Gianluca Vinti

Lucrezia Rinelli, Arianna Travaglini, Nicolò Vescera et al.

This study evaluates two approaches applied to computed tomography (CT) images of patients with abdominal aortic aneurysm: one deterministic, based on tools of Approximation Theory, and one based on Artificial Intelligence. Both aim to segment the basal CT images to extract the patent area of the aortic vessel, in order to propose an alternative to nephrotoxic contrast agents for diagnosing this pathology. While the deterministic approach employs sampling Kantorovich operators and the theory behind, leveraging the reconstruction and enhancement capabilities of these operators applied to images, the artificial intelligence-based approach lays on a U-net neural network. The results obtained from testing the two methods have been compared numerically and visually to assess their performances, demonstrating that both models yield accurate results.

Francesco Asdrubali, Giorgio Baldinelli, Francesco Bianchi et al.

In this paper, we develop a procedure for the detection of the contours of thermal bridges from thermographic images, in order to study the energetic performance of buildings. Two main steps of the above method are: the enhancement of the thermographic images by an optimized version of the mathematical algorithm for digital image processing based on the theory of sampling Kantorovich operators, and the application of a suitable thresholding based on the analysis of the histogram of the enhanced thermographic images. Finally, an accuracy improvement of the parameter that defines the thermal bridge is obtained.

Danilo Costarelli, Federico Cluni, Anna Maria Minotti et al.

In this paper, we present some applications of the multivariate sampling Kantorovich operators $S_w$ to seismic engineering. The mathematical theory of these operators, both in the space of continuous functions and in Orlicz spaces, show how it is possible to approximate/reconstruct multivariate signals, such as images. In particular, to obtain applications for thermographic images a mathematical algorithm is developed using MATLAB and matrix calculus. The setting of Orlicz spaces is important since allow us to reconstruct not necessarily continuous signals by means of $S_w$. The reconstruction of thermographic images of buildings by our sampling Kantorovich algorithm allow us to obtain models for the simulation of the behavior of structures under seismic action. We analyze a real world case study in term of structural analysis and we compare the behavior of the building under seismic action using various models.