Classify

Algorithm

The Classify operation performs a multi-spectral image classification according to training pixels in a sample set.

The following classification methods are available:

Explanation of terms:

Classification methods

Prior to any classification, empirical statistics are drawn from the training pixels in the input sample set. These sample statistics are calculated per class of training pixels and per band. For instance, for a single class (i), n mean values are calculated when there are n input bands; these n mean values together are called the class mean (vector) for that class (mi).

Depending on the selected classification method, the following statistics are calculated:

 

For each feature vector to be classified, these statistics are used to calculate the shortest 'distance' towards the training classes. All classification decisions are thus based on these statistical empirical parameters.

Box classifier:

For each class, a multi-dimensional box is drawn around the class mean.

 

For each class, the size of the box is calculated as:

  

(class mean ± standard deviation per band) * multiplication factor

  

Minimum Distance to Mean:

For each feature vector, the distances towards class means are calculated.

Minimum Mahalanobis distance:

For each feature vector, the Mahalanobis distances towards class means are calculated. This includes the calculation of the variance-covariance matrix V for each class i.

The Mahalanobis distance is calculated as:

  

di(x) = yTVi-1y

  

For an explanation of the parameters, see Maximum Likelihood classifier.

  

Maximum Likelihood:

For each feature vector, the distances towards class means are calculated. This includes the calculation of the variance-covariance matrix V for each class i.

 

The formula used in Maximum Likelihood reads:

  

di(x) = ln|Vi| + yTVi-1y

  

where:

di

distance between feature vector (x) and a class mean (mi) based on probabilities

Vi

the n x n variance-covariance matrix of class i, where n is the number of input bands

|Vi|

determinant of Vi

Vi-1

the inverse of Vi

y

x - mi ; is the difference vector between feature vector x and class mean vector mi

yT

the transposed of y

  

Maximum Likelihood including Prior Probabilities:

For each feature vector, the distances towards class means are calculated. This includes the calculation of the variance-covariance matrix V for each class i. Furthermore, for each class, the prior probabilities are taken into account; these are listed in a column of a table.

 

The formula used in Maximum Likelihood with Prior Probabilities reads:

  

di(x) = ln|Vi| + yTVi-1y - 2 ln(P(Ci))

  

where:

P(Ci)

the prior probability for class i

For an explanation of the other parameters, see Maximum Likelihood classifier.

  

Reference:

See also: