Applications of sampling Kantorovich operators to thermographic images for seismic engineering
This work addresses seismic engineering by providing incremental improvements in image reconstruction for structural analysis.
The paper tackles the problem of reconstructing thermographic images for seismic engineering by applying multivariate sampling Kantorovich operators, resulting in models that simulate building behavior under seismic action, with analysis of a real-world case study.
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.