Quality Map Generation in Two-Dimensional Phase Unwrapping Process by Using Edge Detection Techniques

Abstract

Two-dimensional phase unwrapping is the task of recovering the true phase values, given the wrapped phase values in an image. Phase unwrapping arises in several branches of applied optics, physics, medicine and engineering, such as homomorphic signal processing, solid-state physics, optical interferometry, adaptive or compensated optics, magnetic resonance imaging, synthetic aperture radar interferometry, and optical and electron holography (Volkov & Zhu, 2003). In these applications, the measured information is denoted by a two-dimensional phase distribution called the wrapped phase image. In wrapped phase images, the phase is the interval (-π, π] or (0, 2π] due to the use of the mathematical arctangent function (Bone, 1991). Since this wrapped phase suffers from 2-π phase jumps, it is unusable until the phase discontinuities are removed. In order to recovering the true continuous phase values to denote real physical quantity, a phase unwrapping process is needed to recovering the true phase values. The procedure of phase unwrapping is performed by either adding or subtracting integer multiples of 2π to all successive pixels when a phase discontinuity encounters, which are based on some kind of threshold mechanism (Ghiglia et al., 1987). However, many factors, such as surface discontinuities, noise, under-sampling, or shadow, would produce unreliable phase data, which make the recovery of the wrapped phase challenging. To solve the problem, many phase unwrapping algorithms have been developed during the last three decades. These phase unwrapping algorithms can be found in a very good reference book (Ghigli & Pritt, 1998) and review papers such as (Baldi et al., 2002; Jenkinson, 2003; Su & Chen, 2004; Zappa & Busca, 2008). In many phase unwrapping algorithms, a quality map, which evaluated the quality or the reliability of the phase data, is used for completing the phase unwrapping process. In wrapped phase images, the quality of a pixel is low if it is located in areas where the surface discontinuities, noise or undersampling exists. On the contrary, the quality of a pixel is high if it is located in areas where the variation of phase value is low. From the mathematical point of view, quality map is a matrix of the same size of phase image that assign a quality value to each pixel. The quality values are usually normalized in the range [0, 1], where a large value means high reliability of the corresponding pixel. In most phase unwrapping algorithms, a quality map is necessary to guide the phase unwrapping process for achieving desire results. Furthermore,