Image transformations and slicing
Institute for Environmental and Spatial Analysis...University of North Georgia
Contents
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
1.2 Image negatives
\[s=L-1-r\]
- Enhances white or gray detail embedded in dark regions
- E.g., Digital mammograms
- negative.py
- Fig0304(a)(breast_digital_Xray).tif
- standard_test_images.zip
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
\[s=cr^\gamma\]
- power_transformations.py
- Similar to log transformations, but $\gamma$ controls the overall shape of mapping curves
- Many devices use a power-law transformation
- Have you heard of gamma correction?
- Process used to correct a power-law response from the monitor
- power.py
- Fig0309(a)(washed_out_aerial_image).tif
1.5 Linear contrast stretching
\[T(r)=L_\text{min}+\frac{L_\text{max}-L_\text{min}}{r_\text{max}-r_\text{min}}\times(r-r_\text{min})\]
2 Image slicing
2.1 Gray-level slicing
Highlights a specific range of gray levels.
For example, enhancing water bodies in satellite imagery
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