Funciones Radiales de Base para Desenvolvimiento de Fase

An important step in fringe pattern analysis is the so called phase unwrapping. Although this task can be performed easily using path dependent algorithms, most times, however, these algorithms are not robust enough specially in the presence of noise. On the other hand, path independent methods such as least-squares based or regularization based may be little convenient due to programming complexity or time consuming. In this paper we describe an alternative algorithm for phase unwrapping based in the determination of weights to linearly combine a set of radial basis functions (RBFs). As described, our algorithm is fast and can be easily implemented following a simple matrix formulation. Numerical and real experiments with good results show that our method can be applied in many kinds of optical tests.Un importante paso en el análisis de patrones de franjas es el llamado desenvolvimiento de fase. Aunque esta tarea puede ser realizada fácilmente usando algoritmos dependientes del camino, muchas veces, sin embargo, estos algoritmos no son suficientemente robustos especialmente con la presencia de ruido. Por otro lado, los métodos independientes del camino tales como los basados en mínimos cuadrados o regularización pueden ser poco convenientes debido a la complejidad de programación o al tiempo de procesado. En este artículo describimos un algoritmo alternativo para desenvolvimiento de fase basado en la determinación de pesos para combinar linealmente un conjunto de funciones radiales de base (FRBs). Como se describe, nuestro algoritmo es rápido y puede ser fácilmente implementado siguiendo una formulación matricial simple. Experimentos numéricos y reales con buenos resultados muestran que nuestro método puede ser aplicado a muchos de los tipos de pruebas ópticas

Funciones Radiales de Base para Desenvolvimiento de Fase

An important step in fringe pattern analysis is the so called phase unwrapping. Although this task can be performed easily using path dependent algorithms, most times, however, these algorithms are not robust enough specially in the presence of noise. On the other hand, path independent methods such as least-squares based or regularization based may be little convenient due to programming complexity or time consuming. In this paper we describe an alternative algorithm for phase unwrapping based in the determination of weights to linearly combine a set of radial basis functions (RBFs). As described, our algorithm is fast and can be easily implemented following a simple matrix formulation. Numerical and real experiments with good results show that our method can be applied in many kinds of optical tests.Un importante paso en el análisis de patrones de franjas es el llamado desenvolvimiento de fase. Aunque esta tarea puede ser realizada fácilmente usando algoritmos dependientes del camino, muchas veces, sin embargo, estos algoritmos no son suficientemente robustos especialmente con la presencia de ruido. Por otro lado, los métodos independientes del camino tales como los basados en mínimos cuadrados o regularización pueden ser poco convenientes debido a la complejidad de programación o al tiempo de procesado. En este artículo describimos un algoritmo alternativo para desenvolvimiento de fase basado en la determinación de pesos para combinar linealmente un conjunto de funciones radiales de base (FRBs). Como se describe, nuestro algoritmo es rápido y puede ser fácilmente implementado siguiendo una formulación matricial simple. Experimentos numéricos y reales con buenos resultados muestran que nuestro método puede ser aplicado a muchos de los tipos de pruebas ópticas

Bayesian nonparametric mrf and entropy estimation for robust image filtering

We introduce an approach for image filtering in a Bayesian framework. In this case, the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is complemented using Márkov random fields, for instance the Semi-Huber Markov random field (SHMRF), which is used as prior information into the Bayesian rule, and the principal objective of it is to eliminate those effects caused by the excessive smoothness on the reconstruction process of signals which are rich in discontinuities. Accordingly to the hypothesis made for the present work, it is assumed a limited knowl- edge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of new Maximum a posteriori (MAP) robust estimators, and considering that real systems are always exposed to continuous perturbations of unknown nature. Some promising results have been obtained from two new MAP entropy estimators (MAPEE) for the case of robust image filtering, where such results have been compared with respect to the classical median image filter

Semi-Huber Half Quadratic Function and Comparative Study of Some MRFs for Bayesian Image Restoration

The present work introduces an alternative method to deal with digital image restoration into a Bayesian framework, particularly, the use of a new half-quadratic function is proposed which performance is satisfactory compared with respect to some other functions in existing literature. The bayesian methodology is based on the prior knowledge of some information that allows an efficient modelling of the image acquisition process. The edge preservation of objects into the image while smoothing noise is necessary in an adequate model. Thus, we use a convexity criteria given by a semi-Huber function to obtain adequate weighting of the cost functions (half-quadratic) to be minimized. The principal objective when using Bayesian methods based on the Markov Random Fields (MRF) in the context of image processing is to eliminate those effects caused by the excessive smoothness on the reconstruction process of image which are rich in contours or edges. A comparison between the new introduced scheme and other three existing schemes, for the cases of noise filtering and image deblurring, is presented. This collection of implemented methods is inspired of course on the use of MRFs such as the semi-Huber, the generalized Gaussian, the Welch, and Tukey potential functions with granularity control. The obtained results showed a satisfactory performance and the effectiveness of the proposed estimator with respect to other three estimators

MAP entropy estimation: Applications in robust image filtering

We introduce a new approach for image filtering in a Bayesian framework. In this case the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is based on the generalized Gaussian Markov random fields (GGMRF), a class of Markov random fields which are used as prior information into the Bayesian rule, which principal objective is to eliminate those effects caused by the excessive smoothness on the reconstruction process of images which are rich in contours or edges. Accordingly to the hypothesis made for the present work, it is assumed a limited knowledge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of Maximum a posteriori (MAP) robust estimators, since the real systems are always exposed to continuous perturbations of unknown nature. Some promising results of three new MAP entropy estimators (MAPEE) for image filtering are presented, together with some concluding remarks

Localización acústica en 3D mediante DTI y DNI en un modelo biomimético usando grabación binaural

Este trabajo presenta el análisis de diferencia de tiempo inter-aural (DTI) y de diferencia de nivel interaural (DNI) para diferentes tonos senoidales puros, usando grabación binaural y un maniquí tipo KEMAR, se obtienen las características de potencia y retardo de los tonos. Estas características permiten la correcta localización de tonos puros

Fast flame temperature estimation using a point diffraction interferometer and non-negative least square method

Some of the interferometry methods proposed for flame temperature measurements from its projection could be complex and demand so much computing time. Assuming a circular symmetric and smooth flame temperature distribution, it is possible to use a linear combination of Gaussian functions with weights constrained to non-negative values

Phase Unwrapping using Chebyshev Polynomials

Phase unwrapping is an intermediate step for interferogram analysis. The phase associated with an interferogram can be estimated using a curve mesh of functions. Each of these functions can be approximated by a linear combination of basis functions. Chebyshev polynomials in addition to being a family of orthogonal polynomials can be defined recursively. In this work a method for phase unwrapping using Chebyshev polynomials is proposed. Results show good performance when applied to synthetic images without noise and also to synthetic images with noise

Phase unwrapping using a regular mesh grid

Phase unwrapping is a key step in the fringe pattern analysis. Although there are many algorithms for recovering continuous phase from wrapped phase maps, many of them are computationaly heavy, even for smooth phase maps. The smoothness characteristics of a phase map allow the use of radial basis functions to model the unwrapped phase. This method helps to reduce the processing time when unwrapping the phase. The processing time can be reduced even more when the reconstruction does not take into account all the pixels of the phase map image. In this paper we describe an algorithm for phase unwrapping where the phase map is reconstructed from a subset of pixels of the phase image using radial basis functions (RBFs). The proposed method is compared with the algorithm based on the same radial basis functions (RBFs) but using all the phase image pixels