Box-Neighbor Correlation Technique For Estimating Hausdorff Dimension of Chaotic Attractors

概要

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Hausdorff dimension is an important quantity for characterizing both of the geometric structure of chaotic attractor sets and the data texture in a large number of physical and biological sciences. The problem of estimating the Hausdorff dimension of chaotic attractors, profile or an image patterns is more difficult and devious than theory suggests. Many different methods have been proposed for estimating the Hausdorff dimension. The most popular methods are the Box-counting and the correlation methods. The major problems of these methods are that, the calculation of Hausdorff dimension is limited by large memory and time requirements. Moreover, these methods leads to results with a very high percentage of error. This paper recovers such problems by manipulating the computation of the correlation method with a new algorithm, which we will call Box-neighbor correlation algorithm. The proposed technique is efficient in time computation, relatively easy and converges rapidly. Moreover, it can be applied in many different application fields such as medical imaging because of its optimal speed and its use of a less storage memory.
社団法人映像情報メディア学会の論文
1999-08-26