Applications of Approximation Theory to thermographic images in earthquake engineering

Cluni, Federico; Costarelli, Danilo; Minotti, Anna Maria; Vinti, Gianluca

doi:10.1002/pamm.201510321

Cited by 20 publications

(27 citation statements)

References 18 publications

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“…For references about the generalized sampling series the reader can see, e.g. [13,[16][17][18][19][20][21]29,35], while for results about similar operators see, e.g., [10,14,15,[24][25][26][27]37].…”

Section: Applicationsmentioning

confidence: 99%

Discrete operators of sampling type and approximation in ‐variation

Angeloni

Vinti

2017

Mathematische Nachrichten

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The paper deals with approximation results with respect to the φ‐variation by means of a family of discrete operators for φ‐absolutely continuous functions. In particular, for the considered family of operators and for the error of approximation, we first obtain some estimates which are important in order to prove the main result of convergence in φ‐variation. The problem of the rate of approximation is also studied. The discrete operators that we consider are deeply connected to some problems of linear prediction from samples in the past, and therefore have important applications in several fields, such as, for example, in speech processing. Moreover such family of operators coincides, in a particular case, with the generalized sampling‐type series on a subset of the space of the φ‐absolutely continuous functions: therefore we are able to obtain a result of convergence in variation also for the generalized sampling‐type series. Some examples are also discussed.

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Section: Applicationsmentioning

confidence: 99%

Discrete operators of sampling type and approximation in ‐variation

Angeloni

Vinti

2017

Mathematische Nachrichten

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“…The algorithm developed in this paper is characterized by various steps, based on mathematical method of approximation theory and on techniques of Digital Image Processing (D.I.P.). Firstly, the thermographic images are reconstructed and enhanced in their resolution, by the application of the sampling Kantorovich (S-K) algorithm, see e.g., [25,18,19]. The latter method can be deduced from some approximation results concerning the theory of the well-known S-K operators, which has been deeply investigated in last years, see e.g., [24,26,27,23,42].…”

Section: Introductionmentioning

confidence: 99%

Detection of thermal bridges from thermographic images by means of image processing approximation algorithms

Asdrubali

Baldinelli

Bianchi

et al. 2018

Applied Mathematics and Computation

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“…Moreover, also not necessarily continuous signals can be reconstructed. In this case, sampling operators of the Kantorovich type seems to be the most appropriate to perform this task, see, e.g., [9,33,34,22,23,35,36,37]. As showed in Remark 2.1, the density functions φ s (x) dened in this paper satisfy all the typical properties of the approximate identities and then, can be used as kernels in the above sampling operators in the univariate case.…”

Section: Discussion Of the Results And Nal Conclusionmentioning

confidence: 86%