Color measurements

Color measurement is one of the most obvious image quality entities. There has to be a metric that defines how well a camera reproduces colors from the original scene. CIEDE colorimetry standards of the CIE organization have been acknowledged the most usable color difference metrics even though there has been competition between organizations like the Colour Measurement Committee (CMC) and ISO. However, the acknowledgment of the CIEDE colorimetry highlights the fact that the document is approved as a joint international standard between the ISO and CIE organizations (ISO/CIE 11664-6 2014; Habekost 2013).

Color measurements are usually made by capturing images from the Macbeth color chart, whose color values are known precisely (Figure 17). The images are captured in different ambient lights and corresponding color differences are calculated.

Figure 17 Macbeth color chart

The history of the CIE standardization starts as early as year 1931, but the first color difference standard was published in 1976. The first standard published a metric called ∆E, which defines a color difference between an original scene and a captured image in L*a*b* color space. L*a*b* color space was meant to be a color space which is perceptually uniform (Wyszecki and Stiles, 2000), later on it was revealed, that the approximation was not accurate enough (Mokrzycki and Tatol 2012). It is noticeable, that ∆E metric contains both lightness error (∆L = L2 – L1) and color errors as defined in (4). The equation is, in practice, the Euclidean distance in L*a*b* color space between captured image values Lab2 and original values Lab1.

(4) ∆E_ab = (L*₂−L*₁)²+(a*₂−a*₁)²+(b*₂−b*₁)²

Here L* is a luminance value, a* is a green-red chrominance and b* blue-yellow chrominance. Normally the L*a*b* values are average values of uniformly colored test patches. The first version of the standardized color difference metric pointed the way to calculate color fidelity. Until now, the metric has been based on the exact difference between known reference values and captured values. However, the importance of the perceptual color quality is starting to change this method.

Since the first version of CIEs ∆E metric, the standard has been updated first by CMC in 1984 and then twice by CIE in 1994 and 2000. When new equations of ∆E

were published in 1994, also new metrics called chrominance error and hue error were established. The latest equation, ∆E 2000 or ∆E⁰⁰, compensates better for perceptual non-uniformities of the L*a*b* color space and thus correlates better with perceptual color difference than earlier equations (Mokrzycki and Tatol 2012).

Equation 5 contains a ∆E⁰⁰ calculation and shows the extent of its evolution since the first version of the CIEDE standard.

(5) 00 ^{( )2 ( )2 ( )2 ( )( )}

∆L, ∆C, ∆H are lightness error, chrominance error and hue error correspondingly.

SL, SC, and SH represent lightness-, chrominance-, and hue-dependent scaling functions. k values can be used to compensate experimental environments.

However, the in the reference conditions k values are set to value 1. Finally, RT is a rotation function dependent on hue and chrominance and compensate the hue angle characteristics especially in case of blue color. If (5) is expanded to use only L*a*b* values and k parameters, it becomes extremely complicated.

Zhang and Wandell have suggested adding a spatial extension to the ∆E^ab color difference measurements and they named the result S-CIELAB or ∆E^s. The extension transforms an image into an opponent color space and each color space is filtered by a visual spatial sensitivity function of the color space. The visual spatial sensitivity function mimics the human vision system and highlights the color differences for frequencies to which the eye is most sensitive. (Zhang and Wandell 1997)

In year 2003, Johnson and Fairchild improved the S-CIELAB method to work with CIEDE2000 equations (Johnson and Fairchild 2003). Even though the spatial extension of the color difference measurement is not yet accepted to the color difference standards, the same approach is still used in visual noise measurements defined in section 4.2.2.

Changing ambient light makes the color measurement challenging. Whenever the light temperature of the captured scene changes, the spectrum of the luminated light (reflected light from the scene) also changes. This means that the camera system has to adapt to the ambient light and adjust the colors to be same, even if one picture is captured in sunlight and another in fluorescent light. The algorithm, auto white balance (AWB), is one of the most difficult feature to implement in the image processing pipeline. Human brains are extremely good at transforming the visual signal from the eyes according to the ambient light. If the camera system fails to adjust colors correctly, the error is very visible to the human vision system.

Even though ∆E00 is accepted by the ISO standardization organization, ISO still has its own standard to describe color accuracy, ISO 17321. This standard defines a sensitivity metamerism index (SMI), which measures color error of the image.

The maximum value of SMI is 100 which means a perfect color accuracy, in practice this would mean the camera system mimics exactly the human vision system. As an example of the SMI scale, the standard defines value 50, which represent the difference for a certain color illuminated in daylight or in fluorescent light. (ISO 17321-1 2012)

The SMI is calculated as defined in (6).

(6) SMI =100−5.5∆Eab_i

Here ∆Eabi is the mean of the color differences calculated according to CIEDE ∆Eab

from year 1976, but using only eight color patches. As the formula 6 describes, the SMI can have also negative values. (ISO 17321-1 2012)

According to the DxO’s measurements, DSLRs get SMI values between 75 and 85, whereas low-end cameras reach 40. DxO defines SMI as a not very discriminating metric and uses it as an informative value. (DxO Color sensitivity)