Supervised classification (contrasted with Unsupervised classification, or clustering) starts with the user selecting training regions on the satellite image that represent a particular surface category like water, vegetation, or urban areas. Regions should be as homogenous as possible; mixed or boundary pixels will have a value intermediate between the two categories involved. The computer then calculates basic statistics for each pixel in the training region.

The table below shows the mean (top line) and standard deviation (bottom line) in each of 7 bands for three categories. Note that in this typical example the water has lower reflectances than the other categories, and lower standard deviations as well; water presents a very uniform reflector with low albedo. The vegetation has very high reflectances in the near and mid IR, bands 4, 5, and 7.

`Category statistics, subset from DC TM tape`

` Band 1 2 3 4 5 6 7`

`Class n= `

```
Water 2790 58.5 21.2 16.9 8.9 5.5 105.6 3.3
1.35 0.69 0.63 0.60 0.78 0.50 1.01
Vegetation 306 66.4 28.4 28.1 57.4 64.6 115.2 24.1
4.17 2.35 4.30 7.01 9.66 1.07 4.81
Urban 210 71.0 29.0 30.2 28.7 40.4 121.1 22.1
8.36 4.49 5.21 6.34 9.55 1.74 6.03
```

The training sets can also be displayed on a scattergram with two of the bands. In the case below, the three categories have overlapping reflectance distributions in Band 2 but Band 4 clearly differentiates them.

While we can easily only display the reflectance relationships for two bands on a scattergram, and we can conceptualize the relationships on a three dimensional graph for three bands, the mathematical relationships extend to higher dimensionality. In the case of Landsat TM imagery we can use seven dimensional statistics to classify the scene. In seven dimensional space each category will occupy a particular region of space.

We can define each category by the region surrounding its mean for each band. The size of the region in each dimension (band) can be modeled by the variability or standard deviation for that band; we can pick an allowable number of standard deviations around the mean. The larger the region, the more points we will assign to the category.

To classify the scene, for every pixel in the scene we compute the distance in n dimensional space (n is the number of spectral bands used for the classification) to the mean of each of the categories using the Pythagorean theorem. The pixel belongs to the category to which it is closest, provided it lies within a specified number of standard deviations from the category mean. We can exclude some bands from the classification; thermal band 6 of the TM often does not add much to a classification because of its much lower spatial resolution.

Supervised Classification Directions

Unsupervised classification (clustering)

*Last revision 12/13/2017*