Browsing by Author "Costa, Luciano da Fontoura"

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    1D and 2D Fourier-based approaches to numeric curvature estimation and their comparative performance assessment.
    (2003) Estrozi, Leandro Farias; Rios Filho, Luiz Gonzaga; Bianchi, Andrea Gomes Campos; César Júnior, Roberto Marcondes; Costa, Luciano da Fontoura
    A careful comparison of three numeric techniques for estimation of the curvature along spatially quantized contours is reported. Two of the considered techniques are based on the Fourier transform (operating over 1D and 2D signals) and Gaussian regularization required to attenuate the spatial quantization noise. While the 1D approach has been reported before and used in a series of applications, the 2D Fourier transform-based method is reported in this article for the first time. The third approach, based on splines, represents a more traditional alternative. Three classes of parametric curves are investigated: analytical, B-splines, and synthesized in the Fourier domain. Four quantization schemes are considered: grid intersect quantization, square box quantization, a table scanner, and a video camera. The performances of the methods are evaluated in terms of their execution speed, curvature error, and sensitivity to the involved parameters. The third approach resulted the fastest, but implied larger errors; the Fourier methods allowed higher accuracy and were robust to parameter configurations. The 2D Fourier method provides the curvature values along the whole image, but exhibits interference in some situations. Such results are important not only for characterizing the relative performance of the considered methods, but also for providing practical guidelines for those interested in applying those techniques to real problems.
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    Comparing curvature estimation techniques.
    (1999) Estrozi, Leandro Farias; Bianchi, Andrea Gomes Campos; Rios Filho, Luiz Gonzaga; César Júnior, Roberto Marcondes; Costa, Luciano da Fontoura
    This article presents a careful comparative evaluation of two techniques for numerical curvature estimation of 2D closed contours (more specifically closed, regular and simple parametric curves). The considered methods are: (a) a 1-D Fourier-based approach; and (b) a 2-D Fourier-based approach involving the embedding of the contour into a 2-D regular surface (presented for the first time in this article). Both these techniques employ Gaussian smoothing as a regularizing condition in order to estimate the first and second derivatives needed for curvature estimation. These methods are considered according to a multiresolution approach, where the standard deviation of the Gaussians are used as scale parameters. The methods are applied to a standard set of curves whose analytical curvatures are known in order to estimate and compare the errors of the numerical approaches. Three kinds of parametric curves are considered: (i) curves with analytical description; (ii) curves synthesized in terms of Fourier components of curvature; and (iii) curves obtained by splines. A precise comparison methodology is devised which includes the adoption of a common spatial quantization approach (namely square box quantization) and the explicit consideration of the influence of the related smoothing parameters. The obtained results indicate that the 1- D approach is not only faster, but also more accurate. However, the 2-D approach is still interesting and reasonably accurate for applications in situations where the curvature along the whole 2-D domains is needed.
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    Inferring shape evolution.
    (2003) Bianchi, Andrea Gomes Campos; Santos, Marinilce Fagundes dos; Hamassaki, Dânia Emia; Costa, Luciano da Fontoura
    Dynamic shapes represent an important issue in several scientific and technological contexts. The current article presents a model-based mathematic-computational approach for inferring the processes of neural evolution, including analytical mappings, convolution models and normal wavefront propagation, illustrated with respect to stationary and non-stationary evolutions along time and space.