11.2 Estimation of Population Statistics

a. Supervised classification
In order to determine a decision rule for classification, it is necessary to know the spectral characteristics or features with respect to the population of each class. The spectral features can be measured using ground-based spectrometers. However due to atmospheric effects, direct use of spectral features measured on the ground are not always available. For this reason, sampling of training data from clearly identified training areas, corresponding to defined classes is usually made for estimating the population statistics (see Figure 11.2.1). This is called supervised classification. Statistically unbiased sampling of training data should be made in order to represent the population correctly.

b. Unsupervised Classification
In the case where there is less information in an area to be classified, only the image characteristics are used as follows.

(1) Multiple groups, from randomly sampled data, will be mechanically divided into homogeneous spectral classes using a clustering technique (see 11.3).
(2) The clustered classes are then used for estimating the population statistics. This classification technique is called unsupervised classification (see Figure 11.2.2).

c. Estimation of Population Statistics
Maximum likelihood estimation is the most popular method by which the population statistics such as mean and variance, are estimated to maximize the probability or likelihood from a defined probability density function within the feature space.

In most cases, the probability density function is selected to be a multiple normal distribution. The multiple normal distribution gives the following the maximum likelihood estimator.

Variance - covariance matrix

where m: number of bands
n: number of pixels

Before adopting the maximum likelihood classification, it should be checked to determine if the distribution of training data will fit the normal distribution or not.