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The paper proposes an algorithm for reducing the number of colors in an image. The proposed adaptive color reduction (ACR) technique achieves color reduction using a tree clustering procedure. In each node of the tree, a self-organized neural network classifier (NNC) is used which is fed by image color values and additional local spatial features. The NNC consists of a principal component analyzer (PCA) and a Kohonen self-organized feature map (SOFM) neural network (NN). The output neurons of the NNC define the color classes for each node. The final image not only has the dominant image colors, but its texture also approaches the image local characteristics used. Using the adaptive procedure and different local features for each level of the tree, the initial color classes can be split even more. For better classification, split and merging conditions are used in order to define whether color classes must be split or merged. To speed up the entire algorithm and reduce memory requirements, a fractal scanning subsampling technique is used. The method is independent of the color scheme, it is applicable to any type of color images, and it can be easily modified to accommodate any type of spatial features and any type of tree structure. Several experimental and comparative results, exhibiting the performance of the proposed technique, are presented.

In this paper a new set of descriptors appropriate for image indexing and retrieval is proposed. The proposed descriptors address the tremendously increased need for e±cient content-based image retrieval (CBIR) in many application areas such as the Internet, biomedicine, commerce and education. These applications commonly store image information in large image databases where the image information cannot be accessed or used unless the database is organized to allow e±cient storage, browsing and retrieval. To be applicable in the design of large image databases, the proposed descriptors are compact, with the smallest requiring only 23 bytes per image. The proposed descriptors' structure combines color and texture information which are extracted using fuzzy approaches. To evaluate the performance of the proposed descriptors, the objective Average Normalized Modi¯ed Retrieval Rank (ANMRR) is used. Experiments conducted on¯ve benchmarking image databases demonstrate the e®ectiveness of the proposed descriptors in outperforming other state-of-the-art descriptors. Also, a Auto Relevance Feedback (ARF) technique is introduced which is based on the proposed descriptors. This technique readjusts the initial retrieval results based on user preferences improving the retrieval score signi¯cantly. An online demo of the image retrieval system img(Anaktisi) that implements the proposed descriptors can be found at http://www.anaktisi.net.

A new technique for color reduction of complex document images is presented in this article. It reduces significantly the number of colors of the document image (less than 15 colors in most of the cases) so as to have solid characters and uniform local backgrounds. Therefore, this technique can be used as a preprocessing step by text information extraction applications. Specifically, using the edge map of the document image, a representative set of samples is chosen that constructs a 3D color histogram. Based on these samples in the 3D color space, a relatively large number of colors (usually no more than 100 colors) are obtained by using a simple clustering procedure. The final colors are obtained by applying a meanshift based procedure. Also, an edge preserving smoothing filter is used as a preprocessing stage that enhances significantly the quality of the initial image. Experimental results prove the method's capability of producing correctly segmented complex color documents where the character elements can be easily extracted as connected components.

785coefficients -ym (location of the borders between the regions). Thus, the behavior of an n-dimensional system having a piecewise-linear continuous vector field with o-regions and parallel boundaries (4) is uniquely determined by the n eigenvalues of A, n eigenvalues of A + deT, n . a eigenvalues of A + bmey for m = 1, . . . , a, and a locations of the borders between the regions which makes a total of 2 . n + n . a + a parameters. IV. CONCLUSIONWe have shown that vector fields in Lur'e form having identical eigenvalue patterns and belonging to the same family ( ( n , f) are linearly conjugate. Hence, their attractor dimensions, Lyapunov exponents and entropies are identical. Furthermore, we have suggested the construction of a canonical system (10) that retains all features of its family of vector fields in Lur'e form and has reduced number of parameters by n2 -n compared to other members of the same family that have the same eigenvalue pattern. ACKNOWLEDGMENTThe authors wish to thank the anonymous reviewers for their valuable comments and helpful suggestions on earlier version of this paper that have improved the quality and clarity of the presentation.Abstract-In this brief, a new method is proposed for the design of digital integrators. The new method is based upon the formulation of an appropriate linear programming problem which assures a satisfactory minimax approximation error for the magnitude response in a predefined frequency range. In comparison with existing methods the new design approach constructs a novel class of digital integrators by optimal determining more than one independent coefficients. Their capability to approximate in the minimax sense the ideal integrator with a good accuracy is shown. Well-known integrators can be obtained as special cases of the proposed methodology. Appropriate constraints can be introduced to accommodate signals with low frequencies.

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