The first step of most image interpretation problems including microscopic image processing is feature extraction. Feature vectors represent or summarize a given image. In many problems, image classification is then performed using the feature vectors instead of actual pixel values. Ordinary feature extraction methods are developed for regular images and they may not work optimally for microscopic images. Furthermore, microscopic images are huge in size, which requires the feature extraction process to be computationally efficient in order to rely on supercomputers or computer clusters in the future.

One of the feature extraction methods that we are going to try will be based on the covariance method, which was recently introduced in [15,16,17] and successfully used in image texture classification and object recognition. Covariance method features are extensively used in texture classification and recognition in image and video. Texture classification techniques can be used on microscopic images to classify them into groups and recognize specific types of diseases.

The covariance matrix of an image region is defined as follows:
 

, (1)

where f_k is the feature vector, containing various parameters of the k-th pixel such as color component values, wavelet coefficients and gradients. µ is the mean vector

The computation complexity of the covariance matrix is relatively large ( where is the size of the image). Computational cost becomes especially important when a large image needs to be scanned at different scales. Due to the large size of FL images, supercomputers are used for processing microscopic images at OSU. Recently, BILKENT developed a co-difference method that can replace the covariance method in feature extraction. In the co-difference method, an operator based on additions instead of the multiplications in the covariance method is used. This methodology gives comparable results in regular texture classification [18]. The new operator is defined as follows:
 

. (2)

This operator is a monoid function, i.e. it satisfies totality, associativity and identity properties. Therefore it is a semi-group on real numbers. The operator is basically a summation operation but the sign of the results behaves like the multiplication operation. As a result, the computational complexity of microscopic image analysis can be decreased significantly.
Another important issue that needs to be addressed is the choice of entries of the vector. The obvious choice will be the color pixel values, however, these may not be descriptive enough. In addition, wavelet or wavelet packet coefficients may be included in the feature vector. WARWICK has developed a wavelet transform-domain method, which adaptively selects the best wavelet features that are optimal in discriminating between different classes of histology images. The best choice for the feature vector of microscopic images will be investigated in this WP. It may even be possible to have an adaptive selection of wavelet coefficients for different parts of an image. Ph.D. students will work on this problem at BILKENT, WARWICK and OSU. The feature vectors developed in WP will be used in the 2nd and 3rd WP’s.