Recently, there has been significant interest in robust fractal image coding for the purpose of robustness against outliers. However, the known robust fractal coding methods (HFIC and LAD-FIC, etc.) are not optimal, since, besides the high computational cost, they use the corrupted domain block as the independent variable in the robust regression model, which may adversely affect the robust estimator to calculate the fractal parameters (depending on the noise level). This paper presents a Huber fitting plane-based fractal image coding (HFPFIC) method. This method builds Huber fitting planes (HFPs) for the domain and range blocks, respectively, ensuring the use of an uncorrupted independent variable in the robust model. On this basis, a new matching error function is introduced to robustly evaluate the best scaling factor. Meanwhile, a median absolute deviation (MAD) about the median decomposition criterion is proposed to achieve fast adaptive quadtree partitioning for the image corrupted by salt & pepper noise. In order to reduce computational cost, the no-search method is applied to speedup the encoding process. Experimental results show that the proposed HFPFIC can yield superior performance over conventional robust fractal image coding methods in encoding speed and the quality of the restored image. Furthermore, the no-search method can significantly reduce encoding time and achieve less than 2.0 s for the HFPFIC with acceptable image quality degradation. In addition, we show that, combined with the MAD decomposition scheme, the HFP technique used as a robust method can further reduce the encoding time while maintaining image quality.

This paper uses the ultrametric clustering which is based on time series of stock prices. By calculating the ultrametric distance-matrix of the stocks in Shanghai-Shenzhen 300 index, a minimum spanning tree (MST) which has certain topological meaning can be drawn. And this MST explains the physical correlation between the topological structure and economic classification of the stocks trading on markets.

In this correspondence, we first establish a strong limit theorem for countable nonhomogeneous Markov chains indexed by a homogeneous tree. As corollaries, we obtain some strong limit theorems for frequencies of occurrence of states and ordered couple of states for these Markov chains. Finally, we prove the strong law of large numbers and the asymptotic equipartition property (AEP) for finite nonhomogeneous Markov chains indexed by a homogeneous tree.

We take the point of view that a Markov random field is a collection of so-called full conditional mutual independencies. Using the theory of I-measure, we have obtained a number of fundamental characterizations related to conditional mutual independence and Markov random fields. We show that many aspects of conditional mutual independence and Markov random fields have very simple set-theoretic descriptions. New insights into the structure of conditional mutual independence and Markov random fields are obtained. Our results have immediate applications in the implication problem of probabilistic conditional independency and relational database. We obtain a hypergraph characterization of a Markov random field which makes it legitimate to view a Markov random field as a hypergraph. Based on this result, we naturally employ the Graham reduction, a tool from relational database theory, to recognize a Markov forest. This connection between Markov random fields and hypergraph sheds some light on the possible role of hypergraph theory in the study of Markov random fields.

The critical distortion d/sub c/ of the Potts models on a number of lattices is shown to be related to the radius of convergence R of Mayer's series by d/sub c/=(q-1)R/(1+R). By using the matrix representation of Mayer's series, a recursive approach is applied to estimate R, and hence d/sub c/ for Ising models for which q=2.

It was shown by C.M. Newman and G.A. Baker (1991) that the critical distortion d/sub c/ of the Ising model on z/sup k/ is related to the radius of convergence R of the classical Mayer series by d/sub c/=R/(1+R). An approach from statistical mechanics to estimate R as well as d/sub c/ by using the matrix representation of Mayer series is found.>

The link between epsilon -entropy for binary random fields and the Lee-Yang theorem in statistical mechanics makes it possible to prove the existence of positive critical distortion for most binary random fields with pair interactions and some with many body interactions. Lower bounds for critical distortion of random fields on two-dimensional (2-D) lattices have been obtained. In particular, the new lower bounds for some 2-D Ising models improve upon previously known bounds.>

The existence of the entropy rate of shift-invariant random fields on binary trees is proven. Alternative representations of and bounds for the entropy rate and surface entropy rate are obtained in terms of conditional entropy. Particular emphasis is placed on Markov chain fields on trees; explicit results are obtained, some of which extend to a more complicated class of tree models.>