Unit IV – Chapter 6 (Color Image Processing)

Color Transformations

• Color transformations involve processing components of a color image within a single color model, rather than transformations between different color models.

• These transformations are applied to each pixel individually.

Formulation of Transformation

• A transformation can be modeled for multispectral images.

• $i$ is a subscript indicating a different transformation for each input component image.

• $n$: Total number of component images.

• $r_i$: Intensity values of the input component images.

• $s_i$: Spatially corresponding intensities in the output component images.

• $T<em>i$: Set of transformations that operate on $r</em>i$ to produce $s_i$.

• Example transformation:

  • $k = 0.7 \cdot I$ (for intensity I)

  • This can be applied in H, S components.

  • The same results can be achieved using formulas for RGB, CMY, and HSI.

• In the HSI color space, only the intensity component image needs modification.

  • Use two identity transformation functions ($T<em>1$ and $T</em>2$) and one constant transformation ($T_3$).

• In the RGB color space, all three components need modification by the same constant transformation.

Color Complements

• Color complement replaces each color with its opposite color on the color circle of the Hue component.

• Analogous to image negative in a grayscale image.

• Transformations:

  • Original image.

  • Complement transformation functions.

  • Complement based on RGB mapping functions.

  • Approximation of RGB complement using HSI transformations.

Color Slicing Transformation

• Slicing can be performed in color space.

• If the color of each pixel is farther than a threshold distance from a desired color, the color is set to a specific color (e.g., gray).

• Otherwise, the original color is retained.

• Formulas:

  • Set to gray if distance > threshold: $i = 1, 2, …, n$

  • Keep the original color if distance <= threshold: $i = 1, 2, …, n$

• Examples:

  • Detecting reds within an RGB cube of width $W = 0.2549$ centered at (0.6863, 0.1608, 0.1922).

  • Detecting reds within an RGB sphere of radius 0.1765 centered at the same point.

  • Pixels outside the cube and sphere are replaced by color (0.5, 0.5, 0.5).

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Tonal Correction

• Brightness and contrast are adjusted while keeping color unchanged.

• This is achieved by using the same transformation for all RGB components.

• Power law transformations.

• Contrast enhancement.

Color Balancing

• Color imbalance occurs when primary color components in the white area are not balanced.

• These components can be measured using a color spectrometer.

• Color balancing is performed by adjusting color components separately.

• Example: Color balancing a CMYK image.

Histogram Equalization of a Full Color Image

• Histogram equalization of a color image is performed by adjusting color intensity uniformly while leaving color unchanged.

• The HSI model is suitable because only the Intensity (I) component is equalized.

• $s = T(r)$, where r and s are intensity components of input and output color image.

Color Image Smoothing & Sharpening

• Smoothing & sharpening involves changing each pixel of a color image based on its surrounding pixels.

Color Image Smoothing

• Smoothing in grayscale images:

  • Spatial filtering operation with coefficients of the filtering kernel having the same value.

  • Each pixel is replaced by the average of pixels in the neighborhood encompassed by the kernel.

• In color images, two non-equivalent methods exist for different color models:

  1. Per-component-plane Method:

     • Deal with voxels instead of scalar intensity values.

     • Smooth each color plane with its own moving averages.

     • Used by RGB/CMY models.

  2. Smoothing the Intensity Component in HSI Model:

     • Smooth only the intensity component and leave the hue and saturation values fixed.

     • The HSI model decouples intensity and color information.

     • More efficient to smooth only the intensity component of the HSI.

Color Image Sharpening

• In the RGB/CMY Models:

  • Use the Laplacian for image sharpening.

  • The Laplacian of a vector has components equal to the Laplacian of the individual scalar components of the input vector.

  • In the RGB color system, the Laplacian of vector c can be computed component-wise.

  • Compute the Laplacian of a full-color image by computing the Laplacian of each component image separately.

• Can be performed with the same techniques as in color image smoothing:

  1. Per-color-plane method for RGB, CMY images.

  2. Sharpening only I component of a HSI image.

• The results are different between sharpened results from the two methods; therefore, the methods are not equivalent.