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Image transformations and slicing

Dr. Huidae Cho
Institute for Environmental and Spatial Analysis...University of North Georgia

1   Image transformations

An image transformation function $T$ can be expressed as \[g(x,y)=T[f(x,y)]\] where $f(x,y)$ and $g(x,y)$ are the original and transformed images, respectively.

Typically, the operator $T$ takes neighbor pixels of $(x,y)$.

If the size of the neighborhood is $1\times 1$, $g$ is a function of $f$ only.

  • Gray-level (also intensity or mapping) transformation function $s=T(r)$ where $r=f(x,y)$ and $s=g(x,y)$
  • Also called point processing

1.1   Basic transformations

basic-gray-level-transformations

1.2   Image negatives

\[s=L-1-r\]

1.3   Log transformations

\[s=c\log(1+r)\]

  • Spreading low $r$ values
  • Compressing high $r$ values
  • Effects?
    • Emphasizing dark pixels
    • Making pixel values more manageable: $\log(10^6)\rightarrow 6$
  • log.py
  • Fig0305(a)(DFT_no_log).tif
  • Inverse log: Opposite effects

1.4   Power-law transformations

\[s=cr^\gamma\]

1.5   Linear contrast stretching

\[T(r)=L_\text{min}+\frac{L_\text{max}-L_\text{min}}{r_\text{max}-r_\text{min}}\times(r-r_\text{min})\]

linear-contrast-stretching

2   Image slicing

2.1   Gray-level slicing

Highlights a specific range of gray levels.

For example, enhancing water bodies in satellite imagery

gray-level-slicing-binary

gray-level-slicing-identity

2.2   Bit-plane slicing

Highlights contributions by specific bits.

Useful

  • to identify which bit planes are significant
  • to determine the number of bits required
  • for image compression

3   DIP Toolbox for ArcGIS Pro