Image Regions and Region Features

An image region is a set of pixels that share useful features. A region can be represented by a mask or by its boundary, and different regions receive different labels.

Main idea

A region groups pixels by what they share. The useful feature can be intensity, colour, texture, or semantic meaning.

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Region Features

Feature	What it describes	Example use
Intensity	Pixel brightness	Separate dark text from light paper
Colour	Colour values or channels	Separate road, vegetation, and sky
Texture	Repeated local patterns	Distinguish stripes from smooth surfaces
Semantics	Meaning learned from labelled data	Label road, car, person, and sky

Region processing supports document separation, road-scene segmentation, medical-image segmentation, and object-mask extraction.

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Region Mean and Variance

For a region $R$ with $N$ pixels, the mean intensity is:

$${\mu }_R=\frac{1}{N}\sum _{(x,y)\in R}f(x,y)$$

The region variance is:

$${\sigma }_R^2=\frac{1}{N}\sum _{(x,y)\in R}{\left(f(x,y)-{\mu }_R\right)}^2$$

Quantity	Meaning
${\mu }_R$	Average brightness in the region
${\sigma }_R^2$	Amount of pixel-value variation in the region
$N$	Number of pixels in the region

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Worked Region Example

Consider this 16-pixel region:

$$R=\left[\begin{array}{cccc}80& 82& 78& 76\\ 81& 85& 83& 77\\ 79& 84& 86& 80\\ 75& 78& 80& 79\end{array}\right]$$

The sum of all values is $1283$, so:

$${\mu }_R=\frac{1283}{16}=80.1875$$

Using this mean:

$${\sigma }_R^2=\frac{1}{16}\sum _{(x,y)\in R}{\left(f(x,y)-80.1875\right)}^2=9.40234375$$

These two numbers summarize brightness and spread, but they do not show where each value occurs.

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Limitation of Mean and Variance

Two regions can have similar mean intensity while their spatial patterns are very different. Variance measures value spread, but it does not preserve where those values occur.

Pattern	Spatial property
Checkerboard	Alternating high-contrast structure
Fine noise	Random local changes
Stripes	Repeated structure with a main orientation
Smooth patch	Low local variation

Mean and variance describe value statistics. Texture describes the repeated spatial arrangement of those values.

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Filter Banks and Gabor Features

A Gabor filter bank contains filters with different orientations and scales.

flowchart LR

P["Image patch"] --> G["Gabor filter bank<br/>several scales and orientations"]
G --> R["Filter responses<br/>r1, r2, r3, ..."]
R --> F["Feature vector"]
F --> C["Cluster or classify pixels"]

The feature vector is:

$$\mathbf{r}=[r_1,r_2,r_3,\dots ]$$

Each response measures how strongly the local image matches one filter. Pixels can then be grouped or classified in this feature space. See Image Filtering for the filtering process and Colour Representation for colour-based features.

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Classical and Semantic Segmentation

Classical segmentation	Semantic segmentation
Uses intensity, colour, or texture	Learns features from labelled data
Groups visually similar pixels	Assigns meaning-aware category labels
Does not require an object category	Predicts categories such as road, car, person, or sky
Includes thresholding, [[Otsu Thresholding	Otsu]], and k-means

Both approaches assign pixels to regions. Their difference is whether the output represents visual similarity or learned meaning.