Combining fractal and deterministic walkers for texture analysis and classification

• Published in: Pattern recognition Vol. 46; no. 11; pp. 2953 - 2968
• Main Authors: Gonçalves, Wesley Nunes, Bruno, Odemir Martinez
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-11-2013; Elsevier
• Subjects: Applied sciences; Detection, estimation, filtering, equalization, prediction; Deterministic walkers; Exact sciences and technology; Fourier analysis; Fractal analysis; Fractal dimension; Fractals; Information, signal and communications theory; Mathematical analysis; Pattern recognition; Pixels; Signal and communications theory; Signal processing; Signal, noise; Surface layer; Telecommunications and information theory; Texture; Texture analysis; Texture analysis; Pattern recognition; Fractal dimension; Texture; Deterministic walkers; Performance evaluation; Gabor filter; State of the art; Occurrence frequency; Shortest path; Fractal; Deterministic approach; Content analysis
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2013.03.012

In this paper, we present a novel texture analysis method based on deterministic partially self-avoiding walks and fractal dimension theory. After finding the attractors of the image (set of pixels) using deterministic partially self-avoiding walks, they are dilated in direction to the whole image by adding pixels according to their relevance. The relevance of each pixel is calculated as the shortest path between the pixel and the pixels that belongs to the attractors. The proposed texture analysis method is demonstrated to outperform popular and state-of-the-art methods (e.g. Fourier descriptors, occurrence matrix, Gabor filter and local binary patterns) as well as deterministic tourist walk method and recent fractal methods using well-known texture image datasets.
•A texture analysis method based on fractal dimension and deterministic walkers is proposed.•The walkers seek attractors into the image and they are used to estimate the fractal dimension descriptors.•The fractal estimation is based on a special dilation operation, which combines the Euclidean distance and pixels intensity.