ELEN0450 · Multimedia Systems

Lecture 3

Colorimetry & color spaces

How we describe color to match

the human eye and save bits

www.viulab.be

Recap: where we are in the pipeline

2

Last lecture: How a digital picture becomes numbers sampling, bit depth, and file formats

Definition of a digital image, bit depth and indexed-colors, dithering, raster versus vector image, and image format.

This lecture: the human visual system and color spaces.

Representation

Digitization

Acquisition Capture

Compression Storage

Distribution Transmission

Display

Render

Scope of the course

3

What you'll be able to do

Why this lecture is built this way

Color is physics (light) + biology (the eye) + engineering (models).

We follow that chain: spectrum → cones → CIE numbers → color spaces → bit-savings.

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces

Natural scenes

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Natural scenes are made up of objects that are:

• Either self-luminous (the sun, a light bulb, etc.), called sources,
• or reflect or transmit light coming from the sources to the visual observer or the camera.

The natural scene light is projected to the retina or a camera sensor by either the iris and crystalline lens or a camera lens, creating still or moving images.

Light spectrum

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Monochromatic radiations

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Monochromatic radiation contain only one wavelength, with a one-to-one correspondence between color and wavelength. They can be seen in a rainbow and are very saturated.

• Yet, we perceive more color in a natural scene than in the rainbow (e.g., white, pink, pastel colors, etc.).

A spectrum is composed of several monochromatic radiations (several wavelengths).

Monochromatic radiation

Spectrum

Spectral power distribution

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Monochromator - Newtons prism

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A monochromator delivers light of a single wavelength from a light source with broad spectrum.

• Control which wavelength to isolate based on the angle of prism.

Color vision

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A Simplified Functional View of Photoreceptors

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Image formation

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Surfaces reflect selectively

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Spectral sensitivity of the eye

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Relative percentage of photons absorbed assuming

lights at each wavelength have the same power/energy

Normalization

The brain only receives LMS signals, not lights

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A particular LMS combination leads to a particular color sensation.

This is a huge dimensionality reduction: the light spectrum is a very high dimensional vector (numerous wavelengths) but is transformed by the retina to only a three-dimensional vector!

The brain’s interpretation of colors is not only physical

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Our brains interprets color not only based on the stimulus but also based on what he knows of the objects and the environment.

What color is this dress?

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The LMS color space

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LMS color space. By expressing any light’s color as a (L, M, S) triplet, we have inherently defined a 3D color space, in which every color is a point.

Questions:

1. Does any arbitrary point in the LMS space correspond to a color?
2. Will there be multiple lights that correspond to the same point, i.e., color in the LMS space?
3. What if we uniformly double the power at each wavelength? How would the corresponding color change?

Calculating the total cone responses

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Metamerism

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In colorimetry, metamerism is a perceived matching of colors with different (nonmatching) spectral power distributions.

• Colors that match this way are called metamers.
• Hence, we can fool our visual system and reproduce most colors with few wavelengths.

Implication of metamers

Two different spectra can excite the S,M,L cones identically → they look the same: they are metamers.

This is why a 3-primary display can fool the eye (more on this in Session 6)

Can there be no solution?

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Seeing impossible colors

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Try crossing your eyes until these two squares mix!

What do you see?

Color Gamut of the Human Visual System (HVS)

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HVS Color Gamut: the set of all the colors that human can see.

• The HVS color gamut encapsulates all the LMS points for which the system of linear equations below has a non-negative solution.
• In reality, the gamut has no boundary, since we can arbitrarily increase the light power and this 3D volume will extend to infinity.

Color deficiency

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces

The matching problem

How do we specify a color precisely, so that anyone can recreate it?

Idea: match any test color by mixing 3 fixed monochromatic primary lights.

The three amounts needed = the color's coordinates.

