Sensitivity analysis in optimized parametric curve fitting

Purpose – Curve fitting from unordered noisy point samples is needed for surface reconstruction in many applications -- In the literature, several approaches have been proposed to solve this problem -- However, previous works lack formal characterization of the curve fitting problem and assessment on the effect of several parameters (i.e. scalars that remain constant in the optimization problem), such as control points number (m), curve degree (b), knot vector composition (U), norm degree (k), and point sample size (r) on the optimized curve reconstruction measured by a penalty function (f) -- The paper aims to discuss these issues -- Design/methodology/approach - A numerical sensitivity analysis of the effect of m, b, k and r on f and a characterization of the fitting procedure from the mathematical viewpoint are performed -- Also, the spectral (frequency) analysis of the derivative of the angle of the fitted curve with respect to u as a means to detect spurious curls and peaks is explored -- Findings - It is more effective to find optimum values for m than k or b in order to obtain good results because the topological faithfulness of the resulting curve strongly depends on m -- Furthermore, when an exaggerate number of control points is used the resulting curve presents spurious curls and peaks -- The authors were able to detect the presence of such spurious features with spectral analysis -- Also, the authors found that the method for curve fitting is robust to significant decimation of the point sample -- Research limitations/implications - The authors have addressed important voids of previous works in this field -- The authors determined, among the curve fitting parameters m, b and k, which of them influenced the most the results and how -- Also, the authors performed a characterization of the curve fitting problem from the optimization perspective -- And finally, the authors devised a method to detect spurious features in the fitting curve -- Practical implications – This paper provides a methodology to select the important tuning parameters in a formal manner -- Originality/value - Up to the best of the knowledge, no previous work has been conducted in the formal mathematical evaluation of the sensitivity of the goodness of the curve fit with respect to different possible tuning parameters (curve degree, number of control points, norm degree, etc.)

On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds

Multiresolution analysis (discrete wavelet transform) through Daubechies family for emotion recognition in speech

We propose a study of the mathematical properties of voice as an audio signal -- This work includes signals in which the channel conditions are not ideal for emotion recognition -- Multiresolution analysis- discrete wavelet transform – was performed through the use of Daubechies Wavelet Family (Db1-Haar, Db6, Db8, Db10) allowing the decomposition of the initial audio signal into sets of coefficients on which a set of features was extracted and analyzed statistically in order to differentiate emotional states -- ANNs proved to be a system that allows an appropriate classification of such states -- This study shows that the extracted features using wavelet decomposition are enough to analyze and extract emotional content in audio signals presenting a high accuracy rate in classification of emotional states without the need to use other kinds of classical frequency-time features -- Accordingly, this paper seeks to characterize mathematically the six basic emotions in humans: boredom, disgust, happiness, anxiety, anger and sadness, also included the neutrality, for a total of seven states to identify

Double Fourier analysis for Emotion Identification in Voiced Speech

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech -- Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions -- A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds -- Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions -- Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it -- Finally features related with emotions in voiced speech are extracted and presented