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Nonparametric Estimation Of Fractal Dimension

Nonparametric techniques for estimating fractal dimension are discussed. These techniques are shown to be more robust and efficient when compared with the standard least-squares estimation techniques currently in use. In particular, two alternative nonparametric schemes are presented and their use in image modeling applications is discussed. Theoretical and practical reasons are given to indicate why nonparametric methods lead to improved dimension estimation algorithms. Test results are provided that demonstrate the potential of these methods for use in dimension estimation problems, such as image modeling, where small sample sizes are necessary.