Classification of textures using higher-order fractal dimensions
IEA/AIE '88 Proceedings of the 1st international conference on Industrial and engineering applications of artificial intelligence and expert systems - Volume 2
Multifractal multipermuted multinomial measures for texture characterization and segmentation
Imaging and vision systems
Synthesis of bidimensional α-stable models with long-range dependence
Signal Processing - Signal processing with heavy-tailed models
On the Calculation of Fractal Features from Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Depth Estimation from Image Structure
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fractal capacity dimension of three-dimensional histogram from color images
Multidimensional Systems and Signal Processing
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Many objects in images of natural scenes are so complex and erratic, that describing them by the familiar models of classical geometry is inadequate. In this paper, we exploit the power of fractal geometry to generate global characteristics of natural scenes. In particular we are concerned with the following two questions: 1) Can we develop a measure which can distinguish between different global backgrounds (e.g., mountains and trees)? and 2) Can we develop a measure that is sensitive to change in distance (or scale)? We present a model based on fractional Brownian motion which will allow us to recover two characteristics related to the fractal dimension from silhouettes. The first characteristic is an estimate of the fractal dimension based on a least squares linear fit. We show that this feature is stable under a variety of real image conditions and use it to distinguish silhouettes of trees from silhouettes of mountains. Next we introduce a new theoretical concept called the average Holder constant and relate it mathematically to the fractal dimension. It is shown that this measurement is sensitive to scale in a predictable manner, and hence, provides the potential for use as a range indicator. Corroborating experimental results are presented.