Fuzzy sets on 2D spaces for fineness representation

• We propose to model the fineness property of texture by means of fuzzy sets defined on the domain of pairwise combinations of fineness measures.
• The membership functions of the proposed fuzzy sets are obtained by taking into account the human perception of fineness.
• The bidimensional models proposed in this paper are able to represent the presence degree of fineness, matching what a human would expect.

The analysis of the perceptual properties of texture plays a fundamental role in tasks like semantic description of images, content-based image retrieval using linguistic queries, or expert systems design based on low level visual features. In this paper, we propose a methodology to model texture properties by means of fuzzy sets defined on bidimensional spaces. In particular, we have focused our study on the fineness property that is considered as the most important feature for human visual interpretation. In our approach, pairwise combinations of fineness measures are used as a reference set, which allows to improve the ability to capture the presence of this property. To obtain the membership functions, we propose to learn the relationship between the computational values given by the measures and the human perception of fineness. The performance of each fuzzy set is analyzed and tested with the human assessments, allowing us to evaluate the goodness of each model and to identify the most suitable combination of measures for representing the fineness presence.