3.2 Color Spaces

Color Spaces Overview

1. RGB Color Space

Definition

RGB stands for Red–Green–Blue, an additive color model used in displays, cameras, and digital imaging. Each pixel’s color is expressed as a combination of the three primary light intensities:

Color=(R,G,B),R,G,B∈[0,255]\text{Color} = (R, G, B), \quad R,G,B \in [0, 255]

Key Concepts

  • Based on additive color mixing — combining red, green, and blue light yields all visible colors.

  • Examples:

  • (255,0,0)(255, 0, 0) → Red

  • (0,255,0)(0, 255, 0) → Green

  • (0,0,255)(0, 0, 255) → Blue

  • (255,255,255)(255, 255, 255) → White

  • (0,0,0)(0, 0, 0) → Black

Characteristics

  • Device-dependent: same RGB values can appear different across devices.
  • Not perceptually uniform: brightness and color hue are mixed in the same space.

Applications

  • Image display, digital photography, computer graphics, rendering pipelines.

2. HSV Color Space

Definition

HSV (Hue–Saturation–Value) reformulates RGB into a model that aligns more closely with human perception.

Color=(H,S,V)\text{Color} = (H, S, V)

Components

  • H (Hue): type of color, represented as an angle on a color wheel [0∘,360∘)[0^\circ, 360^\circ)

  • 0° = Red, 120° = Green, 240° = Blue

  • S (Saturation): color intensity or purity (0 = gray,1 = vivid)(0 \text{ = gray}, 1 \text{ = vivid})

  • V (Value or Brightness): lightness level (0 = black,1 = full brightness)(0 \text{ = black}, 1 \text{ = full brightness})

Conversion (conceptual)

V=max⁡(R,G,B)V = \max(R, G, B) S=V−min⁡(R,G,B)VS = \frac{V - \min(R, G, B)}{V} H=f(R,G,B)(depends on which channel is maximum)H = f(R, G, B) \quad (\text{depends on which channel is maximum})

Characteristics

  • Separates chromatic content (H, S) from brightness (V).
  • More intuitive for selecting and adjusting colors.
  • Not perceptually uniform — equal distances do not equal equal visual differences.

Applications

  • Color selection tools (e.g., Photoshop, color pickers)
  • Image segmentation and object tracking (using hue thresholding)

3. YCbCr Color Space

Definition

YCbCr is a luminance–chrominance color model used primarily in digital video, compression, and broadcasting. It separates brightness information from color information.

Components

  • Y: Luma (brightness)
  • Cb: Blue-difference chroma component
  • Cr: Red-difference chroma component

Transformation (BT.601 standard)

[Y Cb Cr]=[0.2990.5870.114−0.169−0.3310.50.5−0.419−0.081][R G B]+[0 128 128]\begin{align*} &\begin{bmatrix} Y \ Cb \ Cr \end{bmatrix} \\ &= \begin{bmatrix} 0.299 & 0.587 & 0.114 \\ -0.169 & -0.331 & 0.5 \\ 0.5 & -0.419 & -0.081 \end{bmatrix} \begin{bmatrix} R \ G \ B \end{bmatrix} + \begin{bmatrix} 0 \ 128 \ 128 \end{bmatrix} \end{align*}

Key Concepts

  • YY carries the luminance — most important to human vision.
  • Cb,CrCb, Cr carry chroma — can be stored at lower resolution (chroma subsampling).
  • Exploits the fact that human eyes are more sensitive to brightness than color detail.

Applications

  • JPEG and MPEG compression
  • Broadcast television formats (e.g., YUV)
  • Digital cameras and video codecs

4. CIELAB (Lab) Color Space

Definition

CIELAB (often just Lab) is a perceptually uniform color space defined by the CIE (International Commission on Illumination). Equal distances in Lab roughly correspond to equal perceived color differences.

Components

  • L∗L^*: Lightness (0 = black, 100 = white)
  • a∗a^*: Green–Red axis (negative = green, positive = red)
  • b∗b^*: Blue–Yellow axis (negative = blue, positive = yellow)

Transformation from CIEXYZ

Given (X,Y,Z)(X, Y, Z) and reference white (Xn,Yn,Zn)(X_n, Y_n, Z_n):

L∗=116f(YYn)−16L^* = 116 f\left(\frac{Y}{Y_n}\right) - 16 a∗=500[f(XXn)−f(YYn)]a^* = 500 \left[f\left(\frac{X}{X_n}\right) - f\left(\frac{Y}{Y_n}\right)\right] b∗=200[f(YYn)−f(ZZn)]b^* = 200 \left[f\left(\frac{Y}{Y_n}\right) - f\left(\frac{Z}{Z_n}\right)\right]

where

f(t)={t1/3,t>0.008856 7.787t+16116,t≤0.008856f(t) = \begin{cases} t^{1/3}, & t > 0.008856 \ 7.787t + \frac{16}{116}, & t \le 0.008856 \end{cases}

Key Characteristics

  • Perceptually uniform: ΔE distances approximate perceived color differences.
  • Device-independent: based on human color vision, not display technology.

Applications

  • Color correction and matching across devices
  • Measuring color differences (ΔE)
  • Printing, paint matching, and machine vision

Comparison Summary

PropertyRGBHSVYCbCrCIELAB (Lab)
Model TypeAdditive light modelPerceptual cylindricalLuminance–chrominancePerceptually uniform
ComponentsR, G, BH, S, VY, Cb, CrL*, a*, b*
Separates brightness?❌ No✅ Partially (V)✅ Yes (Y)✅ Yes (L*)
Perceptual uniformity❌❌❌✅
Device independence❌❌❌✅
Common usesDisplays, graphicsColor editing, segmentationCompression, videoColor measurement, correction
Human interpretationLowHighLowVery high

Conceptual Summary

  • RGB → How screens create color (device-based, additive).
  • HSV → How humans perceive and describe color intuitively.
  • YCbCr → How images store color efficiently for compression.
  • Lab → How humans compare and measure color perceptually.