• Color Sampling:
  • Converting from a continuous "rainbow" of colors to a discrete finite palette of colors
  • Sometimes called quantization
• Spatial Sampling:
  • Another name for spatial discretization
  • The most common scheme involves the use of a finite grid with equal size cells

• The Result:
  • A grid (or matrix) of picture elements (or pixels), each of which contains a single color in the palette
  • Sometimes called a raster representation
• An Illustration:
  • 

• Single-Input/Single-Output Operations:
  • Some can be performed "in place" and some require a destination image
• Multiple-Input/Single-Output Operations:
  • Are generally not performed "in place"

• An Observation:
  • We want the "gray scale" to be the same brightness/luminance as the color image
• What We Know:
  • Perceived luminance is a function of the total signal transmitted to the brain. So, \(R_g + G_g + B_g = R_c + G_c + B_c\)
  • Shades of gray are mixtures of black and white. So, \(R_g = G_g = B_g\)
• The Implication:
  • \(R_g = G_g = B_g = (R_c + G_c + B_c) / 3 \)

• An Observation:
  • We probably want to keep colors that are "similar to" to the given color
• Metrics and the Meaning of "Similar to":
  • A variety of different metrics can be used
  • Conceptually, one might want to use an HSV color model rather than an RGB color model

• Defined:
  • Use a look-up table to transform the source into the destination
• Implementation:
  • Use an array in which the index corresponds to the possible colors in the source and the value in the array is the color to substitute
• Types:
  • Use one array for all three components (i.e., the same look-up array for R, G, and B)
  • Use one array for each component (i.e., a different look-up array for R, G, and B)

• Common Color Spaces:
  • RGB (an additive color model)
  • CMY (a subtractive color model)
  • HSV (hue in degrees, saturation in percent, value in percent)
  • HSL (hue in degrees, saturation in percent, lightness in percent)
  • YIQ (used by the National Television System Committee)
• RGB\(\leftrightarrow\)CMY are Simple Conversions:
  • 

\( \left[ \begin{array}{c c} Y \\ I \\ Q \end{array} \right] = \left[ \begin{array}{r r r} 0.299 & 0.587 & 0.114 \\ 0.596 & -0.275 & -0.321 \\ 0.212 & -0.523 & 0.311 \\ \end{array} \right] \left[ \begin{array}{c c} R \\ G \\ B \end{array} \right] \)

\( \left[ \begin{array}{c c} R \\ G \\ B \end{array} \right] = \left[ \begin{array}{r r r} 1.000 & 0.956 & 0.621 \\ 1.000 & -0.272 & -0.647 \\ 1.000 & -1.105 & 1.702 \\ \end{array} \right] \left[ \begin{array}{c c} Y \\ I \\ Q \end{array} \right] \)

• Defined:
  • Extraction of a rectangular "sub-image" from an image
• Algorithm:
  • Should be obvious