http://www.ens-lyon.fr/DI/wp-content/uploads/2009/07/LopesBetrouni.pdf

Fractal and multifractal analysis: a review.

https://my.ece.msstate.edu/faculty/du/PR-FD.pdf

An improved box-counting method for image fractal dimension estimation

A critical evaluation of image and video indexing techniques in the compressed domain

The fractal dimension is a fascinating feature highly correlated with the human perception of surface roughness, and has been successfully applied to texture analysis, segmentation, and classification. Several approaches have been developed to estimate the fractal dimension. Among them, the box-counting (BC) method is nonstochastic and popular in estimating the fractal dimension of a two-tone image. The differential box-counting (DBC) method, a generalization of the classical BC method, was proposed to compute the fractal dimension for a 2-D gray-level image. However, the classical BC and the DBC methods have several major drawbacks, such as overcounting and undercounting the number of boxes. Hence, the real value of the fractal dimension cannot be reached. In this work, two algorithms that can obtain more accurate estimates of the fractal dimension are proposed. The first one, a modified algorithm of the DBC method, is called the shifting DBC (SDBC) algorithm, and the second one is called the scanning BC (SBC) algorithm. We theoretically prove that the SDBC algorithm approaches the estimated value closer to the exact fractal dimension than the DBC method. Simulation results show that the two proposed algorithms can resolve the drawbacks that the BC and the DBC methods possess. Compared to the DBC method, the two proposed algorithms consistently give more satisfactory results on synthetic and natural textured images.

Two algorithms to estimate fractal dimension of gray-level images

Fractal coding was applied to image segmentation and contour detection. The encoding method was the same as in conventional fractal coding, and the compressed code, which we call the fractal code, was used for image segmentation and contour detection instead of image reconstruction. An image can be segmented by calculating the basin of attraction on a mapping that is a set of local maps from the domain block to the range block. The local maps are parameterized using the fractal code, and contours of the objects in the image are detected by the inverse mapping from the range block to the domain block. Some objects in the test image Lena were segmented, and the contours were detected well. The proposed methods are expected to enable compressed codes to be used directly for image processing.

Image segmentation and contour detection using fractal coding

Applying fractal coding to image segmentation was attempted as its new application. The encoding method is the same as the conventional fractal coding method, and the fractal-code is used for image segmentation. An image can be segmented by calculating basins on a dynamical system parametrized by the fractal-code. It is shown that the new method has the ability to segment regions that have fine pixel-patterns as masses.

T. Ida

Papers

Image segmentation and contour detection using fractal coding

Image segmentation using fractal coding