Abstract
Image analysis has found more and more acceptance in fractal analysis. We now discuss some special aspects which appear in connection with some of the applied techniques for measurement of the fractal dimension. The following sources of error and limitations have been considered:
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the dilation method underestimates the fractal dimension if open-ended structures are regarded;
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for the mass-radius relation technique the chosen object centre influences the measured value of fractal dimension;
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the stereological intercept censoring technique has been improved, now giving stable results in a reliable measuring time.
These implementations are part of a program package which has been developed in our laboratory. The package includes the majority of methods known for measurement of the fractal dimension by manual and general computer techniques. Our software consequently applies image analysis operations and is adapted to evaluate structures in a two-dimensional binary image format. Additional image analysis tools are available to correct the above-mentioned shortcomings. As a result, fractal dimensions can be measured more exactly and decisions about appropriate methods for a given type of object become possible.
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Eins, S. (1998). Special Approaches of Image Analysis to the Measurement of Fractal Dimension. In: Losa, G.A., Merlini, D., Nonnenmacher, T.F., Weibel, E.R. (eds) Fractals in Biology and Medicine. Mathematics and Biosciences in Interaction. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8936-0_6
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DOI: https://doi.org/10.1007/978-3-0348-8936-0_6
Publisher Name: Birkhäuser, Basel
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