Keywords: Image Segmentation, Karhunen-Loeve Transform, Otsu Algorithm, Multithresholding, Co-occurrence Matrix.

Abstract:
Multispectral remote-sensing image segmentation can be achieved by using a multithresholding technique, for which an automatic threshold selection method is presented in this paper. The monchrome version of the multispectral image is first derived by using Karhunen-Loeve Transform (KLT). The co-occurrence matrix method is then computed from this image, and used to construct a histogram. The threshold values are automatically determined from this histogram by using Otsu algorithm, and finally used for image segmentation by multithresholding. The better results were obtained by this method comparing with the direct application of Otsu algrithm.

1.Introduction
For image segmentation which is the process for subdividing an image into the homogeneous regions, thresholding is a well known technique and a widely used tool. Many threshold selection methods have been proposed (Sahoo, 1988). Each method can be suitably applied for some application depending on the purpose and the accuracy required. The basic and easiest way to determine the threshold of image in the case of binary image is based on finding two peaks of normal distribution from image histogram separated by a valley corresponding to the intermediate gray levels, which is used to divide the object and background into bilevel.

A segmentation algorithm of multispectral images has been proposed in our previous work(Dulyakarn, 1999). It is performed by applying a multithresholding technique, using otsu algorithm, on the first principal component image resulted from KLT of the input image. In this paper, an improvement to that work will be described. The idea is to use the gray-level co-occurrence matrix for histogram transformation prior to the application of Otsu algorithm.

2.The Proposed Method
Our segmentation algorithm of multispectral remote-sensing images can be depicted by the block diagram in Figure 1. first, Karhunen -Loeve or Hotelling Transform (KLT) is applied to the input multispectral image to produce the first principal component image. The co-occurrence matrix method is then computed from this image, and used to construct a histogram. The threshold values are automatically determined from this histogram by using Otsu algorithm, and finally used for image segmentation by multithresholding. The following subsections are dexcribed for more detail of these steps.

Figure 1: Block diagram of the proposed method.
2.1 Karhunen-Loeve Transform
The Karhunen-Loeve Transform (KLT) or Hotelling transform (Richards, 1994) is a rotation transformation that aligns the data with the eigenvectors, by the other hand this alignment is precisely the mechanism that decorrelates the data. The transformed image may make evident features not discernable in the original data or alternatively it might be possible to preserve the essential information content of the image for a given application with a reduced number of the transformed dimensions. The KLT can be considered by the eigenvalues and eigenvectors for developing a new co-ordinate system in the multispectral vector space, in which the data can be represented without correclation as defined by:

Y = Gx            (1)
where y    is a new co-ordinate system,
G    is a linear transformation of the original co-ordinates that is the transposed matrix of eigenvector of the pixel data's covariance in x space
x     is an original co-ordinate system

By (1), we can get the principal components and choose the first principal component from this transformation that seems to be the best monochrome representation of the input image.