Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Sistema de reconhecimento de impressões digitais baseado em FPGA

Trabalho de Projeto para obtenção do grau de Mestre em Engenharia de Eletrónica e Telecomunicações

Features combination for art authentication studies: brushstroke and materials analysis of Amadeo de Souza-Cardoso

This work presents a tool to support authentication studies of paintings attributed to the modernist Portuguese artist Amadeo de Souza-Cardoso (1887-1918). The strategy adopted was to quantify and combine the information extracted from the analysis of the brushstroke with information on the pigments present in the paintings. The brushstroke analysis was performed combining Gabor filter and Scale Invariant Feature Transform. Hyperspectral imaging and elemental analysis were used to compare the materials in the painting with those present in a database of oil paint tubes used by the artist. The outputs of the tool are a quantitative indicator for authenticity, and a mapping image that indicates the areas where materials not coherent with Amadeo's palette were detected, if any. This output is a simple and effective way of assessing the results of the system. The method was tested in twelve paintings obtaining promising results.