In this paper, we propose a new sensor for the detection and analysis of dusts (seen as powders and fibers) in indoor environments, especially designed for applications in the field of Cultural Heritage or in other contexts where the presence of dust requires special care (surgery, clean rooms, etc.). The presented system relies on image processing techniques (enhancement, noise reduction, segmentation, metrics analysis) and it allows obtaining both qualitative and quantitative information on the accumulation of dust. This information aims to identify the geometric and topological features of the elements of the deposit. The curators can use this information in order to design suitable prevention and maintenance actions for objects and environments. The sensor consists of simple and relatively cheap tools, based on a high-resolution image acquisition system, a preprocessing software to improve the captured image and an analysis algorithm for the feature extraction and the classification of the elements of the dust deposit. We carried out some tests in order to validate the system operation. These tests were performed within the Sistine Chapel in the Vatican Museums, showing the good performance of the proposed sensor in terms of execution time and classification accuracy.

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In this paper, a new approach is presented for the evaluation of membership functions in fuzzy clustering algorithms. Starting from the geometrical representation of clusters by polygons, the fuzzy membership is evaluated through a suited point-to-polygon distance estimation. Three different methods are proposed, either by using the geometrical properties of clusters in the data space or by using Gaussian or coneshaped kernel functions. They differ from the basic trade-off between computational complexity and approximation accuracy. By the proposed approach, fuzzy clusters of any geometrical complexity can be used, since there is no longer required to impose constraints on the shape of clusters resulting from the choice of computationally affordable membership functions. The methods illustrated in the paper are validated in terms of speed and accuracy by using several numerical simulations.

A new approach to fuzzy clustering is proposed in this paper. It aims to relax some constraints imposed by known algorithms using a generalized geometrical model for clusters that is based on the convex hull computation. A method is also proposed in order to determine suitable membership functions and hence to represent fuzzy clusters based on the adopted geometrical model. The convex hull is not only used at the end of clustering analysis for the geometric data interpretation but also used during the fuzzy data partitioning within an online sequential procedure in order to calculate the membership function. Consequently, a pure fuzzy clustering algorithm is obtained where clusters are fitted to the data distribution by means of the fuzzy membership of patterns to each cluster. The numerical results reported in the paper show the validity and the efficacy of the proposed approach with respect to other well-known clustering algorithms.

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