Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.

Reverse Engineering tools: development and experimentation of innovative methods for physical and geometrical data integration and post-processing

In recent years, the use of Reverse Engineering systems has got a considerable interest for a wide number of applications. Therefore, many research activities are focused on accuracy and precision of the acquired data and post processing phase improvements. In this context, this PhD Thesis deals with the definition of two novel methods for data post processing and data fusion between physical and geometrical information. In particular a technique has been defined for error definition in 3D points’ coordinates acquired by an optical triangulation laser scanner, with the aim to identify adequate correction arrays to apply under different acquisition parameters and operative conditions. Systematic error in data acquired is thus compensated, in order to increase accuracy value. Moreover, the definition of a 3D thermogram is examined. Object geometrical information and its thermal properties, coming from a thermographic inspection, are combined in order to have a temperature value for each recognizable point. Data acquired by an optical triangulation laser scanner are also used to normalize temperature values and make thermal data independent from thermal-camera point of view.