Summary of How we measure color difference (ΔE)

## Understanding Color Difference: The $\Delta E$ Metric and CIELAB Color is a crucial aspect of our visual world, but how we describe it can be very personal. To overcome this subjectivity in fields like printing, textiles, and digital displays, we need an objective way to measure color. This is where **colorimetry** and the **$\Delta E$ (Delta E) metric** become essential. ### The CIELAB Color Space To standardize color description, the International Commission on Illumination (CIE) developed various color spaces. One of the most widely used is **CIELAB**, also known as $L^*a^*b^*$. This color space is designed to be **perceptually uniform**. This means that a specific numerical difference between two colors in CIELAB should correspond to a similar perceived visual difference, no matter where those colors are in the color space. While not perfectly uniform, it's a significant improvement over simpler color spaces like RGB or CMYK. CIELAB defines a color using three coordinates: * **$L^*$ (Lightness):** Represents how light or dark a color is. It ranges from $0$ (pure black) to $100$ (pure white). A higher $L^*$ value means a lighter color. * **$a^*$ (Red-Green Axis):** Shows the color's position on the red-green scale. Positive $a^*$ values mean more redness, while negative $a^*$ values mean more greenness. A value of $0$ indicates a neutral gray on this axis. * **$b^*$ (Yellow-Blue Axis):** Shows the color's position on the yellow-blue scale. Positive $b^*$ values mean more yellowness, while negative $b^*$ values mean more blueness. A value of $0$ indicates a neutral gray on this axis. Together, these $L^*$, $a^*$, and $b^*$ values pinpoint a unique color in a three-dimensional space, allowing for precise and device-independent color communication and measurement. > ### Device-Independent Color Space > A color space like CIELAB that describes colors based on human perception, rather than specific device outputs (like RGB for screens or CMYK for printers), ensuring consistent color communication across different mediums. Did you know that the CIELAB color space was designed to approximate human vision, meaning it aims to represent how humans actually perceive color differences more accurately than device-dependent models? ### The $\Delta E$ (Delta E) Color Difference Metric Once colors are represented in a perceptually uniform space like CIELAB, we can quantify the difference between two colors using a metric called **$\Delta E$**, or Delta E (from the German "Empfindung," meaning sensation). $\Delta E$ quantifies the magnitude of the difference between two colors as perceived by the human eye. A higher $\Delta E$ value means a greater perceived difference. #### $\Delta E_{ab}^*$ (CIE76) The simplest form of $\Delta E$, known as $\Delta E_{ab}^*$ or CIE76, calculates the **Euclidean distance** between two colors in the CIELAB space. If we have two colors, Color 1 ($L^*_1$, $a^*_1$, $b^*_1$) and Color 2 ($L^*_2$, $a^*_2$, $b^*_2$), the $\Delta E_{ab}^*$ formula is: $$\Delta E_{ab}^* = \sqrt{\left(L^*_2 - L^*_1\right)^2 + \left(a^*_2 - a^*_1\right)^2 + \left(b^*_2 - b^*_1\right)^2}$$ While straightforward, $\Delta E_{ab}^*$ still has some non-uniformity issues, though less severe than RGB. It often overestimates differences for saturated colors and underestimates them for neutral colors. This led to the development of more advanced $\Delta E$ formulas. > ### Euclidean Distance > In a 3D coordinate system, the Euclidean distance between two points is the straight-line distance, calculated using the Pythagorean theorem, similar to finding the hypotenuse of a right triangle in 2D. #### $\Delta E_{00}$ (CIEDE2000) The CIEDE2000 ($\Delta E_{00}$) formula, introduced in 2000, is the most advanced and widely accepted color difference formula. It more effectively addresses the perceptual non-uniformities of CIELAB by incorporating several **weighting functions** and corrections. These adjustments account for var