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Perception-based fuzzy sets for visual texture modelling

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Abstract

Texture is one of the most used low-level features for image analysis and, in addition, one of the most difficult to characterize. Although there is not an accurate definition for the concept of texture, it is usual for humans to describe visual textures according to some perceptual properties like coarseness, directionality, contrast, line-likeness or regularity. In this paper, we propose to model texture on the basis of its perceptual properties. To do this, fuzzy sets defined on the domain of some of the most representative measures of each property are employed. This approach achieves a double objective: first, to obtain models that allow to represent the imprecision related to texture properties, and second, to identify the most appropriate measure for each of these properties. In order to define the fuzzy models, parametric membership functions are proposed, where the corresponding parameters are obtained by learning a functional relationship between the computational values given by the measure and the human perception of the corresponding property. The performance of each fuzzy set is analyzed and checked with the human assessments, and a ranking of measures is obtained according to their ability to represent the perception of the property, allowing to identify the most suitable measure. In order to explain the proposed methodology, we focus our study on coarseness, contrast and directionality, that are considered the three most important texture properties.

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Notes

  1. Let us remark that “coarseness” and “fineness” are opposite but related textural concepts. The advantage of modelling the concept of fineness is that the maximum presence of this property in the image is delimited by the size of pixel.

  2. To simplify the notation, as it is usual in the scope of fuzzy sets, we will use the same notation \(\mathcal {T}^p_k\) for the fuzzy set and for the membership function that defines it.

  3. As mentioned in Sect. 3, the measures used in this study are not size dependent. Therefore, the models obtained by means of the fitting process don’t depend on the window size. Sub-images smaller than \(32\times 32\) are not considered because they would break texture primitives.

  4. Note that this function is defined for measures that decrease according to the perception of fineness. For those that increase, the function needs to be changed appropriately, i.e. it takes the value \(0\) for \(x<\beta \), it takes the value \(1\) for \(x>\alpha \), and the polynomial function is computed for \(\beta \le x \le \alpha \).

  5. Actually, note that an ideal mapping would not be exactly as shown in the figure, because pixels near the boundary of different textures would have an intermediate fineness value of both textures.

  6. Actually, note that an ideal mapping would not be exactly as shown in the figure, because the contrast degree in the border area between different textures would depend on the contrast of each texture as well as the contrast between them.

  7. Actually, note that an ideal mapping would not be exactly as shown in the figure, because the directionality degree of the pixels near the boundary of adjacent textures would decrease as the orientation of both texture primitives is different.

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Acknowledgments

This work has been partially supported by the Government of Spain under Research Program Consolider Ingenio 2010: Multimodal Interaction in Pattern Recognition and Computer Vision (CSD2007-00018) and under the TIN2009-08296 project. We also would like to thank Dr. Daniel Sánchez for his valuable assistance in the field of fuzzy logic, as well as Elena Galán-Perales for her contribution in the human assessment collection.

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Authors and Affiliations

  1. Department of Computer Science and Artificial Intelligence, University of Granada, C/Periodista Daniel Saucedo Aranda s/n, 18071 , Granada, Spain

    Jesús Chamorro-Martínez & Pedro Manuel Martínez-Jiménez

  2. Department of Computer Architecture, Electronics and Electronic Technology, University of Córdoba, Campus Universitario de Rabanales, 14071 , Córdoba, Spain

    José Manuel Soto-Hidalgo

  3. Department of Software Engineering, University of Granada, C/Periodista Daniel Saucedo Aranda s/n, 18071 , Granada, Spain

    Belén Prados-Suárez

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  1. Jesús Chamorro-Martínez
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  2. Pedro Manuel Martínez-Jiménez
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  3. José Manuel Soto-Hidalgo
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  4. Belén Prados-Suárez
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Correspondence to Pedro Manuel Martínez-Jiménez.

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Communicated by V. Loia.

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Chamorro-Martínez, J., Martínez-Jiménez, P.M., Soto-Hidalgo, J.M. et al. Perception-based fuzzy sets for visual texture modelling. Soft Comput 18, 2485–2499 (2014). https://doi.org/10.1007/s00500-014-1226-8

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