A Study of Euclidean classifier
Subash Chelliah
Remote Sensing Division
Birla Institute of Scientific Research
Jaipur, India
Abstract
The most familiar point to distance measure is Euclidean distance. The classifier based on this distance measure is direct and simple. The mean class values are used as class centers to calculate pixel-center distances for use by the Euclidean distance rule. For major level classification of a momogeneous area this scheme is better. Its advantageous nature comes from the minimum time it takes to classify.
Introduction
Image analysis includes vast application areas. The main aim of the user is to obtain in some form a classification of the observation relevant to his applications. The main concerns of a classification systems are how much one should spend for the systems and what one will get out of it. The classification procedure can be defined as extrapolation within the scene to the remaining portion of the scene. (M. MARUHACHALAM, 1985].
That is, the classification is based on the spectral values of individual pixels. A pixel is assigned to one of a set of previously-trained classes, using a per-pixel classifier (SWAIN and DAVIS, 1978). In the present scheme the mean class values are used as class centers to calculate pixel-center distances for use by the Euclidean distance rule.
In this paper a subscene of Lands at Thematic Mapper Scene of Madras area was selected for the study. Comparison of Euclidean classifier with Maximum likelihood classifier is also discussed.
Subscene details : The following Lands at TM scene was selected :
| Path |
Row |
Day of the year |
| 142 |
51 |
159/86 |
Bands 1-4 of Lands at Thematic Mapper of the red hills area of Madras which is having various classes with wide distribution was selected for the study.
Eight classes were chosen as being representative of the area. Training and verification areas were chosen using a combination of map a, site visits, and local knowledge. This provided a common base to compare the two algorithms. We do not suggest that the classified images produced represent highly accurate land cover classification of the area.
Methods of classification
Classification techniques was first published by FISHER 1936. The maximum likelihood classifier using a priori probability was applied in Remote Sensing by KING SUN FU 1971. Fu K.S. has incorporated a threshold limit. HOGG. H. GAIG 1970, used quadric term in the Maximum likelihood estimation metric for classification. EPPLER 1975 used Cholesky triangular decomposition
of the covariance matrices to improve computational efficiency of maximum likelihood classifier. Monti Carlo methods was used to demonstrate that, increase in the number of sub-class per cover type yield modest increases in accuracy.
A most commonly used algorithm for image classification is the Euclidean classifier. With this algorithm. Each unknown pixel with feature Vector X is classified by assigning it to the class whose mean vector (M) is closest to X. With this method the clusters are approximated by N-dimensional spheres. In addition to the infinitive a peal and computational simplicity of this approach, it can be shown that it is a very special case of the general maximum likelihood classifier. The Euclidean distance is defined as
The euclidean distance is computed for all classes and the pixel is assigned to the class for which the distance "d" is minimum.
