to different colors means that even when two colors possess the same Delta E value, they may appear noticeably different to our eyes due to their chromatic variations.

To address the intricacies of human color perception and achieve more accurate color representation, researchers have undertaken a deep exploration of color vision, resulting in the development of advanced color difference formulas. Among these equations, CIE dE2000 stands out as a prominent example. CIE dE2000 takes into account the non-uniform nature of human vision and embraces the physiological nuances that influence our perception of colors. By considering the influence of lightness, chroma, and hue, the refined CIE dE2000 formula offers a more holistic understanding of color differences. The comprehensive nature of CIEDE2000 renders it an invaluable tool, especially in industries where precise color communication holds paramount importance. Particularly, in the printing and packaging industries!

Here is the CIE dE2000 formula in all its glory (courtesy of http://www.brucelindbloom.com):

dECMC equation from http://www.brucelindbloom.com/index.html?ColorDifferenceCalc.html

The CIE dE2000 formula takes into account several factors to better align with human visual perception. These factors include differences in lightness (L*), chroma (C*), and hue (h). The formula also incorporates corrections for the specific sensitivities of the human eye to different colors, addressing the non-uniformity of color perception. Yes, the formula appears somewhat intimidating and complex, involving various mathematical calculations, but let us break it down into its key components for you:

  • Lightness Difference (ΔL*): Represents the difference in brightness between two colors.
  • Chroma Difference (ΔC*): Measures the difference in color intensity or saturation between two colors.
  • Hue Difference (Δh*): Describes the difference in hue angle between two colors.
  • Chroma and Hue Weighting Functions: These functions adjust the chroma and hue differences based on the lightness and chroma of the colors being compared, accounting for the non-uniformity of human color perception.
  • The DeltaE (ΔE) Value: The final color difference value obtained by combining the calculated differences in lightness, chroma, and hue, along with the weighting functions.

Printing and packaging industries have witnessed a growing adoption of the CIEDE2000 formula, which has become a preferred method for quantifying color differences. In fact, Techkon has equipped its flagship handheld device, SpectroDens 4, with the ability for users to select different color difference equations that align with their specific printing and press requirements, whether it’s CIEDE2000, CIELAB, or any other industry-standard equation.

As depicted in Images 1 & 2 below, users have the flexibility to easily modify each weighting factor value according to their specific requirements. It is important to bear in mind that assigning a larger value than the original factory settings (as shown in the picture) effectively reduces the sensitivity of that attribute. In simpler terms, when operating within the same delta E tolerance, a larger weighting function value allows for more color discrepancies compared to a smaller one.

Image 1 – dE CIE 2000 Function on SpectroDens
SpectroDens 4 Display Screen
Image 2 – SpectroDens’ Multiple dE CIE Formula Functions

The beauty of having a sophisticated spectrophotometer like the SpectroDens 4 lies in its ability to offer an objective and scientific approach to color measurement, eliminating subjectivity and bias from the process. CIE Color calculations are performed instantly! Unlike human observers whose perception of color can be influenced by external factors such as varying lighting conditions, fatigue, and individual differences, the SpectroDens 4 provides unwavering color data.  Aligned with globally acknowledged standards, such as the CIEDE2000 color formula, the SpectroDens 4 becomes your Rosetta Stone of sorts, deciphering the often difficult and abstract language of color communication. But wait there’s more (of course there is!). This advanced spectrophotometer seamlessly integrates with our ChromaQA color QC platform, further amplifying its benefits. By implementing the CIEDE2000 formula in ChromaQA, you forge a unified equation across all press locations, actively nurturing your brand’s color fidelity. And just like that, you can say goodbye to discrepancies and welcome an era of globally harmonized color reproduction!

Eager to explore how our technology leverages CIE formulas to enhance your printing and packaging workflows? Get started here, and one of Techkon’s technical representatives will reach out with an exclusive online-only offer.

…or if you’re curious to see deltaE values through various CIE dE equations for yourself, download our complimentary calculator: deltaE calculator