Research and development of the classification algorithm based on the method of reference planes

Abstract

In this paper a classification algorithm for hyperspectral images based on the reference planes using the values of the contingency table is developed and researched. We propose a new procedure for generating the reference planes. The training vectors areformed with the use of vectors from other classes. The results of experiments on the test image are given.

Keywords

• hyperspectral images
• method of reference planes
• classification
• conjugacy indices

1. Introduction

Thematic classification of hyperspectral images is gaining popularity. Studies in remote sensing are useful in many fields such as agriculture, mineralogy, physics, surveillance, forensics etc. Remote sensing of the Earth surface allows us to survey the productivity of the lands, forest fires, construction of roadsand various objects.

The most widely used algorithms of thematic classification for solving the above problems are based on methods of spectral angle and support vector machine (SVM). This paper presents a classification algorithm based on the method of reference planes using the values of the conjugacy indices.

2. Statement of the problem

The source data is a hyperspectral image obtained by remote sensing [ 1 ]. It is a data structure in which intensity values are stored with the coordinates X, Y, Z, which includes spatial coordinates (X, Y) and spectral coordinates (Z). The objective is to find the given object in this hyperspectral image. R mean (n)  (Rj )2

N n where Qk  Xk XTk Xk 1 XTk , x j is vector j from the class n  k , j  1,...,N n . Thus, we have N n values of conjugacy indices Rk . For these indices the root-mean-square (RMS) value can be calculated as following

It is assumed that each of spatial coordinates of the hyperspectral image belongsto one of K classes. Each class represents some object (for example, field of corn, field of wheat, roads, etc.).

3. Description of the classification algorithm

To describe the algorithm, consider the k th class. In this class we will choose the reference plane Xk [ 2 ] consisting of a pair of hypervectors. For selected reference plane k class index of conjugacy [ 3 ] with the vectors from other classes can be calculated with the following expression: where n  (1,...,K ) \ k . Next, we do the same with the remaining classes. For all remaining K  1 values R mean , we calculate RMS value R(i)  (R mean (n)) 2

K  1 where n  (1,...,K ) \ k , i  1,...,C N2n .

Further, we similarly define conjugacy indicesfor all planes Xk of k th class and calculate C N2n values of R(i) , where i  1,...,C N2n .Then the minimum value R(i) is sought among them R  min R(i) .

i1,C Nn2

The hyperplane which corresponds to the received minimum value R is stored. Let us denote it as Yk . Thus, we get the reference plane with the highest value of the conjugacy index with its class. This plane allows us to effectively recognize the chosen class. At the same time, it will be less responsive to vectorsof other classes. This allows us to enhance the effectivity of the hyperspectral images classification.

On recognition stage [ 4 ] it is necessary to choose the minimum threshold of conjugacy. It is performed by calculating the conjugacy indiceswith the reference plane Yk RY (m)  xTmQY x m , xT x

m m where QY  Yk YkT Yk 1 YkT , x m is vector m from class k , m  1,...,N k , and N k is the number of vectors in class k . The N k values obtained from this procedure are sorted in ascending order. Then first (lowest) or Nth value from ordered sequence of RY is chosen.

4. The results of the experiment

The algorithm was tested on a Salinastest image from open dataset of hyperspectral image MultiSpec. This image was obtained within AVIRIS program (AirborneVisible/ InfraredImagingSpeсtrometer). The image size is 512×217 hyperpixels. Each hyperpixelhas 224 spectral bands. A sample of hyperspectral layer and classified test image are shown in figures 1a), 1b), respectively.

a) b)

The algorithm was applied to detect the 4th, 5th, and 11th classes (the area with roughlyplowed fields, smooth ground, four-week lettuce, respectively). The figure shows the location of the fifth and eleventh class vectorswith skipping the 20% lowest conjugacy indices. The figuresshowsa few falsely recognized hyperpixels from other classes.

5. Conclusion

The choice of an appropriate reference plane in the proposed algorithm has a high computational complexity. Recognition quality depends on the choice of the minimum conjugacy threshold. A small value of the threshold increases the number of recognition errors associated with “wrong detection” from other classes. The increase in the threshold leads to thepoints loss in a recognized class.

References

1. Lowengart RA . Remote sensing. Models and methods for image processing . Moscow: Technosphere, 2010 ; 560 p.

2. Zherdev DA , Kazanskiy NL , Fursov VA . Object recognition by the radar signatures of electromagnetic field scattering on base of support subspaces method . Computer Optics , 2014 ; 38 ( 3 ): 503 - 510 . [in Russian]

3. Fursov VA . Training in Pattern Recognition from a Small Number . 15th International Conference on Pattern recognition , 2000 ; 2 : 119 - 121 .

4. Fursov VA , Bibikov SA , Baida OA . Thematic classification of hyperspectral images using conjugacy indicator . Computer Optics , 2014 ; 38 ( 1 ): 154 - 157 . [in Russian]