# Image transformations and slicing

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 ### 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

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

## 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