Three-dimensional images constructed by CT and MRI has been recently taken as routine diagnosis in medicine and so measures such as fractal dimensions. Lacunarities for 3-dimensional networks or textures are expected to be used as diagnostic parameters. The method of moments and the box counting method to estimate the fractal dimensions of images were examined for their reliability, using image...

We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well known multi-fractals. By comparing characteristic correlations obtained from the original data with those that occur in artificially generated multi-fractal...

In this short paper we introduce a proper method to perform Korcak-analysis and obtain the correct Korcak-exponent on a set of patches, embedded into two-dimensions. Both artificial and natural data sets are used for the demonstration. The independence of the Korcak-exponent from the classical (Hausdorff) fractal dimension is also demonstrated. 2012 Elsevier B.V. All rights reserved.

The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially geometry Euclidean spaces. We survey these developments, emphasis on connections computable functions the reals, recent uses proving new theorems classical (non-algorithmic) geometry, and directions for future research.

background & objectives: cancer is a serious problem for human being and is becoming a serious problem day-by-day .a prerequisite for any therapeutic modality is early diagnosis. automated cancer diagnosis by automatic image feature extraction procedures can be used as a feature extraction in the field of fractal dimension. the aim of this survey was to introduce a quantitative and objectiv...