A Study of Euclidean classifier

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.

Accuracy assessmentt
Accuracy assessment was carried out using contingency tables (confusion matrices) generated from the comparisons between the test data and classified images. Approximate accuracies were then determined by calculating the percentage of pixels correctly classified along the row of the matrix, the calculating similar percentage for columns of the matrix and taking the average of these values.

Euclidean distance classifier was used to classify the test area and the output was written on a magnetic tape. The classification was performed by using the training sets for 8 classes. The output displayed is shown in Fig. 2. That is Maximum likelihood classifier is shown in fig3. The raw data of the test area is shown in Fig 1. The Result are given in Table 1,2 and 3.

Fig. 1 Raw Data

Fig. 2 Classified output
(Euclidean)

Fig. 3 Classified output
(Maximum likelihood)

Results and conclusion
The classification was performed with Euclidean and Maximum-likelihood classifiers. The results obtained with these schemes were used to compare the classification software and to conclude this study. The time taken for classification and the accuracy attained with the classification scheme are the important view points of any user. The amount of information needed is also a measure o compare the classification software.

Euclidean classifier takes very lesser time when compared to the Maximum likelihood estimation, still the accuracy attained with this method is encouraging. From the table it is clear that the Maximum-likelihood classifier is relatively slow because of the classification of a data sample requires the evaluation of the decision function for each class being considered. The size of the data set is immaterial to the process since each data point is classified independently.

Table. 3 Clasification Accuracy and rates

S.No.	Classifier	No. of Pixels	Time taken (seconds)	Percentage accuracy (training set)	Percentage accuracy (Field verification)
l.	Euclidean	49,000	720	93.00	60
2.	Maximum Likelihood	49,000	2400	97.92	75

References

Eppler, "Applied Multivariate Analysis", Academic Press, New York 1975.
Fisher, R.A. "The se of multiple measurements in taxonomic problems", 1936.
Hogg & Gaig, "Introduction to Mathematical Statistics", Macmillan Pub., New York, 1970.
King Sun Fu, "Pattern Recognition in Remote Sensing", 9th Proc. University of Felonies, 1971.
Maruthachalam, M. "familiarization course on Digital Image Processing of Remotely Sensed Data". Institute of Remote Sensing, Anna Univ., madras, 1985.
Morrison, "Statistical Data Analysis", Macmillan Pub. New York, 1970.
Snain and Davis (Eds.). "Remote Sensing-A quantitative approach, 1978.