11.6 Minimum Distance Classifier

The minimum distance classifier is used to classify unknown image data to classes which minimize the distance between the image data and the class in multi-feature space. The distance is defined as an index of similarity so that the minimum distance is identical to the maximum similarity. Figure 11.6.1 shows the concept of a minimum distance classifier. The following distances are often used in this procedure.

(1) Euclidian distance

Is used in cases where the variances of the population classes are different to each other. The Euclidian distance is theoretically identical to the similarity index.

(2) Normalized Euclidian distance
The Normalized Euclidian distance is proportional to the similarity in dex, as shown in Figure 11.6.2, in the case of difference variance.

(3) Mahalanobis distance
In cases where there is correlation between the axes in feature space, the Mahalanobis distance with variance-covariance matrix, should be used as shown in Figure 11.6.3.

where X : vector of image data (n bands)
X = [ x1, x2, .... xn]
k : mean of the kth class
k = [ m1, m2, .... mn]

k : variance matrix

k : variance-covariance matrix

Figure 11.6.4 shows examples of classification with the three distances.


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