The color matching experiment

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CIE 1931 Color Matching Experiments

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Spectral Locus in the CIE 1931 RGB Space

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Expressing arbitrary light using color matching functions (CMFs)

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A Note on “RGB”

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• There is no one single definition of “red”, “green", and “blue”.
• Usually “RGB” is just synonyms for “primary lights", which usually are so chosen that they look red, green, and blue.
• Primary lights don’t have to be monochromatic spectral lights.
• A color space must define what “one unit” of each primary light is.
• In CIE 1931 RGB color space, the “unit system” is that 1 unit of R, G, and B provides the same color as a special light called “Equal-Energy White”, which has the same power over all wavelengths.

How to explain the color matching experiment?

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Intuition behind this experiment

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Why do we only need three primary colors?

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If only two primary colors: the system of equations has two unknowns with three equations, which generally doesn’t have a solution, i.e., no way of finding a match, generally. Over-determined system.

More than three primaries: more unknowns than equations, so there are infinitely many ways of combining the primary lights to match the target color. Under-determined system.

Geometric transformation perspective

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So far we’ve seen two ways to express a color in a 3D space:

• A color can be expressed as its three cone responses (l, m, s)
• A color can also be expressed as the amount of primary lights (r, g, b) needed

How are the two expressions related?

Expressing a color from the [l, m, s] coordinate system to the [r, g, b] coordinate system is a geometric transformation.

Geometric transformation perspective

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Equivalently, it’s a transformation of the coordinate systems (color spaces)!

• Because the transformation matrix is constant, metamers in RGB space are metamers in LMS space too.

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Transformation matrix from the RGB

space to the LMS space

RGB

space

LMS

space

CIE 1931 RGB ⟷ LMS Spaces

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A Slight Issue with CIE RGB Color Space

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Issue: Some colors are expressed in negative RGB values, which is mathematically OK but not very intuitive.

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Objective: design a color space so that all colors have positive values.

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How? Transforming the coordinate system so that all colors are in the positive quadrant

Color-matching functions → CIE XYZ

CIE RGB to XYZ Color Space Transformation

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XYZ to RGB transformation matrices.

Pure red (R,G,B)=(1,0,0) → (X,Y,Z)=(0.394, 0.212, 0.019)

x = 0.394/0.625 = 0.63, y = 0.212/0.625 = 0.34, z=0

→ red lands at (0.63, 0.34, 0) on the CIE XYZ diagram.

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces

Scaling the intensity of a light

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The Geometry of chromaticity

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Properties of the chromaticity

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The xy-chromaticity diagram

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Linear transformation

Interpreting the xy-Chromaticity Plot

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1. The curve is the spectral locus.
2. Points on locus: spectral lights.
3. Connect two points on the locus: all the colors that are can be produced from mixing those two spectral lights. Because any point on a line segment is a positive linear combination of the two end points.

Interpreting the xy-Chromaticity Plot

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4. Points inside locus: colors of nonspectral lights. They can be produced from some combination of other lights.
5. Points outside locus are imaginary colors; can’t be produced from any combination of real lights.
6. The area enclosed by the spectral locus represents the gamut of human visual system, i.e., all the colors we can see.

Gamut of a color space

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The gamut of a color space is the specific range or subset of colors that can be accurately represented, displayed, or captured by a device or defined within a color space.

• Pick three points on or inside the locus as the primary lights.
• A point inside the triangle is a color that can be physically produced by mixing the chosen primary lights because every point inside a triangle can be expressed as a positive linear combination of the vertices.

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Colors outside the triangle but inside the spectral locus are real colors, but they can’t be physically produced by mixing the primary lights of this color space.

Another way to put it: the three chosen primaries form a color space, and the triangle represents the color gamut of the color space.

• The actual gamut of a color space is 3D (considering the luminance dimension)
• Primary lights does not need to be spectral lights.

Representing a color space in the xy-chromaticity plot

Color that can’t be produced from these two color spaces

Implication of this triangular limitation

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No color space made of physically real lights can reproduce all visible colors.

No matter how many primaries are used in the color space.

Why? Can you give the intuition?

The locus is convex. No polygon whose vertices are on or inside the spectral locus can cover the complete interior of the locus.

