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Fractal Descriptors of Texture Images Based on the Triangular Prism Dimension

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Abstract

This work presents a novel descriptor for texture images based on fractal geometry and its application to image analysis. The descriptors are provided by estimating the triangular prism fractal dimension under different scales with a weight exponential parameter, followed by dimensionality reduction using Karhunen–Loève transform. The efficiency of the proposed descriptors is tested on four well-known texture data sets, that is, Brodatz, Vistex, UIUC and KTH-TIPS2b, both for classification and image retrieval. The novel method is also tested concerning invariances in situations when the textures are rotated or affected by Gaussian noise. The obtained results outperform other classical and state-of-the-art descriptors in the literature and demonstrate the power of the triangular descriptors in these tasks, suggesting their use in practical applications of image analysis based on texture features.

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Authors and Affiliations

  1. Institute of Mathematics, Statistics and Scientific Computing, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Cidade Universitária “Zeferino Vaz” - Distr. Barão Geraldo, Campinas, SP, CEP 13083-859, Brazil

    João Batista Florindo

  2. Scientific Computing Group, São Carlos Institute of Physics, University of São Paulo, PO Box 369, São Carlos, SP, 13560-970, Brazil

    Odemir Martinez Bruno

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  1. João Batista Florindo
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Correspondence to João Batista Florindo.

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O. M. Bruno gratefully acknowledges the financial support of CNPq (National Council for Scientific and Technological Development, Brazil) (Grant #307797/2014-7 and Grant #484312/2013-8) and FAPESP (The State of São Paulo Research Foundation) (Grant #14/08026-1). J. B. Florindo gratefully acknowledges the financial support of FAPESP Proc. 2013/22205-3, 2012/19143-3 and 2016/16060-0 and CNPq Grant #301480/2016-8.

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Florindo, J.B., Bruno, O.M. Fractal Descriptors of Texture Images Based on the Triangular Prism Dimension. J Math Imaging Vis 61, 140–159 (2019). https://doi.org/10.1007/s10851-018-0832-y

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