Radial Basis Functions for Phase Unwrapping

Funciones radiales de base para desenvolvimiento de fase

Jesús Villa Hernández, Ismael de la Rosa Vargas, Enrique de la Rosa Miranda

Laboratorio de Procesamiento Digital de Señales Facultad de Ingeniería Eléctrica, Universidad Autónoma de Zacatecas Av. Ramón López Velarde #801, Zacatecas, México, C.P. 98000. E–mail: jvillah@uaz.edu.mx, ismaelrv@yahoo.com, edelarosam@yahoo.com.mx

Abstract

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.

Keywords: Phase unwrapping, Radial basis functions.

Resumen

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.

Palabras clave: Desenvolvimiento de fase, Funciones radiales de base.

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