No display can display all the colors.

Usually, people find the closest displayable colors to show there (called gamut mapping)

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces

Let’s build a color cube color space�

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How to build a color cube?

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1. Choosing the RGB primaries

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Choosing RGB primaries, three constraints:

1. reachable set = triangle within the locus
2. primaries must be physically emittable
3. ‘white’ must lie inside

2. White point & color temperature

'White' isn't one color it depends on the illuminant.

Black-body radiation is the thermal electromagnetic radiation emitted by an idealized, perfectly opaque object that absorbs all incoming light and reflects none

Chromatic adaptation: our brain automatically re-normalizes the ‘white’ it sees.

Black-body radiation

2. White point & color temperature

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The colors of black body radiation under different temperatures form a curve when plotted in the xy-chromaticity diagram. It’s called the Planckian locus.

• A color on this locus has a color temperature.
• Colors of actual lights closer to a color of black body radiation can be assigned a correlated color temperature. The two are (mis)used interchangeably.

Choosing the right white color in your home

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2. White point & color temperature

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1-2. Map the gamut to a cube

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3. Quantize the color cube

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3. Quantize the color cube - Encoding power vs brightness evenly

In color science, people empirically define the relationship between the perceived brightness and the light power using a power law. It doesn’t mean the actual human brightness perception follows this exactly; it’s more of an engineering convenience.

3. Quantize the color cube - Gamme correction

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3. Quantize the color cube – encoding power vs brightness evenly

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3. Quantize the color cube - Gamma color encoding

Gamma used by the sRGB colorspace

Colors on vertices have equal mix of 2 or 3 primaries with maximum quantity.

Colors outside of the cube are either:

• physically unrealizable or
• realizable but can’t be produced from the chosen primaries.

4. Handling out-of-gamut colors

A device-independent color (x,y) may fall OUTSIDE the triangle.

• Then the color space would need a negative primary impossible to display.

Gamut mapping: clip / compress into the gamut (a design choice).

Tying it together: color management

Every device speaks its own color space so connect them through a common space.

Device → ICC profile → CIE XYZ/Lab → gamut-map → other device.

This is why the same photo can look (in)consistent screen-to-print or even screen-to-screen.

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces

Additive vs subtractive

Additive (RGB, light): start black, ADD → white. Used in screens.

Subtractive (CMY, ink): start white, SUBTRACT → black. Used in Print.

Worked: RGB → CMY

(R,G,B) = (200,100,50)/255 = (0.78, 0.39, 0.20)

→ (C,M,Y) = (0.22, 0.61, 0.80)

Lots of magenta + yellow ink, little cyan → an orange.

Why K? Undercolor removal → CMYK

Printer vs monitor gamut

Ink gamuts differ from RGB gamuts and are usually smaller.

Some screen colors can't be printed, and vice-versa.

→ Similarly to out-of-gamut correction for the color cube, use 'soft proofing' & gamut mapping before you print.

Note

Multi-ink printers

Note

Multi-ink printers increase the gamut of printers through adding light-cyan, light-magenta, orange, green inks (6–12 total).

Each new ink extends the gamut & smooths gradients.

Photo printers use this for near-continuous tone.

Camera-dependent color

Color spaces designed for displays

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RGB-based color spaces

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sRGB is what we commonly refer to as the RGB space in the real world.

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Adobe RGB has a wider gamut.

All RGB color spaces are just one linear transformation away from each other.

sRGB is the most common color space, but its gamut is very small. CMYK is used in printers. ProPhoto RGB is a conceptual color space; its primaries are not real colors.

Luma + chroma: YUV, YIQ, YCbCr

YUV (analog PAL format), YIQ (analog NTSC format), YCbCr (digital) all split brightness (luma Y′) from color (chroma). They are all linear transforms of gamma corrected R’G’B’.

