Minimum Distance Classification - Lecture Material - Completely Remote Sensing tutorial, GPS, and GIS - facegis.com
Minimum Distance Classification

We initiate our exemplification of Supervised Classification by producing one using the Minimum Distance routine. This involves fairly simple calculational procedures. Look at this diagram (for simplification, just two bands are used):

The data points for DNs from two bands are dots; the mean for each clustered data set are square. For point 1, an unknown, the shortest straight-line distance to the several means is to the class "heather". Point 1, then, is assigned to this category. Point 2 is slightly closer to the "soil" category but lies within the edge of the "urban" spread. Here, the classification seems ambiguous. By the minimum distance rule, it would go to "soil" but this may be erroneous ("urban" would have been a greater likelihood). Point 3 is not near any of the class DN clusters, but is about equidistance between "urban", "water", "forest", and "heather". If one plays the odds, "urban" is just a tad closer to 3; but this situation indicates how misclassification might occur.

The IDRISI program acts on DNs in multidimensional band space to organize the pixels into the classes we choose. Each unknown pixel is then placed in the class closest to its mean vector in this band space. For Morro Bay, the resulting classification image consists of 16 gray levels, each representing a class, to which we can then assign any color on the computer. We can elect to combine classes to have either color themes (similar colors for related classes) and/or to set apart spatially adjacent classes by using disparate colors. Examine this Minimum Distance classification below, in which we use all seven TM bands, including the thermal. Study it in relation to your acquired knowledge of this scene from the preceding pages in this section and compare it with the classifications we show on the next page.

A variant of this classifier is known as the Nearest Neighbor Classifier.

Source: http://rst.gsfc.nasa.gov