A Three Dimensional Box Counting Method for Measuring Fractal Dimensions of 3D Models

M.T. Suzuki (Japan)

Keywords

Fractal Dimension, BoxCounting, 3D Models, Similarity Retrieval, Hurst Analysis

Abstract

A large number of 3D model are used for various com puter graphic related fields reflecting recent advancements in computer hardware. Since the number of 3D models is increasing rapidly as databases, various retrieval techniques have been proposed for handing 3D model data efficiently. In our retrieval technique, complexity and self-similarity of 3D models were evaluated, whereas typical retrieval tech niques evaluate outer shape similarities of the 3D models. In the experiments, a database of 3D tree models was ana lyzed. Both a box counting method and the Hurst analysis method were applied to each 3D tree model for estimating fractal dimensions. The computed fractal dimension values were used for measuring complexities and self-similarities of each 3D model. An experimental web-based system was implemented for retrieving 3D tree models from the data base. The system successfully estimated fractal dimensions (shape features) of each 3D tree model, and the 3D models were sorted and classified based on the complexities of the shapes.

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