Parent Topic: Supervised Algorithms

Minimum Distance

The distances between the pixel to be classified and each class centre are compared. The pixel is assigned to the class whose centre is the closest to the pixel.

The minimum Euclidian distance classifier is defined by the following equation:

                T
  Gi(X) = (X-Ui) * (X-Ui)

        = SUM[(xj-uj)**2]  for j = 1 to d.

Gi(X)          is the result for class i on pixel X
T              indicates transposition of the elements in brackets
d              is the number of channels in the classification
X=(x1,...,xd)  is the (d by 1) pixel vector of grey-levels
Ui=(u1,...,ud) is the (d by 1) mean vector for class i
j              is the subscript of jth element of a vector
SUM[]          is the total of elements inside brackets


If for all i not equal j, Gj(X) < Gi(X),
then X is classified as j.

The diagram below illustrates the classification of 4 pixels into 3 classes. Pixels are classified to the nearest class centre.

|             Class A                    *   class centre
|  .    a                      .        ...  class boundary  
|     .           *          .
|        .  b             .               Pixel      Class
|          .          .                  
|              .    .                       a           A
|          c     .                          b           A
|                .                          c           B
|          *      .     *  Class C          d           C
|                 .  d                                          
|       Class B   .                        
|                .                             
|                              
+----------------------------------

Reference:

Hodgson, M.E., 1988. "Reducing the computational requirements of the minimum-distance classifier." Remote Sensing of Environment, Vol. 24.

Parent Topic: Supervised Algorithms
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