Worked: RGB → YCbCr (Rec.601)

Pixel (R,G,B) = (200, 100, 50):

Y = 59.8 + 58.7 + 5.7 = 124.2

Cb ≈ 86, Cr ≈ 182 (Cr > 128 ⇒ reddish)

Why luma/chroma helps compression

Why the luma/chroma decomposition helps compression:

• The eye is sharp for brightness and blurry for color.
• Idea: Keep Y at full resolution, shrink Cb, Cr (invisibly).
• Impossible in RGB (all three channels carry brightness).

Chroma subsampling: 4:4:4 → 4:2:0

To further decrease the required space to store pixel information, keep every luma sample; share chroma over 2×2 pixels (4:2:0).

Worked: the savings

4:4:4 = 3 samples/pixel (Y,Cb,Cr).

4:2:0 = 1 luma + ¼ Cb + ¼ Cr = 1.5 samples/pixel.

→ 2× less data before we even compress and nearly invisible.

Note

4:2:0 is used in consumer video, streaming, JPEG.

4:2:2 is used broadcast/professional capture (more color headroom).

4:4:4 is used graphics, screen capture, chroma-key/VFX (need full colour).

CIELAB: perceptually uniform

Weber's law: equal (x,y) distances ≠ equal perceived differences.

CIELAB warps XYZ so that distance ≈ perceived difference.

L* = lightness, a* = green–red, b* = blue–yellow.

ΔE: measuring color difference

ΔE is the euclidean distance between two colors in CIELAB.

ΔE ≈ 1 is the just-noticeable difference; ΔE < 2–3 ≈ 'a good match'.

Used in print quality control, camera calibration, and image-quality metrics.

HSV: a perceptual handle

HSV = Hue, Saturation, Value, how humans talk about color.

Hue = which color; Saturation = how vivid; Value = how bright.

• HSB/HSV/HSL don’t change the gamut; they just map a cube to a cylinder
• Great for color pickers & selection; just a transform of RGB.

Naming colors: Munsell

Note

Munsell (1900s): name color by Hue, Value (lightness), Chroma (saturation).

A perceptually spaced, human-friendly naming system.

Still used in computer vision, art, soil science, design.

Color palettes

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Help you choose matching colors for your designs based on color distances.

https://color.adobe.com/create/color-wheel

Where color matters in this course

Digital sensors and displays sensitivity (Sessions 5 and 6)

YCbCr + chroma subsampling → JPEG (Session 9) and video compression (Session 10).

ΔE / CIELAB → image-quality metrics.

Gamma & gamut → every capture and display stage.

Summary

• Trichromacy: 3 cone classes reduce a spectrum to 3 numbers → metamerism.
• CIE XYZ: device-independent reference, one linear transform from CIE RGB, itself one from LMS.
• xy chromaticity: perspective projection of XYZ, separates chromaticity from intensity, 3D shown in 2D.
• Gamut: 3 primaries span a triangle, visible region is curved → no space covers all colors, hence gamut mapping.
• A color space = primaries + white point + quantization; white from blackbody/daylight; quantization on perceived lightness, i.e., gamma.
• Spaces by purpose: RGB additive, CMYK subtractive (absorptive media only), HSV selection, YCbCr compression with ~2x from chroma subsampling.
• CIELAB and ΔE: perceptual uniformity improved over XYZ.

Image: where each stage lands

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Next time & further reading

• Session 4: Analog & digital video (Ch.5, p.119)

Source: Fundamentals of Multimedia, Ch.4 (p.83–117)

Source: https://cs.rochester.edu/courses/259/fall2025/decks/lect6-color.pdf

https://cs.rochester.edu/courses/259/fall2025/decks/lect7-colorimetry.pdf

• Questions?

Table of content

The human visual system (HVS)

– Light physics

– Color vision

– LMS color space

Measuring color

– Color matching experiment

– CIE 1931 RGB color space

– CIE XYZ color space

Color models for images

– xy-chromaticity diagram

– Gamut of a color space

Building a color cube

– RGG primaries and white point,

– Quantization and out-of-gamut

Other color spaces

– Subtractive color spaces

– YUV, YIQ, YCbCr

– Perceptual color spaces