Correlated Percolation, Fractal Structures, and Scale-Invariant Distribution of Clusters in Natural Images


Natural pictures are scale invariant with structures in the slightest degree length scales.We have a tendency to formulated a geometrical view of scale invariance in natural images using percolation theory, which describes the behavior of connected clusters on graphs.We tend to map images to the percolation model by defining clusters on a binary representation for images. We tend to show that essential percolating structures emerge in natural images and study their scaling properties by identifying fractal dimensions and exponents for the dimensions-invariant distributions of clusters. This formulation leads to a method for identifying clusters in pictures from underlying structures as a starting point for image segmentation.

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